How to Make a Noise: Frequency Modulation Synthesis

How to Make a Noise: Frequency Modulation Synthesis by Simon Cann

Published by
Coombe Hill Publishing
33 Melrose Gardens
New Malden
Surrey KT3 3HQ
United Kingdom

coombehillpublishing.com

Copyright © Simon Cann 2005, 2007, 2011

All rights reserved. No part of this publication may be reproduced in any form or by any means without the prior permission of the publisher.

While every effort has been taken to ensure accuracy, the author and the publisher make no representations about the accuracy of the information contained in this book and cannot accept responsibility for any errors or omissions, or for any loss based on the content of this book.

FM8 is part of Komplete and was created by Native Instruments GmbH.

This book has not been endorsed by any of the corporations or individuals listed. Equally, neither the publisher nor the author endorse or offer any support for any of the products mentioned in this book.

Front cover background image © Vazzermag | Dreamstime.com

ISBN 978-0-9554955-5-7

20111001-1.0

About the Author

Simon Cann is a writer based in London. He is the author of a number of music- and business-related books.

His music-related books include: Cakewalk Synthesizers: From Presets to Power User, Becoming a Synthesizer Wizard: From Presets to Power User, and Jumpstart Your Music Career. His business-related books feature the experiences of international entrepreneurs who have built successful companies in the hottest business locations around the world.

Connect and Keep Up-to-Date

You can find out more about Simon and keep up-to-date in many places:

Read more about Simon at his website, simoncann.com.

Check out his other music-related books and videos at his Noise Sculpture website, noisesculpture.com.

Find and Circle him on Google+, profiles.google.com/simon.cann.

Keep up to date with his publications by joining his mailing list.

Follow @simonpcann on Twitter.

Like the Noise Sculpture page on Facebook, facebook.com/noisesculpture.

If you do the RSS thing, subscribe to his news feed.

Introduction

Welcome and thank you for buying this book.

How to Make a Noise: Frequency Modulation Synthesis introduces the tools and techniques so you can create and control sounds using frequency modulation synthesis.

Creating and controlling sound is not simply about making fun and/or cool sounds. It's about finding a sound that works in context. If you draw a parallel with a symphony orchestra, sound design is about choosing (in other words, programming) the right instrument and ensuring the appropriate playing technique is adopted in order to create the tonal effect the composer (you) wants. In other words, sound design is all about trying to find and create the appropriate medium to express your ideas.

Many synthesizers offer some sort of FM capability. The techniques in this book can be applied wherever FM is available, however, this book is more focused on dedicated FM synthesis techniques which can be applied to the fullest extent in synthesizers whose primary means of sound creation is frequency modulation. The techniques are illustrated in this book with a specific synthesizer—FM8 from Native Instruments—but they can be applied to virtually any synthesizer.

And by the way, this book looks at sounds. It is not "the missing manual" for FM8 (since it comes with a very good manual). It is about how to create and control sounds, and in that context, it doesn't claim to show you how to use every control on every synthesizer you will encounter.

The book is intended as a ground-up learning experience so we'll start creating sounds from first principles rather than deconstructing existing sounds. At all stages I would encourage you to try things out and get your hands dirty: there is no need for precision—get out there and create the sounds that sound good to you!

1983: The Year FM Synthesis Changed the World

... or at least something like that...

In 1983, the world of synthesis changed: Yamaha launched the DX7, the first reasonably priced frequency modulation synthesizer. Soon you could hear the distinctive sound everywhere.

The DX7 went on to be one of the biggest selling synthesizers ever and the sound was further popularized with many other DX synthesizers using similar sound generating techniques.

So what was it about the sound?

First, it was different to any sound that had been heard before. Before 1983, most sounds had come from electric pianos, monophonic analog synthesizers, and organs. Suddenly the DX7 was creating bright sparkly sounds. It wasn't just one sound but a whole range: metallic textures, Rhodes piano-like sounds but brighter, clean bright guitars, bells, chimes, and solid basses. There was power, precision, and delicacy giving a sound which (at the time) was unique and completely different to analog (although in many ways it was, and still is, the perfect complement to analog).

And for the player, not only did these sounds have tone, nuance, and playability; the DX7 was polyphonic and the price was good. Sure, it might seem expensive by today's standards, but for the time, it was good.

If there was downside, it was the complexity of programming sounds. It wasn't that FM was hard to program as such—it was more that all you had was one slider and two lines on a grayscale LCD screen for a completely new type of synthesis which made its sound with sine waves and gave you control over hundreds of parameters.

Programming got much easier in 2001 when Native Instruments released FM7 a software incarnation of the DX7 where all the parameters were exposed. In 2006, FM7 was upgraded to FM8 (which is featured in this book). This new synth did everything the old one did but improved the quality and added some more bells and whistles.

Today we have a range of synthesizers that feature FM; many of them are available as software for a fraction of the price of the old DX7. In addition, they also offer a range of waves (it's not just about sine waves) and have a comprehensive array of FX units built in. In addition to FM8, the software variants of these new synthesizers include: Operator from Ableton, Sytrus from Image Line, Rhino from Big Tick, Octopus from LinPlug, and Blue from Rob Papen.

Once you have a grasp of the principles set out in this book, you can apply them to any of these synthesizers or any other synth with frequency modulation sound generating capabilities.

Understanding Synthesis

Synthesis and sound creation comes in many forms.

A key to creating sound with any synthesizer is to understand the strengths and the limitations of your chosen tool (and by implication, the strengths and limitations of the synthesis techniques available on your chosen synthesizer). There's no point in using the wrong tool for a job.

When it comes to synthesizers, there are three main choices for creating sounds:

frequency modulation synthesis, and

analog synthesis

sample-based synthesis.

Let's briefly look at these in turn.

Frequency Modulation Synthesis

This book looks at frequency modulation synthesis (or FM synthesis as it is more often called). FM synthesis adopts a completely different approach to creating sounds when compared with either analog or sample-based synthesis.

Instead of starting with a bright sound and making it dull and/or shaping it with a filter, FM synthesis starts with a simple wave—usually a sine wave—and distorts it (usually with another sine wave). The interaction between the two (or more) waves creates and shapes the sound over time.

The sound from FM synthesizers is often characterized as being harsh or cold. It can be, but more significantly, FM synthesis is capable of creating a broad, detailed, highly nuanced range of tones which can be controlled with an exceptional level of detail.

In some ways FM seems complex since it offers an infinite range of possibilities and permutations. However it is this range of choices which gives the broad array of tonal nuances. These different sonic characteristics make FM synthesis an ideal complement to work alongside analog sounds.

By the way, if you do want to complicate FM synthesis, then get into the mathematics around the subject. This book is about creating sounds, so I have not covered the sums.

Analog Synthesis

Analog or subtractive synthesis is used in many classic synthesizers such as the Moogs (Mini Moog, Moog Modular, Taurus, Little Phatty), the Oberheim synths (OB-8, OB-X), the Rolands (SH-1000, Juno-6, Jupiter-4, and Jupiter-8), Prophet-5 from Sequential Circuits, and the ARPs (ARP 2500, Arp 2600).

You will hear people describe analog synthesizer sounds as warm, rich, simple, and powerful. They are all of these and more.

Analog synthesis works by taking a sound source and shaping it. These techniques are fast and powerful, and if you are prepared to invest the time you will find complexity and delicacy.

Sample-Based Synthesis

Sample-based synthesis offers the facility to recreate the sound of real instruments with a high degree of sonic fidelity and musical control. It then allows the musician to go further and create super-real instruments in that the sampled instrument never goes out of tune, never has a bad microphone located in the wrong position, and can have effects (such as EQ and compression) built-in to the sound.

Beyond that, sample-based synthesis can take raw waveforms, then twist and manipulate them in the digital domain and by applying a range of analog-like tools and techniques to create wholly new sounds. And of course, sample-based synthesis can be used to create and control loops as well as other drum and percussion elements.

Analog synthesis and sample-based synthesis are covered in separate books which are discussed in greater detail in the Further Resources section.

The Featured Synthesizer: FM8

This book is about creating sounds with frequency modulation synthesis techniques

To make the link from the page to synthesizers, the book shows the practical application of the techniques with FM8 (see Figure 1), one of the most popular software synthesizers using FM techniques.

Figure 1 FM8 from Native Instruments.

FM8 traces its architecture back to the Yamaha DX7. Indeed, it is capable of loading DX7 sounds.

Like the DX7, FM8 is a six operator FM synthesizer. Each operator has a dedicated amplitude envelope and a range of other settings to give the musician a detailed level of control. I am using this synthesizer to illustrate specific points: FM8 is capable of more than could be achieved in the DX7 (for instance FM8 offers multi-stage envelopes and a range of waveforms) and much more than I am demonstrating in this book.

There are other great synthesizers out there—the techniques set out in this book can be applied to many of them. However FM8 has been chosen to illustrate the techniques covered by this book and was selected because: (1) it is a tool of the highest quality and is well supported by Native Instruments (2) it is popular and widely used (3) it sounds great, and (4) it is available in PC and Mac versions. And just to reiterate the disclaimers at the start of this book, Native Instruments have not been endorsed this book and equally, neither the publisher nor the author endorse or offer any support for any of the products featured in this book.

One feature that FM8 offers is an Easy page. This is in effect an overlay that controls the underlying functions of the synth. Its advantage is that it can control several factors with one single knob—you can turn a knob and all of the modulators will be simultaneously tweaked, for example. The disadvantage is that—as a musician—you don't see what underlying parameters are being changed. Accordingly, I will not be talking about this functionality.

Format of this Book

This book is only available in electronic form and has been designed, and optimized, to be read on electronic reading devices such as the Kindle, nook, and iPad, as well as the desktop version of any reading tools.

The graphics have been have been optimized for the intended reading medium and are in color. These color images render on a grayscale eInk screen without any problems. The layout (including the images) has been designed to work on a wide range of screens including a standard 6" eInk screen, a phone-sized screen, and an iPad-sized screen.

There are, of course, a few limitations with this format—perhaps the biggest relates to the graphics. Many electronic readers can only deal with graphics of a certain file size. Accordingly the graphics have been squeezed to extremes. This is not a problem for the line drawings (such as the images of the envelopes), but it is more of a challenge for the screenshots (which are reduced in terms of pixel size as well as file size). With this extreme compression, some of the very fine details simply do not render as clearly as I would like on an eInk screen.

You will also see that I have included clickable links to external websites (which will require an internet connection). To differentiate between the internal and external links, external links have a small image to their right, thus.

Navigating this Book

The clickable links in the book are intended to make it easier for you to jump to a specific point. This means that you can go straight to the section you are looking for, and if you don't like the order in which I've put the chapters, then you can read them in the order you want to and hopefully there are links to any earlier material that is necessary to get a full understanding in the later chapters.

And on the subject of the order that the information is presented, the book is structured as follows:

Chapter 1: Getting a Grip on Frequency Modulation Synthesis. Chapter one introduces you to the basic principles of frequency modulation synthesis.

Chapter 2: Envelopes. Chapter two looks at envelopes, the automatic level controls which shape the sound in real time.

Chapter 3: Low Frequency Oscillators. Chapter three looks at low frequency oscillators, another tool to control levels.

Chapter 4: Putting the Pieces Together. Chapter four looks at how to take the elements of FM synthesis—operators, envelopes, and LFOs—and put them together to create and control a sound using FM techniques.

Chapter 5: Algorithms and Sonic Building Blocks. Chapter five looks at how operators can be grouped together to create different tones using FM techniques. These grouping are the building blocks of FM sounds that can be built by deploying these algorithms.

Chapter 6: Waves. Chapter six looks at creating and controlling FM sounds with different wave forms.

Chapter 7: Filters. Chapter seven looks at filters which can further shape the tones created with FM synthesis.

Chapter 8: FX. Chapter eight looks at the effects units that are available to the musician and how they can be used to create and shape sound.

Chapter 9: Creating Sounds with Frequency Modulation Synthesis. Chapter nine looks at the practicalities of creating sounds using frequency modulation synthesis techniques.

Further Resources. If you're wondering what to do after you've read this book, then the further resources section will give you some ideas, including directing you to some free books and videos.

OK. That's enough introduction: let's get on with the music.

Chapter 1: Getting a Grip on Frequency Modulation Synthesis

If you know anything about synthesis—in particular, if you know anything about analog/subtractive synthesis, then forget it, and forget it now. Frequency modulation synthesis is different. That's not to say it's better or worse; it's just different, and if you bring "analog thinking" to the problem, you'll just get confused.

FM Synthesis: The Basics

With analog synthesis, we start with a noisy sound source—an oscillator—and shape the sound with a filter. By contrast, with FM synthesis the sound is created and shaped (usually in real-time) at the sound source—there is no need for subsequent filtering.

With FM synthesis, the initial sound source is a sine wave (see Figure 1.1).

Figure 1.1 A sine wave, the basic component of frequency modulation synthesis.

To create and shape the tone, the pitch of the sine wave is then modulated by another sine wave—this is the frequency modulation from which FM synthesis takes its name. This modulation is variously described as one sine tickling or distorting another. However you want to describe it, the end effect is a sound unlike either of the components.

Let's look at the elements of the FM sound in a bit more depth and see how they are connected in order to create, and control, the sound.

Elements of the FM sound

For many people, FM synthesis falls into the category of "too difficult"—it seems both cumbersome and complicated giving unpredictable results.

However, FM is comparatively simple in concept—it just has a lot of possibilities which makes it appear quite complicated. Let's look at these pieces and permutations.

Operators

Instead of having oscillators, FM synthesizers have "operators".

To create an FM sound, two operators are needed—most commercial synthesizers offer between two and eight operators, with four and six being most prevalent. As you will see as we go through the book, the more operators that are available, the more sonic options the musician has (and the more permutations to fret over).

The early FM synthesizers used sine waves exclusively. Today's FM synthesizers offer a wide range of waves, but sine waves are still often the best choice. Most of the examples in this book will use sine waves, however, I will talk about other waves and the reasons you might choose them in Chapter 5: Algorithms and Sonic Building Blocks.

FM Algorithms

To create an FM sound, two operators are needed—a modulator and a carrier:

Carrier. The carrier is the operator that is connected to the audio output and is therefore heard.

Modulator. The modulator is the operator that modulates (or if you prefer, tickles or distorts) the carrier in order to create and control the tone.

To create a basic FM sound, the modulator modulates the carrier which is attached to the output (see Figure 1.2). This simple stack is the most basic FM algorithm—there are many other algorithms which we will look at later in the book. Different algorithms give different sonic options.

Figure 1.2 A simple FM stack.

The modulator can be thought of as acting in a similar manner to low frequency oscillators in that it modulates the frequency of the carrier. However, the frequency of the modulator is much higher than would be conventional for an LFO. Indeed, the frequency of the modulator is in the audio spectrum so the modulator can be heard if it is connected to an audio output.

The effect of modulating a wave with a signal in the audio spectrum is that the effect is not heard as vibrato as would be the case with an LFO, but instead the tone of the other wave is changed, often quite significantly.

Creating and Controlling the FM Sound

You could use an FM sound source as a static oscillator with a large range of tones available at the tweak of a few controls. You could then push that sound source through a filter and use your FM synthesizer as an analog-like synth (albeit one with a huge selection of waves).

There are good reasons to use a filter in conjunction with FM synthesis—there are some filter characteristics that cannot be replicated with FM techniques alone. In particular, FM synthesis cannot readily replicate filter sweeps, the thwack from a filtered sound, and the squelch of a modulated filter.

However, if you take this approach you will miss the broad range of tones that are available through FM and you rather defeat the purpose of using FM synthesis where, instead of changing the tone by changing the source wave or pushing the sound through a filter, the sound is controlled by adjusting the relationship between the modulator and the carrier.

With FM there are two main factors that control the sound:

Pitch. The pitch of the modulator relative to the carrier. As a general rule, the higher the frequency of the modulator relative to the carrier, the brighter (or more metallic) the character of the sound. Conversely, with a lower pitched modulator you will get much darker tones.

Level. The amount by which the carrier is modulated (or if you prefer, distorted) by the modulator. The higher the output, the brighter the sound will be. This depth of modulation is sometimes called the FM index.

The level of the carrier has no effect on the tone of this sound—it controls the output volume of the carrier. If there is more than one carrier, then each carrier level control adjusts the relative dominance within the patch of the sound created through each carrier.

You will notice that for both factors described above, I've talked about brightness which doesn't really give a satisfactory explanation of the difference between how the two factors affect the sound. Without hearing the effect of each factor, it can be hard to get a grip on the sonic differences between changing a modulator's pitch and changing the modulator's output, but let me give you a parallel.

Think about an orchestra. A composer could write a melody to be played by (say) a viola. To change the tone of that melody, the composer then has two options: change the instrument (for instance so that the melody is played on a violin or a cello) or instruct the musician to change their playing technique. Both are valid choices; each gives a different result.

Pitch. Changing the pitch ratio is analogous to changing instrument. Increasing the pitch of the modulator might give a change in tone similar to changing from a viola to a violin where dropping the pitch of the modulator relative to the carrier might be like switching the melody to be played on a cello.

Level. Changing the level is analogous to changing the playing technique. With an increased level, the effect will be like instructing the player to attack their instrument with increasing ferocity.

The essence of the sound produced by an FM synthesizer is not simply a combination of the individual elements, but the interaction between the modulator and the carrier over time. As one element changes in relation to another there are tonal shifts which give FM its unique character.

The process to set up a simple FM stack and control the sound is different from synthesizer to synthesizer, but it usually contains most of the following steps:

Switch on two operators and decide which is to be the modulator and which to be the carrier.

Set the respective pitch of each operator.

Attach the carrier to the output and set the output level.

Send the output from the modulator to the carrier and set the depth of the modulation.

Take a look at Figure 1.3 where a simple FM stack has been set up in FM8.

Figure 1.3 A simple FM stack in FM8. In this instance, we are looking at the Ops page.

To set up this simple FM stack in FM8:

Operator E and operator F were switched on (in the FM Matrix to the right of Figure 1.3).

Operator F was designated as the carrier. Its output was attached to the output and the level set at 80.

The pitch of the carrier was left unchanged. The pitch of the modulator was doubled (its Ratio was set to 2.0000 in row E to the left of Figure 1.3). Pitch ratios are discussed in greater detail in the next section.

The output from the modulator (operator E) was sent to the carrier (operator F) at a comparatively low level (in this case, the level was set at 32).

This is a static sound, but is the basis for very many FM tones.

Pitch Ratios

One of the key factors determining the tone created by FM synthesis is the pitch of the modulator when compared to the carrier. In this context, absolute pitch is irrelevant—what matters is the ratio of the pitches (remember FM is all about interaction between operators, not the operators acting alone).

At the point that a note is struck, the pitch ratio between operators is usually fixed. It is not impossible, but it is very uncommon, for the pitch ratio to change after a note is struck. The reasons for this are that the results are very hard to control and whatever results you can achieve usually lack any sonic interest.

By contrast, the levels are usually constantly shifting. It is the change in level that gives the tonal changes as a note plays.

The ratio is the ratio between the frequencies of the two notes. So if the carrier's frequency is 440Hz and the modulator's frequency is 660Hz, then the carrier:modulation ratio (the C:M ratio) would be 2:3 (see Figure 1.4).

Figure 1.4 A simple FM stack with a C:M ratio of 2:3.

Clearly, as a musician, you are likely to think in terms of notes rather than frequencies. Staying with the same example, 440Hz is the note A and 660Hz is the note E above A. In other words, in this example, the modulator is pitched seven semitones above the carrier.

Some synthesizers allow you to set the frequencies in terms of semitone differences rather than ratios. I'm not sure this make it any easier for creating sounds since (1) you should be listening to what you're creating not doing mathematics and (2) when you're searching for harmonically pleasing tones, then as a general rule of thumb you get more satisfactory results with integer ratios (and there's no easy way to figure whether you've got an integer ratio when you're using semitones).

The ratios that are open to you are literally unlimited. However, if you're looking for a good place to start, those that are most immediately usable within a musical context are (these are all given as carrier to modulator (C:M) ratios):

4:1. At 4:1, the modulator is pitched two octaves below the carrier. If your carrier's ratio is set at 1, then to achieve this sound, you need to set your modulator to 0.25).

2:1. With the ratio set at 2:1, the modulator is pitched one octave below the carrier.

3:2. At 3:2, the modulator is pitched seven semitones below the carrier.

4:3. At 4:3, the modulator is pitched five semitones below the carrier.

1:1. Both operators at the same pitch. But you figured that, didn't you..?

3:4. At 3:4, the modulator is pitched five semitones above the carrier.

2:3. At 2:3, the modulator is pitched seven semitones above the carrier.

1:2. At 1:2, the modulator is pitched 12 semitones (one octave) above the carrier.

2:5. At 2:5, the modulator is pitched 16 semitones (one octave plus four semitones) above the carrier.

3:8. At 3:8, the modulator is pitched 17 semitones (one octave plus five semitones) above the carrier.

1:3. At 1:3, the modulator is pitched 19 semitones (one octave plus seven semitones) above the carrier.

1:4. At 1:4, the modulator is pitched 24 semitones (two octaves semitones) above the carrier.

1:5. At 1:5, the modulator is pitched 28 semitones (two octaves plus four semitones) above the carrier.

3:16. At 3:16, the modulator is pitched 29 semitones (two octaves plus five semitones) above the carrier.

1:6. At 1:6, the modulator is pitched 31 semitones (two octaves plus seven semitones) above the carrier.

Now of course, some words of caution: these ratios work well over most of the keyboard but at extremes you may find the tone a bit odd in certain cases. Also, don't forget that the tone (and in particular, the musicality of the tone) is very much dependent on the modulation depth (which is controlled by the output level of the modulator).

While you get more sonically pleasing results (in my opinion) with integer ratios, don't limit yourself to integers, and don't limit yourself to the few ratios that I have suggested here. Virtually any ratio can work—it's all a matter of what tone you're after and the output level of the modulator (the extent to which the modulator is modulating the carrier). Lower modulator levels can allow a much wider range of pitch ratios to work thereby giving you and even broader sonic palette.

This is an introduction to the basic sounds. I will look in much more detail at how to create and control these basic tones in the Sonic Building Blocks section in Chapter 5.

Tuning Issues

The perception of pitch is a topic which could take many pages.

Unless you are listening to a sine wave, it may be quite a challenge to determine the pitch of a note. To elaborate—any note will have a fundamental and overtones (which may be pitched above and below the fundamental). These overtones may be harmonious or inharmonious.

The character of the sound is determined by the overtones. The preponderance of harmonious or inharmonious overtones will determine whether the note is perceived as having a clear pitch or as being more atonal. The dominance of any overtones—particularly if they mask the fundamental—will determine how the pitch of the note is perceived.

The basis of FM synthesis is the creation of overtones. The resulting waveforms can include many harmonious and inharmonious elements—if the inharmonious elements are predominant, then the pitch of the note may not be perceived as being the note that is struck.

Sometimes you can account for this behavior and tune the sound by ear. At other times you will need to accept that the sound cannot be tuned and therefore may not be appropriate in conjunction with other instruments.

Modulator Levels

The essence of the sound produced by an FM synthesizer is not simply a combination of the individual elements, but the interaction between the modulator(s) and the carrier(s) over time. The pitch ratio between the operators has an effect on the tone, and you can also control the tone by varying the output of the modulator (see Figure 1.5).

Figure 1.5 You can control the FM tone by varying the output of the modulator.

If the output level from the modulator is fixed, then the tone remains static, but if one element changes in relation to another then there are tonal shifts which gives FM its unique sound.

Once you have sorted your static FM tone, you can then influence the tone in real-time with a range of tools which adjust the level of the modulator thereby giving you control over the sound. This level of control is one of the factors giving the detail to FM sounds.

There are two main tools to control the level of the modulator; we'll look at them all in greater detail throughout the book, but let me briefly introduce them here:

Envelopes. Envelopes are level that change over time. Typically an envelope will be used to control the volume of the patch and to control the level of the modulator. By controlling the level of a modulator over time, the tone of sound can seamlessly shift, mimicking the behavior of natural instruments.

Velocity. By linking MIDI velocity to the modulator level we can control the tone further, mimicking the behavior of a natural instrument.

First FM Sounds

We've now looked at the basic FM algorithm so it's time for you to start making music. Set up a basic FM stack on your synth and start playing with pitch ratios and the modulation depth, listening closely to the range of tones that is available with this limited set up.

In the next chapter we're now going to move on and look at envelopes, one of the key tools for controlling level over time in order to shape sound. In later chapters we'll look at other controllers as well as different algorithms and sounds created with more than two operators.

Chapter 2: Envelopes

The character of FM sounds is a product of the interaction between carriers and modulators. If the relationship between carriers and modulators remains static, then the sound will remain static.

An envelope is a level that changes over time. Envelopes don't make any sound, but what they do is to change other parameters that affect the sound—such as the pitch and the volume—as the note is played. This in turn animates the sound.

In the context of frequency modulation synthesis, envelopes allow us to control the relationship between carriers and modulators—in particular, the output level of the modulator. By controlling the relationship between modulators and carriers we are able to shape the sounds and produce those delicate acoustic-like responses which FM excels at creating.

Envelopes are a one-shot modulation source. When triggered, the envelope begins, executes its level changes, and then ends. If you want continuous modulation, then rather than choose an envelope, an LFO (LFOs are discussed in the next chapter), may be a better choice of tool.

Most FM synthesizers have a range of dedicated envelopes. FM8 has a dedicated level envelope for each operator. Others have a range of dedicated envelopes for different functions (Sytrus from Image Line is one example and has a dedicated level envelope, dedicated panning envelope, and dedicate pitch envelope, among others, for each operator).

Volume Envelopes

The most immediate use for envelopes is controlling volume. In the context of an FM synthesizer, the volume of the sound is determined by the level of the carrier(s). Any envelope which controls the level of a carrier will control the volume of that carrier.

Before we look synthesizer envelopes, think of a note played on a piano. When a key is struck, the note goes from silence to the maximum volume instantaneously. From this peak, there is an immediate reduction in the volume and then the note reaches a level from which it gradually fades to nothing. A simplified picture of the volume of a piano note over time is set out in Figure 2.1.

Figure 2.1 A (simplified) volume envelope of a piano note.

Now if you think about a violin note which slowly fades in, stays at its maximum volume until the note ends, and then gently decays, this volume level may look like the image in Figure 2.2.

Figure 2.2 A typical sustained string envelope.

ADSR Envelopes

The ADSR envelope (see Figure 2.3) is the classic synthesizer envelope. A variant of this envelope is found on many, many synthesizers including the Easy page on FM8 (although there are more detailed envelopes available which I will discuss in a moment).

Figure 2.3 The ADSR envelope.

There are four main controls in the ADSR envelope:

A: Attack time. The attack time governs the time it takes for the level to reach its maximum after the note is triggered. Using the example of a piano, the attack time would be zero—in other words it would take no time for the level to go from nothing to the maximum volume. For a string type sound the attack may be slower.

D: Decay time. The decay time controls how quickly the level drops (to the sustain level) after it has reached its maximum at the end of the attack phase. Again, using the example of the piano, the decay time would be fast, but it would be longer than the attack time.

S: Sustain level. The sustain level is the level of the envelope while a key is held. This level stays constant until the key is released.

R: Release time. The release time is the time it takes the level to decay to zero after a key is released.

You will notice that with an ADSR envelope:

Once the sustain part of the envelope has been reached the note sustains indefinitely—it does not decay to zero until the key is released.

There is no function in the envelope to determine for how long the note sustains (the only control over this is by releasing the key).

DX7 Envelopes

Before the DX7, virtually every synthesizer used an ADSR envelope, and often there were only two envelopes on a synthesizer. One of the reasons why programming sounds in the DX7 was felt to be "too difficult" was that each of the six operators had their own envelope and these envelopes were different when compared to conventional ADSR envelopes.

In reality, the DX7 envelope (see Figure 2.4) simply gave the musician more control which in turn meant that a broader range of sounds could be created.

Figure 2.4 The DX7 envelope.

The DX7 envelope works as follows:

There are four Levels that the musician can set.

The Rate of change between each level can be set.

If the key is still held when the envelope reaches the third level, then the envelope will sustain at that level until the key is released.

Perhaps the most unusual feature of the envelope—at least for a musician used to ADSR envelopes—is the rate changes. ADSR envelopes set the time over which the segment changes. In the DX7 envelope, the rate is set (in other words, the change over time is set).

In practical terms, as Figure 2.5 illustrates, this means that if you are changing a level, the time of the segment will also change.

Figure 2.5 When changing a level (as shown on the left), if the time remains constant (middle) then the rate of change is swifter, but if the rate remains constant (as shown on the right) then the level changes over a much longer period.

Envelope Curves

The ADSR envelope is typical of most envelopes in that the changes are linear, in other words, there's a direct line from one breakpoint to another.

However this is not the case for all synthesizers. Many offer some sort of control over the transition, whether allowing a limited number of curves or making the curve infinitely controllable (as FM8 does). A change in a curve can have a significant effect on how the transition is heard.

A linear curve (see Figure 2.6) gives a smooth, uniform change in level. A slow curve limits the initial changes in the level, but becomes more dramatic during its course. A fast curve makes a large proportion of the level change in the initial stages, but gets slower as it reaches its destination level.

Figure 2.6 A linear, slow, and fast curve.

Multi-Stage Envelopes

The envelopes we have looked at so far have all been fixed: you get a certain number of parameters that you can adjust, and that's it. This approach works well—it is simple and straightforward to understand.

However, it lacks a certain flexibly. And if you want flexibility, then multi-stage envelopes are for you. Multi-stage envelopes vary in their implementation, but FM8 has a good implementation so let me walk you through that. I should remind you that this is just one synthesizer—others offer more than FM8 offers and some offer fewer features.

The approach in FM8 is very straightforward—you add as many breakpoints as you want. For each breakpoint you can set the level, set the time from the previous breakpoint, and you can adjust the curve. If you want to add a loop section, you can. If you want to synchronize the envelope (in other words synchronize the breakpoints) with the beat of a track, you can (and you might want to do this to create rhythmic envelopes).

With this envelope you can recreate an ADSR envelope or create something far more complex as Figure 2.7 illustrates.

Figure 2.7 A multi-stage envelope in FM8.

This envelope offers the musician a detailed level of control and appropriate feedback about the settings. FM8 is also comparatively intuitive to use:

To add a breakpoint, right-click (ctrl-click on a Mac) where you want to add a node (breakpoint).

To remove a breakpoint, right-click (ctrl-click on a Mac) on it.

To move a node, click-and-drag it.

To change the slope between two nodes, click on the red circle and drag it.

If the Sus button in the top row is disengaged, then the envelope plays without a sustain stage (in other words, it will play, and finish, even if the key is held).

If the Sus button is engaged, then the envelope will sustain while a key is held. In this case, as the envelope sustains, its level will continue to loop, following the levels between the two vertical red lines. These vertical red lines can be dragged to change the loop start and end points (and you can have nodes inside and outside of these sustain points).

When you click on a breakpoint, the selected node and the total number of breakpoints is shown in the bottom row (on the left BP#). For that selected node, the bottom row gives details about its setting and some further control:

The Mode selector determines how the other breakpoints are affected when that node is moved. If SLD is selected, all breakpoints to the right of that node are shifted when it is shifted. If FIX is selected, only that breakpoint is moved and every other node remains fixed.

Abs Time displays the time (in seconds) from the start of the envelope to the selected node. This is a display which cannot be adjusted.

Rel Time shows the time (in seconds) between the selected and previous nodes.

Level shows the level of the node.

Slope displays a value for the curve.

This is just a quick illustration of what the envelopes can do in FM8. For a fuller explanation and to find more details about the other functions of the envelope, check out the manual.

Scaling and Envelopes

I want to mention scaling (or tracking as it is sometimes called), briefly. I will mention it again in Chapter 4: Putting the Pieces Together.

In short, scaling means dynamically changing an element of the sound depending on an input. This concept is used in several areas.

Key Scaling

Key scaling means dynamically changing an element of the sound depending on the pitch. So if we think about the volume envelope of a piano, as the notes get higher they sustain for a shorter period and conversely, as the notes get lower they sustain for longer.

If we want to replicate this behavior on a synthesizer we would use key scaling.

You can manually set this function in by modulating each step in an envelope generator (in particular, the attack time, decay time, and release time). The process in FM8 is more straightforward—the Key Scaling setting (at the top of the envelope) adjusts the speed of the whole envelope (in other words, you can set this so that as higher notes are played, the envelope completes its cycle more swiftly.

Velocity Scaling

Velocity means dynamically changing an element of the sound depending on the incoming MIDI velocity.

Staying with FM8 as an example, it allows you to control the speed of an envelope based on incoming MIDI velocity—as you hit the key harder, the envelope plays faster.

Other Modulation Sources

Now we've looked at envelopes let's move on and look at another modulation source in more detail: LFOs.

Chapter 3: Low Frequency Oscillators

In the same way that an envelope changes levels thereby changing the interaction between carriers and modulators, so does a low frequency oscillator, or LFO as they are more often called. Through this constant shifting, a sound is animated.

Envelopes are a one-shot modulation source. When triggered, the envelope begins, executes its level changes, and then ends. An LFO is an oscillator and so repeats its cycle continually modulating the destination. Because of this repetition, the effect of LFO modulation is often more prominent in sounds.

A low frequency oscillator is an oscillator which oscillates at a low frequency—for our purposes it usually oscillates below the audio threshold. In the context of FM synthesis, LFOs are deployed to achieve a range of sonic results:

To modulate pitch, to create vibrato and trill effects.

To modulate the level of carriers to create a tremolo effect or other rhythmic effects.

To modulate the level of modulators to create shifts in tone.

You can, of course, modulate many other destinations with an LFO.

Most FM synthesizers have a number of LFOs and in addition, it is usually possible to also use operators as LFOs (they already modulate the pitch of the other operators—all that is necessary is to drop the frequency).

Wave Shape

The main controls on any LFO are wave shape and depth.

Most synthesizers offer several LFO shapes; the most frequently used are:

Sine

The sine wave (see Figure 3.1) produces an even, rounded modulation source.

Figure 3.1 The sine wave.

Triangle

The triangle wave (see Figure 3.2) has virtually the same effect as the sine wave, but the changes are constant. This may give a crisper sound when compared to the sine wave. Both the sine and triangle are ideal waves for vibrato, tremolo, or tone-shifting effects.

Figure 3.2 The triangle wave.

Sawtooth

Depending on the polarity of the wave, the sawtooth provides either a rising modulation source which drops abruptly after reaching the maximum value or a falling modulation source, rising to a peak and then gently falling (see Figure 3.3). A modulation created by a sawtooth wave gives a more rhythmic effect.

Figure 3.3 The sawtooth wave. On the left, an ascending wave and on the right, a descending sawtooth wave.

Square

The square wave (see Figure 3.4) is either at its maximum or its minimum. This wave tends to be used to create rhythmic effects. It can also be used to modulate the pitch to give trill type effects.

Figure 3.4 The square wave.

Random

Some synths offer a random or more commonly, a sample-and-hold wave (see Figure 3.5). The output from the a random wave is a random value, and for a sample-and-hold wave, the level of the wave steps from level to level—there is no smooth transition meaning that this is an excellent choice for creating rhythmic effects.

Figure 3.5 A sample-and-hold wave which is especially useful for creating rhythmic effects.

Frequency

The frequency control affects the speed of the LFO. So for example, if an LFO is used as a vibrato source, then the frequency control will affect the speed of the vibrato. Most LFOs have a range of around 0.1 cycles per second to about 20 cycles per second.

It is also very common to allow an LFO frequency to be synchronized with the tempo of a track so that the time it takes the LFO to complete a whole cycle is a subdivision of the track's tempo. This option is often used in conjunction with rhythmic effects.

Depth

The depth setting of an LFO controls the extent to which the LFO affects the modulation destination.

This setting needs to be carefully balanced so that an appropriate range of its effect is controlled. For instance, if you are using an LFO to give some vibrato, you probably want a range which is less than (plus or minus) one semitone.

Key Sync

When a note is triggered, any LFO that is applied to that note could be at any stage of its cycle. Usually that's not a problem—indeed, this random element (with a free running LFO) may be desirable for ensemble type sounds—however, there will be times when you want to control where the LFO is in its cycle at the point when a note is triggered. For instance, if the LFO is to be used for rhythmic effect, then you will want to know—with certainty—the starting pitch when the note is triggered.

Sync is also an issue when you start adjusting the phase of an LFO.

Phase

The phase of an LFO is the position in a wave's cycle. The significance of the phase of an LFO is being able to know exactly how much influence it will have over its destination when a key is struck.

For any control over an LFO's phase to be meaningful, you will want to (key) synchronize your LFO (otherwise you're simply adjusting something that is random in order to create something that is still random, but random in a different way).

By combining sync and phase, you can set an LFO to start playing at any specific point in its cycle when a note is triggered.

Delay and Fade

Not every LFO offers delay and fade controls, but if they are available they offer useful additional control over your LFO.

Delay sets the time between the note being struck and the LFO starting to have effect.

Fade sets the time—after the delay phase has been completed—over which the LFO fades in. The LFO has its full effect at the end of the fade phase.

Monophonic/Polyphonic LFOs

LFOs can be monophonic or polyphonic.

Monophonic LFOs

With monophonic LFOs, a single oscillator is used whenever that LFO is invoked. So if you are using an LFO to add some vibrato to a pad, when you play a chord all of the notes will have the rise and fall of their pitch synchronized. The effect may not be particularly natural in this instance.

Polyphonic LFOs

With a polyphonic LFO, each separate note has its own LFO which will start its cycle at a different point from any other LFO (assuming that you haven't engaged the sync function, which would defeat the purpose of using a polyphonic LFO).

Using our pad example again, using a polyphonic LFO to modulate a chord will mean that some notes will have their pitch raised while others are having their pitch flattened. This may give a more desirable result for a pad, but is less use for rhythmic sounds.

Assigning LFOs

Some synthesizers have dedicated LFOs in the same way that they have dedicated envelopes for specific operators. FM8 is an example of a synthesizer which does not have a dedicated LFO. Instead the LFO can be assigned to control its destination. In the case of FM8 the routing assignment and depth are both set through a modulation matrix (see Figure 3.6).

Figure 3.6 The modulation matrix in FM8. In this image, the pitch bend wheel and LFO1 are both assigned to modulate the pitch of the patch.

LFOs and FM Synthesizers

It's not unusual for FM synthesizers to have a limited supply of LFOs—as you have seen in Figure 3.6, FM8 only has two LFOs. The reason for the limited number is simple: the uses for LFOs in FM synthesis are limited.

However, if you want an LFO to modulate pitch, then most FM synthesizers have another trick... Modulators are already modulating the frequency of carriers—in effect, they are operating as LFO, but the frequency of the LFO has been set rather high. If the frequency is dropped, then a modulator can act as an LFO.

To use FM8 as an example, an operator can be set to work as an LFO as follows:

The modulator is switched on and connected to modulate the carrier in the normal way.

The modulator is de-pitched (in other words, it stops responding to pitch information). For FM8, the ratio is set to zero and the Pitch Env setting is disengaged.

The frequency for the operator to act as an LFO is set by the Offset setting (which sets the frequency in hertz).

The depth of the modulation in the FM Matrix controls the amount of pitch modulation.

Figure 3.7 shows this set up in practice.

Figure 3.7 An operator in FM8 working as a low frequency oscillator.

Modulate Some More

We've now looked at the two most common modulation sources: envelopes and LFOs. In the next chapter we'll look at modulation in more depth and the other more detailed modulation source.

Chapter 4: Putting the Pieces Together

We've now looked at the basic concepts for creating an FM sound, envelopes, and LFOs as well as briefly touching on how these elements interact.

However, envelopes and LFOs are not the only control sources and in order to create an interesting, and playable, sound, there are a lot more elements to be considered. We need to look in greater detail at how the pieces can work together, so that sounds can be controlled in real-time.

These additional sources and this level of control are particularly important when you start bringing even more operators to the party (as we will do in Chapter 5: Algorithms and Sonic Building Blocks).

The main technique we're going to look at in this chapter to achieve movement and control—which will then animate the sound—is called modulation. Modulation goes to the heart of creating sounds. It is the technique by which a synthesizer creates the varied nuances of sound. Without modulation sounds may be rich, thick, fat, bright or delicate. However modulation will take a basic sound and animate it, giving it life in the hands of a skilled player.

Modulation: The Concept

The concept of modulation in a synthesizer is simple—something is changed by something else, and usually in real time.

Conventionally, a "source" will modulate a "destination". So if we think about vibrato, a low frequency oscillator would act as the source and the pitch would be the destination.

If you then want more detailed expression, then the extent by which the source modulates the destination can be determined by a "control" (which in turn would be another modulation source, but its modulation destination would be the amount of modulation, rather than the destination).

So staying with our vibrato example, if we have a low frequency oscillator acting as the source to control the pitch of a note, then you could set a modulation wheel as the control to adjust the amount of vibrato in real-time.

Modulation in the Real World

Before we get to the detail, let's think about modulation in the context of an acoustic instrument such as the piano. Taking an over-simplistic view, the factors that have an effect on the sound are:

velocity

pitch, and

time.

Effect of Velocity on a Sound

Velocity is another way to describe loudness, which in the case of a piano would be determined by how hard a key is hit. With a piano, the velocity (the loudness) of a note has an effect in three main areas:

the volume—there is a direct link between how hard a note is struck and its volume

the tone—the harder a key is hit, the brighter the tone of the resulting note, and

the sustain time of the note—the louder the note when it is struck, the longer it will sustain.

Effect of Key Pitch on a Sound

Clearly the piano keyboard controls the pitch of the note played. However, there are other factors affected by the pitch:

the tone—the higher the note, the brighter it sounds, and

the sustain time of the note—the higher the note, the less time that it sustains.

Effect of Time on a Sound

The length of time that a note is held is also a factor in the tone of a piano. Over time:

the sound will get duller (however bright it may have been initially), and

the volume will decay until it finally reaches zero.

Combining the Effect of Velocity, Pitch, and Time

A piano note is far more complex than may be suggested here, however, in broad terms you can see that:

The initial volume of the note is affected by one factor only—velocity. After that, the player has no control over the loudness of the note as it decays naturally.

Tone is affected by three factors—the initial velocity of the note, the pitch of the note, and the length of time it is held. However, the tone increases in line with the increase in pitch (so the higher the note, the brighter it becomes), but the sustain time decreases in line with the increase in the pitch (so the higher the note, the less time it sounds for).

Sustain time (and also volume over time) is affected by two factors—the starting volume (which is in turn controlled by the initial velocity) and the pitch.

To mimic some of the characteristics of an acoustic instrument, we're going to need to use modulation to control many elements within the FM sound. One of the advantages of the apparent complexity of FM synthesis is that it gives you a detailed level of control allowing the behavior of real instruments to be mimicked with a degree of authenticity.

Modulation Destinations

We will approach modulation in a slightly backwards way and look at modulation destinations before we look at modulation sources. Once we understand what can be modulated, we can work back to choose the best source to create the modulation.

I should point out that the following list of modulation destinations is, of course, not complete: it only covers the main destinations that you are likely to want to control. Different synthesizers will offer different amounts of control, so on any specific synth you may be able to modulate more or fewer functions than are set out here.

Volume

Volume is likely to be one of the main destinations you modulate. You may want to:

control the volume of your whole sound—for instance to make the patch touch sensitive or to add a tremolo effect—which you do by consistently modulating the level of all carriers, or

control the volume of individual carriers to blend or cross-fade between two sounds, or to make certain elements more prominent as a sound becomes louder.

Timbre

In the context of FM synthesis, you might also want to modulate the level of your modulators. Modulating the level of your carriers controls the volume of the sound where modulating the level of your modulators will affect the timbre.

Modulating the output level of modulators over time is one of the key tools for creating the tonal shifts to mimic the behaviors of real instruments.

Filter

For pure FM sounds a filter will not be used. However, most FM synthesizers offer a filter for additional tonal shaping possibilities.

The main modulation destination in the filter block is the cut-off frequency, which may be controlled to make a sound less bright over time.

Sometimes the resonance can also be controlled over time to give some additional brightness to a sound. However, in the context of FM, this modulation is used less frequently and isn't always available on every synthesizer.

Pitch

The effects that can be obtained by modulating pitch include vibrato and trills as well as weird special effects. Subtle pitch modulation is also important when trying to mimic the properties of natural instruments where slight inconsistencies can give some richness to a sound.

Pan

The classic use for panning is auto-pan type effects where the sound moves regularly between the left and right channels. There are however more subtle uses of panning, for instance panning can be related to the pitch of a note with low notes panned towards the left and higher notes towards the right as if you were sitting in front of a piano.

Envelope Speed

I've already talked about key scaling (using pitch as a modulation source) and I'll talk about it in greater detail in the next section (Modulation Sources). One frequent modulation destination for key scaling is the envelope, and in particular, the speed of the envelope where key tracking can give the sound a more natural quality by mimicking how higher notes sound for a shorter time than lower notes.

Modulation Sources

Most synthesizers offer and array of modulation sources, each of which operates in a different manner. There are also external sources which can act as modulators—such as MIDI velocity, the pitch bend wheel, and the modulation wheel. These sources can then be used directly as modulation sources or as controllers to control the amount by which another modulation source is modulating a destination.

The modulation sources (or controllers) fall into four main categories:

Single-shot sources. An example of a single-shot modulation controller is an envelope—it begins, executes its level changes, and then ends (after perhaps sustaining for a while). Envelopes parameters were discussed in Chapter 2: Envelopes.

Continuous sources. An example of a continuous source is a low frequency oscillator—the modulation source repeats its cycle continually modulating the destination. LFO parameters were discussed in Chapter 3: Low Frequency Oscillators.

Fixed. Some modulation sources, while being variable, are fixed once a note has been played. The main example of this is MIDI velocity—once a note has been struck, the velocity is fixed.

Variable. Other modulation sources are constantly variable after the note has been struck. One example of a variable source is the modulation wheel which can be continuously tweaked in real-time.

A second aspect to think about in relation to modulation sources is polarity:

Unipolar. Some sources (for instance velocity, the modulation wheel, and conventional envelopes) are unipolar. This means that their output within a single cycle is either positive or negative.

Bipolar. By contrast, bipolar sources (such as LFOs and the pitch wheel) are capable of generating both positive and negative signals within the same cycle.

Let's have a look at some of the modulation sources in a bit more depth (as already noted, the parameters for envelopes and LFOs have already been discussed).

Velocity

When creating sounds, velocity is often used to control:

the loudness of a note (by modulating the level of the carrier or carriers), and

the tone of a note (by modulating the level of the modulators). Of course, velocity can also be used to modulate the cut-off frequency of a filter to control the tone.

Velocity can either be applied directly to modulate the destination (for instance, it can directly control the level of an operator) or it can be used as a modulation source controller to control another source (for instance, an envelope parameter) which, in turn, is modulating the destination.

FM8 allows this form of velocity scaling so that an envelope can be made to play more slowly (with positive velocity scaling) and more quickly (with negative velocity scaling).

Pitch Bender

The pitch bender is usually hardwired to the pitch bend function. However, most synthesizers also allow the pitch bend signal to be assigned to control other functions.

Modulation Wheel

Very often synthesizers will wire the modulation wheel to the vibrato depth so the wheel acts as a modulation controller.

However, the assignment doesn't have to be so—the modulation wheel can also be used as a modulation source (for instance, to control the level of an operator).

Key Scaling

Key scaling (or key tracking as it is sometimes called—the terms are interchangeable) is the process where changes are made according to the pitch of a note.

For example, if you pluck the bottom E string of an acoustic guitar, the sound will last for over 10 seconds. However, if you play the top E string at the highest fret, the sound will barely last for 3 seconds. With key tracking we can seamlessly control the length of an envelope to reflect the behavior of the acoustic instrument.

With subtractive synthesis, key scaling is usually only used to open up the filter a bit when higher notes are played. With FM synthesis, key scaling is far more important.

It is very easy to create metallic sounds with FM synthesis. It is harder to create usable metallic sounds that are playable over the full keyboard. One of the solutions to designing FM sounds is to ensure that the overtones are appropriate. It is quite easy to create a sound which works within a limited key range, but does not work outside of that range. Often this will manifest itself as a sound that begins to sound too harsh. The harshness can be addressed in two ways:

The modulation can be reduced—this may make the sound work outside of the first range, however, it will probably affect the original sound, perhaps making it too dull.

The level of the operator can be reduced in certain key ranges—this is more likely to obtain the desired result. This is what we mean when we talk about key level scaling.

Aftertouch

If your keyboard (or other MIDI controller) gives aftertouch messages, then the pressure on the keys while a note is sustained can be used to control your patch. You could, for instance, use aftertouch to control volume to give a swell to a held string chord.

Aftertouch can either be applied directly to modulate the destination, or it can be used as a modulation source controller to control another source which is modulating the destination.

Expression Pedal

Often the expression controller is hardwired to a synthesizer's volume. As with the modulation wheel, it can also be used as a modulation controller.

MIDI Control Change

Lastly, MIDI Control Change messages (which are generated by external sources) can be used as a source or as a source controller.

Setting Up Modulations

Given the complexity of FM synthesizers and the broad range of parameters that are available to be controlled, most of the modulations have dedicated controllers. However, it is common to also allow some other modulations to be assigned when necessary.

Take FM8 as an example. Figure 4.1 shows the main controls that are available for each operator.

Figure 4.1 The main controls that are available for each operator in FM8.

In FM8:

Each operator has a dedicated level envelope (at the bottom of Figure 4.1).

These dedicated envelopes have their own dedicated key scaling and velocity scaling controls (accessible in the row above the envelope graphic—in Figure 4.1, key scaling is set to 0 and velocity scaling to 22).

The output level of each envelope has its own dedicated control with its own dedicated pan control (both controls are in the amplitude section to the right of the image).

The operator's level also has its own dedicated velocity control (again in the Amplitude section). This directly links the level of the operator to MIDI velocity and scales the effect of velocity on the loudness of the operator. When this knob is set to zero, MIDI velocity has no effect on the loudness of this specific operator. When set to negative values, the operator's level increases as MIDI velocity decreases.

In addition to these fixed modulations, there are a number of assignable modulations which can control the level of the operator. These are accessed and controlled though the matrix in the middle of Figure 4.1.

In this instance:

LFO1 has been set to modulate (the level of) the operator. The depth of the modulation is 15.

Mod has been set at -21.

This second setting needs some explanation:

This assignment relates to LFO2; however, LFO2 has not been directly assigned. Instead, the depth of the modulation is controlled by the modulation wheel (hence mod). When the wheel is set to zero, the LFO has no effect. When the wheel is at its maximum, the modulation depth is -21.

The modulation depth is a negative amount. This means that the modulation source (in this case, the wave in LFO2) is applied with reverse polarity, so if it would normally start with a positive phase, when the polarity is reversed, it will start with a negative phase.

Applying Modulation in Practice

Now we've looked at the principles of modulation, let's move on and look sonic building blocks.

Chapter 5: Algorithms and Sonic Building Blocks

The story so far...

In Chapter 1: Getting a Grip on Frequency Modulation Synthesis we looked at the principles of creating a frequency modulation sounds with two operators.

In Chapter 2: Envelopes we looked at how to control levels over time with envelopes in order that tones can be shaped.

In Chapter 3: Low Frequency Oscillators we looked at how to control levels with low frequency oscillators (and with operators).

In Chapter 4: Putting the Pieces Together with looked at a range of modulation sources and how those can be applied to shape and sculpt your sound (in conjunction with envelopes and LFOs).

With the principles we have looked at so far you can build a wide range of sounds. A typical FM synthesizer, such as FM8 offers six operators—you can therefore deploy three two-operator combinations to create detailed and layered sounds.

But there's so much more we can do to create even more detailed, complex, controllable sounds. The way to do that is to combine operators in different ways, and in the process we'll move past the two operator limit we've had so far.

Before we make too many sounds, could I give a warning that I always give: different synthesizers sound different. Different synthesizers work in different ways. Frequency modulation synthesizers are no different. You could hook up what looks like a similar algorithm built with similar sine waves in two different synths and get completely different sounds. So if you don't hear what I hear:

You're right—I'm wrong. I don't know which synth you're using, so I can't guarantee the results.

Adjust the controls and listen to the tones you can create—a small tweak in an FM sound can make a huge difference.

Algorithms

Algorithms—in other words, the basic combinations of operators—are the building blocks of FM synthesis. In essence, each FM sound is a combination of one or more algorithms from four basic algorithms. Let's have a look at those four building blocks.

Simple FM

Simple FM stack is where one modulator drives one carrier (see Figure 5.1).

Figure 5.1 A simple FM stack where one modulator drives one carrier.

This arrangement is the very essence of FM sound and is the only option we have considered so far.

Most of the classic FM sounds can be built around this arrangement although often several simple FM stacks will be layered together to achieve a thicker sound. Alternatively, some patches may be built around several simple FM stacks providing different elements of the sound: the classic example of this is the FM electric piano sound where the bell and the sustain portions can be built from separate simple FM stacks which are then layered.

Often one modulator/carrier stack alone will give a weak sound, much as a single oscillator in an analog synthesizer can give a weak sound. Modulators and carriers can be doubled to thicken up a sound—again think of how oscillators are doubled in a subtractive synthesizer.

Parallel Carriers

With parallel carriers, one modulator drives two or more carriers (see Figure 5.2).

Figure 5.2 A parallel carrier arrangement with one modulator driving two carriers.

Parallel carriers allow the effect of two simple FM stacks to be achieved by using three operators rather than four. This leads to greater programming efficiency and marginally less CPU load.

The downside of parallel carriers becomes apparent if you detune one carrier (say by a couple of cents) to get a thicker sound. While the sound is thicker, there is also phase cancellation which is primarily heard as tremolo (a rise and fall in the volume). If you use two simple FM stacks and detune both the modulator and the carrier in one stack, a much richer sound can be achieved without such apparent phase cancellation (but you are using more operators and so losing one advantage of parallel carriers).

Parallel carriers do not need to be at the same pitch. For instance, if you take one carrier at the base frequency and another seven semitones higher, you have the basis for a Wurlitzer-type electric piano sound. Equally this arrangement can yield many wooden (as in tuned wooden percussion) type sounds.

As a side note, just because two parallel carriers sound odd when they are played together without any modulation, that does not mean they will not work together when they are both modulated by the same modulator.

Parallel Modulators

With parallel modulators, two or more modulators drive one carrier (see Figure 5.3).

Figure 5.3 A parallel modulator arrangement where two modulators drive one carrier.

Parallel modulators offer far more complicated and rich sounds than are available from a simple FM arrangement. However, more options give more complications and the relationship between the two modulators will have a considerable effect on the sound.

If the modulators are of the same pitch, then the effect of two modulators will be to enhance the amount of modulation. Tonally this means that the brightening effect of the modulation will be increased. The same effect could be achieved with a simple FM stack by increasing the modulation depth.

When the respective pitches of the modulators change, the sounds get interesting. Very simplistically, if the modulators are all set at intervals which correspond to integer multiples of the carrier's frequency, then the sound with parallel modulators will give a harmonious tone. Different intervals can give many different tones—some of which may be useful in a musical context, other of which may fall more to be considered as sound effects.

Another simple, but effective use for parallel modulators is to apply different envelope attack times—used in conjunction with differently tuned modulators, this can give a very natural sound. Again, taking the example of a simple electric piano:

the first modulator could have a very fast attack and a short decay—this could be tuned to a higher pitch than the carrier to give the bell sounds, and

the second modulator could have a slower attack and a longer sustain portion—this could be tuned to a pitch below the carrier to give a more wooden-type tone.

If two modulators are very slightly detuned, then this will lead to interference between the modulators (in the same way as would be the case if two oscillators in a subtractive synth are detuned). However the net effect is that the amount of modulation (and therefore the tone) will constantly shift as the operators cancel each other out. Depending on the particular patch, the results may or may not be desirable.

Cascade

With a cascade, one modulator drives another modulator which itself then drives the carrier (see Figure 5.4).

Figure 5.4 A cascade where one modulator drives another modulator, which itself then drives the carrier.

In a cascade, the first modulator outputs a sine wave. However, the second and subsequent modulators are themselves being modulated. Accordingly their output is a different waveform. Cascades can produce the richest and most complex FM timbres: a similar (but less controllable) effect can be created in a simple FM stack by modulating with waveforms other than the sine wave.

Although not illustrated in the graphic, it is possible to have more than three operators in a cascade, however the results then become less predictable and there is a greater tendency to producing noise.

Other Options

Those are the four basic algorithms, but there are other more specialized options.

Feedback

The output from an operator—in addition to being sent to the audio output or to modulate another operator—can also be fed back into the operator (see Figure 5.5). The Figure shows a carrier feeding back on itself, however, both carriers and modulators can be set to feed back.

Figure 5.5 A carrier with its output being fed back into the audio path (shown by the red arrow).

By feeding back an audio signal, the operator is modulated by itself. In principle this is no different to modulating a carrier with a modulator. However, in practice, feedback gives a brighter, harsher sound which is harder to control and is more prone to noise.

As well as feeding back on itself, an operator can send its signal to an earlier stage in the signal chain (so that effectively two, three, or more operators can be included in a feedback chain). Take a look at Figure 5.6 for an example.

Figure 5.6 A cascade with two points of feedback.

The basis of this algorithm is a cascade—operator D modulates operator E which in turn modulates operator F, the carrier which is connected to the audio output.

Operator F, the carrier, feeds back into itself and feeds the signal back to operator D, so operator D—the original modulator—is itself modulated. Figure 5.7 shows the signal flow as a diagram.

Figure 5.7 A cascade with two points of feedback. The blue arrows show the audio flow and the red arrows the feedback.

And in case you're wondering why we use feedback, the answer is simple: it's another tone on the sonic palette that we can play with.

Modulator or Carrier?

Another option that is available is to route the modulator signal to the audio output (see Figure 5.8).

Figure 5.8 In addition to modulating the carrier, the modulator output can also be fed directly to the audio output.

The effect of this routing is to reinforce the frequency of the sound (at the pitch of the modulator). Generally this will also be perceived as rounding out the tone.

Variations on a Theme

The four algorithms shown in this section are the four basic combinations. Subject to the limitation of your synthesizer, you can include as many operators as you like, for instance with a six operator synthesizer:

you can cascade six operators

you can have five parallel modulators

you can have five parallel carriers, and

you can have three modulators, each individually feeding three carriers (in other words each modulator modulates three destinations, so each carrier is modulated three times, giving a total of nine modulations.

Building Your Own Algorithms

The DX7 and the early FM synthesizers came with a range of fixed algorithms (the DX7 had 32). Today, most synthesizers take the approach adopted by FM8 and have a fully flexible matrix where any operator can been routed to another, but a few synthesizers still have fixed algorithms.

There's no real advantage to having fixed algorithms. Indeed, the biggest downside is the lack of flexibility.

If there is a disadvantage to the flexibility it's the range of choice (32 options can be less daunting than infinite choices). However, if you start with the basic building blocks, the construction of sounds becomes a comparatively straightforward process.

The flexibility in FM8 has another advantage. There are two additional operators: operator X and operator Z. These are not operators in the conventional sense but effects processors: operator X is a noise source and distortion unit, and operator Z is a filter block. (We will look at both functionalities later it the book.) With the flexible routing system, you can control exactly which parts of the algorithm are processed through the effects. As always, this gives a much broader range of sonic options.

Sonic Building Blocks

There is a step between the having a bunch of operators floating around and having a finished sound created with frequency modulation synthesis. That step is marshaling—and deploying—the elements to create building blocks, in other words, getting the tone groupings together.

So for instance, an electric piano-type sound might (simplistically) have two elements, the chime and the sustain tone. Creating those two sonic elements—in other words, making those building blocks which will then be put with other blocks to create the final sound—is about:

finding the right combination of operators (getting the algorithm right)

setting appropriate pitch ratios (in order to create the desired tones)

adjusting the interaction between the elements of the algorithm over time, and

fine-tuning the interaction of the elements (for instance adding some key-scaling to allow a tone to work across the whole keyboard).

Once you have your building blocks, then you can combine several to create your sound.

Earlier in the book we looked at some of the more straightforward ratios that work well for creating basic FM tones. Now that we've looked at the basic structure of algorithms, let's move forward and look at the combinations in a bit more detail. In particular, we'll look at some of the specific combinations and how to control those sounds.

Simple FM Building Blocks

We've spent a lot of time looking at simple FM structures, but we haven't looked at how to control these combinations, and in particular, we have yet to consider how to control the interaction between the two elements in light of any choices about the carrier to modulation ratio.

The carrier to modulation ratio has a significant effect on the tone output by a simple FM algorithm. In highly simplistic terms:

If the modulator is pitched below the carrier, then the output tone is darker. As a broad generalization, these tones are better for adding weight to sounds and make excellent sustain sections.

If the modulator is pitched above the carrier, then the output tone is brighter. Again as a broad generalization, these tones can often find a use for the attack portion of the note—they often impart the strike or pluck element of a sound.

Setting the Ratio

When you apply a carrier to modulation (C:M) ratio to your synthesizer, the absolute figures don't matter. So taking FM8 as our example, in the ratio setting for any operator (see Figure 5.9), you can insert any figure—what matters is the figure you insert in the other operator's ratio field.

Figure 5.9 The ratio control in an operator in FM8. (In this case, the ratio is set to 8, which in and of itself means nothing.)

So if you want a 4:1 ratio for example, this could be achieved in a number of ways:

Set the carrier to 4 and the modulator to 1.

Set the carrier to 1 and the modulator to 0.25.

Set the carrier to 8 and the modulator to 2.

Set the carrier to 1.428 and the modulator to 0.357. You get the idea...

The difference between these settings will only be a difference it the pitch of the end result, not in the tone that is heard. This is akin to shifting the sound over different octaves on a keyboard and to compensate, you may want to use the transpose function on your synth.

However, a word of caution: If you use octave ratios for the carrier, then the carrier will be tuned appropriately for your keyboard (in other words A=440Hz). If you start messing with the pitch of the carrier (for instance by setting its ratio to 1.428) then the pitch of the resulting note may not correspond to the pitch of the played note, so for instance, you may play an A but hear a D.

Setting the Envelope

We looked at envelopes in detail in Chapter 2.

When building any FM sound, there are three basic envelope shapes that are most useful as a starting point.

Organ-Like

The first shape is an organ-like envelope (see Figure 5.10). Here the envelope starts, hits its full level immediately, sustains at that level while the key is held, and then decays to zero when the key is released.

Figure 5.10 An organ-like envelope.

If you look at Figure 5.10, you will see that the attack is not immediate as would be the case for an organ. As a matter of personal taste, I often slightly slow the attack of modulators pitched below the carrier. This gives a cleaner tone and allows other impact elements to be heard more clearly (this is particularly noticeable in the context of parallel modulators). As I say, it's a matter of taste and your taste may vary.

Impulse

The second common shape is an impulse (see Figure 5.11).

Figure 5.11 An impulse envelope.

An impulse envelope gives a burst of energy then ends at a zero level: there is no sustain phase. This is typical of a drum or percussion sound and can be more widely use to introduce an impulse at the start of a note (for instance if you're creating the sound of a string being plucked or the click of an organ key).

Often you will need to tweak the length of the impulse (in other words, tweak the decay time if you're using an ADSR envelope) to get the right character of sound created by the impulse.

An impulse envelope can have a long decay time. For instance, with a bell sound an impulse envelope with a long decay time will work well.

Acoustic-Like

The third common envelope shape gives an acoustic-like behavior (see Figure 5.12).

Figure 5.12 An acoustic-like envelope (with a sustain section).

Like an acoustic instrument—such as a piano or a guitar—these envelopes have an initial impact and then the level falls, but sustains at that lower level. Most acoustic instruments decay to zero, but as we're using synthesizers, we can sustain indefinitely if we want.

You will notice that unlike a conventional ADSR envelope, the decay phase curves. This gives a more acoustic-like response and a smoother sound in the synthesizer. However, the precise curve and the effective decay time will be a matter of taste for any particular sound. Equally, the sustain level will have a significant effect on the ongoing tone of the sound.

Now that we've got that all straight, let's look at making sounds.

Modulator Pitched Below the Carrier

When the modulator is pitched below the carrier, the figure on the left-hand side of the carrier to modulator (C:M) configuration will always be larger than the one on the right (this is logical, the carrier will be at a higher frequency than the modulator).

As you drop the pitch of the modulator (by reference to the carrier), in broad terms, the sound you hear becomes darker. There is a direct correlation between the pitch drop and darkness (so for instance, when the modulator is pitched two octaves below the carrier, the sound is darker than when the modulator is pitched one octave below the carrier).

Broadly speaking, when the modulator is pitched below the carrier you can set the modulation depth to any level. The end result may not be sonically pleasing, but it probably won't be so harsh that you feel your ears starting to bleed (which can be the case when the modulator is pitched above the carrier). The important issue here is that this makes available a broad range of tones for each pitch relationship. More tones = more color = more sonic options.

When you get to ratios beyond 8:1 (8:1 is equivalent to the modulator being three octaves below the carrier) then the tonal effect of the modulator can start to be lost. Depending on the pitch of the note being played, the carrier may fall out of the audio range in which case it would effectively start to act like a fast low frequency oscillator.

The tone created at these large ratios is also often less pleasing from a musical perspective—there is often a grinding or engine-like quality to the sound. However, these tones can have a use as effects.

Equally, these tones can work well in higher key ranges. There are several actions you can take to maximize the effect range of these sounds:

If you create the sound with higher ratios (for instance, if you use a ratio of 16:2 rather than 8:1) the resulting sound will be higher when played on the keyboard.

Alternately you can transpose the result so that it is playable over a wider range.

You can also use some key level scaling to adjust the level of the modulator (and therefore the amount of modulation). If you use key level scaling to reduce the level of the modulator at lower pitches, then the sound will be moderated—if you attenuate the level to extremes, all you will hear is a sine wave (from the carrier).

The results created when the modulators are set one octave (C:M ratio 2:1) or two octaves (C:M ratio 4:1) can provide a broad range of deeper darker tones. A 2:1 combination gives a more cohesive tone where the 4:1 combination gives a rougher sound. These tones are the foundation from which a wide range of bass sounds can be created.

When the modulator is set a major fifth below the carrier—either seven semitones (C:M ratio 3:2) or an octave and seven semitones (C:M ratio 3:1) a more metallic sound is created. When the modulation depth is set to its maximum this tone may be a bit too big bell-like to be readily deployed within a musical context (particularly in the lower keyboard regions). However if you drop the output level of the modulator, you will find a wealth of usable tones.

When the modulator is set a fourth below the carrier—either five semitones (C:M ratio 4:3) or an octave and five semitones (C:M ratio 8:3) another metallic sound is created, but perhaps less reedy. Again, when the modulation depth is set to its maximum this tone may be a bit too metallic to be readily deployed within a musical context without some tweaking (especially without some key level scaling in the lower pitch ranges). However if you drop the output level of the modulator, you will find another wealth of usable tones.

When applying envelopes to control the level of the modulator (and therefore the depth of the frequency modulation effect):

The organ-like style of envelope works best for sustained elements within a sound. If you're looking to create (electric) piano-like elements, go for these envelopes.

The impulse envelopes can be very effective with these pitch combinations, especially at high levels of frequency modulation depth and when the carrier is pitched well below the modulator. These combinations with an impulse envelope can impart a real impact to the start of a note that is felt more than it is heard.

The acoustic-like envelopes are most useful for the pitch combinations that create a metallic sound. If you set the sustain section to a low enough level that the tone is pleasant, you can then tweak the attack peak so that the otherwise unpleasant metallic tone functions as a pluck or hammer-like element.

When you're trying pitch combinations, pay particular attention to the acoustic-like envelope. By keeping the sustain level low you can make a much wider range of pitches work together. They may not work over the whole keyboard—and you can soften these extremes with some key level scaling—but you will find a broad range of useable tones.

Modulator and Carrier at Same Pitch

The most elementary FM configuration is a simple FM stack with both operators pitched at the same level. The sound produced has a reedy/woodwind quality that is perhaps reminiscent of an organ's tone at certain modulation depths.

It's not the most interesting tone, but it can be deployed in many situations.

When you couple this combination with an envelope, try slowing the attack time, so that the modulation depth fades in—this can give you a "mwah"-type sound, almost getting to a quack at certain attack times. You can use this effect in brass sounds to give some spit at the start of a note.

Modulator Pitched Above the Carrier

When the modulator is pitched above the carrier, the figure on the right-hand side of the carrier to modulator (C:M) configuration will always be larger than the one on the left (this is logical, the modulator will be at a higher frequency than the carrier).

As you raise the pitch of the modulator (by reference to the carrier), in broad terms, the sound you hear becomes brighter with a higher incidence of metallic tones. There is a direct correlation between the pitch lift and the brightness of the sound.

The sonic elements created with a modulator raised above a pitch lend themselves to creating the bright elements of a sound—often they will create the hammer or plucking element. As a result the organ-like envelope is often not appropriate. You can use it, but it gives a static bright sound that soon becomes fatiguing on the ears.

By equal measure, the sounds created with a modulator pitched above the carrier can become harsh very quickly. This is great if you want to create an effect, but needs extra care if you're looking for a musical result. Accordingly, the level of the modulation depth has to be carefully controlled and for this:

The impulse envelope can create a range of chiffs, clicks, plucks, clangs, knocks, hammers, and so on. With attention to detail, when using an impulse envelope the tuning of the modulator becomes more about creating character in the initial impact and the pitching is irrelevant (since only the impact is heard). In other words, while we're going to look for the sounds that work harmonically, don't ignore the ones that don't because they may make great chiffs, clicks, plucks, and so on.

The acoustic-like envelope is a good general purpose envelope. To create an appropriate sound there's usually a fine balance to be struck between the decay time and the sustain level.

Also in certain circumstances, an envelope with a slow attack can bring an interesting texture to the sound.

I now want to look at the main ratios. For these, an acoustic-like envelope is often the ideal choice. However, if you're trying to get a bell- or chime-like tone, then you will often want a very low sustain level. Indeed, to mimic the properties of real bells you may want to avoid a sustain portion and simple fade to zero level (but over a longer period than would be the case with an impulse envelope).

Turning to pitch ratios, the octave ratios—when the modulator is set one octave (C:M ratio 1:2), two octaves (C:M ratio 1:4), or three octaves (C:M ratio 1:8)—give a bright but not spectacular tone. You can use higher octaves (C:M ratio 1:16, 1:32, and so on), but those sounds are just bright without any real character (to my ears).

From here on in, there are lots of sharp and/or metallic tones and I'm afraid I lack the vocabulary to really describe the differences in great detail, but I'll try:

When the modulator is pitched four semitones above the carrier (C:M ratio 4:5), an octave plus four semitones above the carrier (C:M ratio 2:5), and two octaves plus four semitones above the carrier (C:M ratio 1:5) the sound has quite an open tone to it. Yes, there's metal in it, but it's not in any way bell- or chime-like.

When the modulator is pitched five semitones above the carrier (C:M ratio 3:4) the sound is fairly dull and not really distinguishable from the C:M 4:5 ratio). However at one octave plus five semitones (C:M ratio 3:8) and two octaves plus five semitones (C:M ratio 3:16) the tone gets more interesting, taking on more of a chime-like character. This is still a long way from being a proper chime and the envelopes need a lot of work to create the right chime-shape, but if a chime is your goal, then this may be a small element of it (although there are better options for the classic FM-bell sound).

With the modulator set seven semitones above the carrier (C:M ratio 2:3) the sound is a classic FM tone (indeed, some may call it a clichéd FM tone). Pushing the modulator up to one octave plus seven semitones above the carrier (C:M ratio 1:3) and the sound gives a fairly clean but high pitched, piercing tone. For most of the keyboard this tone isn't too metallic, but towards the top of the range it gets bright (so you may want to use some key level scaling to calm this effect if you don't like it). Pushing the modulator further still to two octaves plus seven semitones above the carrier (C:M ratio of 1:6) creates a certain pinging metallic tone (in certain key regions). Compared to the 1:3 ratio sounds, these tones are thinner and more piercing.

Setting the modulator to nine semitones above the carrier (C:M ratio 3:5) gives another classic bright FM tone. But things start to get really interesting when you push the modulator to one octave plus nine semitones above the carrier (C:M ratio 3:10) where we find one of the classic 1980s FM chime-like tones. Moving further with the modulator two octaves plus nine semitones above the carrier (C:M ration 3:20) and we find a slightly thinner (although no less classic) FM chime tone.

These permutations are not the only options—these are just a good start point. Beyond simply tweaking the pitch ratios, the overall effectiveness of these building blocks will depend on a range of factors, in particular:

The level of the modulator, in other words, the extent to which the carrier is modulated.

The envelopes. The carrier envelope to shape the volume envelope of the sound and the modulator envelope to control the tone over time.

The key level scaling to control the depth of modulation across the keyboard.

You've got the basics—now go and play before we move on.

Parallel Carrier Building Blocks

The first step when moving from a basic algorithm to creating a finished sound is to bring several algorithms together. For instance, if you are creating a guitar-like sound you could create a pluck and a sustained string sound—by bringing those two elements together you can create the sound of the instrument.

The most simple way to bring two algorithms together is to set up two simple FM stacks in one sound. This approach uses four operators as Figure 5.13 shows.

Figure 5.13 Two simple FM stacks working in parallel.

As you can see in Figure 5.13, operator C modulates operator D with a 1:4 ratio and operator E modulates operator F with a 2:1 ratio. Operator D and operator F are both carriers attached to the output.

You will notice that the two modulators—operator C and operator E—are both set to the same pitch. This is where you can introduce some efficiency in design. Instead of having both operator C and operator E in action, one operator could be used to modulate both carriers. Figure 5.14 shows this implemented with operator E acting as the modulator.

Figure 5.14 A parallel carrier arrangement in practice.

This change, from two separate stacks to one parallel carrier arrangement frees the fourth operator (operator C) to create other sounds.

Assuming that the settings of the two modulators were the same, the parallel carrier arrangement will give exactly the same tone as two simple FM stacks. So all the sounds we've already looked at can be recreated with this technique.

There are, naturally, limitations to the parallel carrier algorithm. The most challenging limitation is that it is difficult to get the right pitch ratios. While it's a trivially simply task to set up the ratios, the end results are sometimes messy.

Let me illustrate. Say you had two simple FM stacks, the first with a C:M ratio of 2:7 and the second with a C:M ratio of 4:1. These pitch ratios could be duplicated into a parallel carrier arrangement by using the following settings:

Modulator pitch ratio: 7

Carrier one pitch ratio: 2 (which maintains the C:M ratio of 2:7)

Carrier two pitch ratio: 28 (which maintains the C:M ratio of 4:1)

So now we have two carriers attached to the audio outputs with the simple FM stack C:M ratios carried through.

And we also have a problem.

You will notice that the two carriers are pitched far apart. The result of this is that each of the separate tones will work over completely different areas of the keyboard where we want the two elements to work together in the same range.

This is a limitation of parallel modulators. As a result, these algorithms are mostly deployed as a simple FM stack. The second carrier is then added either an octave above or an octave below the first carrier.

As I'm sure you've already figured, the only limit to the number of parallel carriers in a sound is the number of operators that are available. Indeed, when using four or five parallel carriers it is possible to get some very interesting organ-like sounds (but with a lot more real-time control than is present in a regular organ).

Parallel Modulator Building Blocks

Like parallel carriers, the parallel modulator algorithm gives the opportunity to bring together two sonic elements in one collection of three operators.

Where a parallel carrier arrangement can sometimes create a challenge to get the pitch of the two elements right, this is not the case with parallel modulators. Having a single audio output—in other words, a single carrier—sets the pitch at the right level for the algorithm. You can then set the appropriate ratios for the two modulators.

However, where a parallel modulator arrangement allows you to bring together two simple FM stacks and reproduce the sound precisely, this is not possible with parallel modulators. You can get a similar tone, but not the same tone.

While different, the tone can often be more pleasing and more cohesive, so the lack of perfect reproduction can often be an advantage.

The parallel modulator structure also gives other options, most significantly, you can cross-feed from one modulator to the other which puts a further range of sonic textures under your control. In addition, you can connect either or both of the modulators to the audio output as well as using feedback on any operator (or from the carrier to either modulator).

As you will have grasped, the number of options means it can take a while to understand the full scope of the sonic textures that can be created with this algorithm.

Anyway, that's enough about the difficulties. Let's look at a sound that works.

Set up a parallel modulator arrangement, set the pitch of the carrier to 1, set the first modulator pitch to 0.5 (C:M ratio 2:1), and set the second modulator pitch to 5 (C:M ratio 1:5). If you set organ-like envelopes, and push the modulation depths to somewhere in the 20 to 30 region, you will get a fairly pleasing tone: warm, with some brightness, and moderately thick. The sound is quite cohesive—in other words, you hear one sound—although at higher pitches you can start to identify two elements.

As a side issue, if you rearrange this as two simple FM stacks then you will get quite a different tone. The sound is softer and two distinct elements can be clearly heard—one higher, almost metallic, the other lower, more organ-like in character.

Anyway, back to the parallel modulator arrangement. Currently the sound has no shape and the tone is fixed. Three envelopes are all that is necessary to change the sound:

The first tweak is to the carrier envelope. Try setting this to give an acoustic-like envelope. However, don't drop the sustain level too far and keep the decay slope fairly gentle—much of the work on this sound will be done with the modulators.

The second envelope to adjust is the modulator pitched below the carrier. This can have a continuing effect on the note as it sustains and so an organ-like sound works here. As I mentioned earlier, I like to slightly slow the attack of these envelopes just to give a bit of room to the attack portion (which in this case is created by the other modulator). At this low modulation level, slowing the envelope giving this element of the sound something of a dull fretless bass vibe.

The third envelope is in the modulator pitched above the carrier. Without adjustment this modulator/carrier combination gives a bright tone, however with a tweak, it can work to give impact to the note. By setting an impact envelope, the character of the sound created by this modulator changes from a bright texture to something more like a wooden impact of a xylophone (but having a more metal character at higher ranges).

And there we have a basic parallel modulator created sound. As you can hear (if you've duplicated this):

The greater complexity from having three operators gives us a much more nuanced sound. In particular, you will notice that while there is a single cohesive tone, there are two elements to it: the strike and the sustain.

The envelopes make a significant difference on what you hear. All we have done is to control the output level over time, but the sonic effect is to create a wholly different sound from the basic structure that we initially created.

And this is just the start. You can build on this, for instance:

With some key level scaling you can set the higher pitched modulator to drop its output in higher key ranges so that the tone doesn't become too metallic.

With some key level scaling you can set the lower pitched modulator to attenuate its output in lower key ranges so that the sound doesn't get too dirty.

Some MIDI velocity can be added to the higher pitched modulator. This will give the sound some touch responsiveness.

You can mess with the pitches of the modulators. It's easy to go wrong when tweaking the lower pitched modulator and end up with something that just sounds out of tune. However, with the higher pitched modulator, try switching through integer ratios. You should hear that the tone and character of the impact of the note changes as the pitch of the modulator changes.

This is just one example that I have constructed to show how you can quickly put these sounds together. I pitched one modulator up and the other down—that was my choice for this example. There are no rules for how you structure these algorithms so you could set both modulators above, or both below, the carrier.

When you start experimenting with this algorithm, first set a simple FM stack, then add another modulator and see what pitches work. If you're having difficulty pitching the second modulator, then set it at an octave interval by reference to the first modulator, so for example if your first modulator has its ratio set at 20 (perhaps there is a C:M ratio of 3:20) then try the second modulator set at 10 (so its C:M ratio would be 3:10).

Cascade Building Blocks

The last basic building block is a cascade. These can create the most detailed sound, but can be hard to control and have a tendency to noise if you're not cautious.

At its most basic, a cascade is where one modulator modulates a second modulator, and that second modulator then modulates the carrier. Since the modulator that modulates the carrier is itself being modulated, the carrier is being modulated with a non-sine wave. The non-sine wave that is doing the modulation will be harmonically richer than a plain sine wave and accordingly, the effect of its modulation is a brighter sound (hence the tendency to noise).

If you're of a mind—and you really like challenges—there are plenty of ways you can mess with the basic structure and mix it up with some of the algorithms we've used already:

Instead of one modulator at the start of the chain, you could have two modulators in parallel.

Instead of one modulator in the middle, you could have two parallel modulators (both modulated by the same first modulator in the cascade).

If you have parallel modulators at any point, you can cross-feed from one to the other.

You can set feedback from any point in the chain (or you can simply have feedback on one modulator).

You could even have more than three operators in your cascade (but good luck on avoiding the noise).

For the moment, let's stick to the notion of a three operator cascade. With this configuration, there are two output levels that can be controlled. Working backwards:

There is the output is from the second modulator, the modulator that drives the carrier. These two operators work as a simple FM stack.

The other output is from the modulator at the start of the chain—this affects the signal coming out of the modulator feeding the carrier.

Having two levels to control gives you some interesting options beyond simply adjusting the envelope, for instance:

You can fix one of the levels. While this would normally give a static sound, since the other level can still be controlled you can still have control over tonal variation. You can fix both level, but that would just give you a static sound.

The levels can be controlled with different tools. For instance, the level going in to the carrier could be controlled by an envelope to shape the tone to mimic a natural instrument. By contrast, the level from the first modulator could be controlled by MIDI velocity. In this way, the tone would be far more sensitive to playing style.

Three operators also gives you more pitch options.

I find that raising the pitch of the modulators doesn't work so well with this combination. You can create a range of very bright sounds, but the tones and textures are hard to control. However, I like the tones you can create with the lower ratios. These can add a lot of weight to the sound.

Let me give you one example. Set the pitch ratio of the first modulator to 0.25, the middle operator to 1, and the carrier to 1. Working from the output, this means that we have a C:M ratio of 1:1 going into the output and a C:M ratio of 1:4 from the first modulator. Set the modulation depth levels at a reasonable amount, say around 30.

This gives a much richer, rounder, more controlled bass-like tone when compared to the kind of tone that can be achieved by a simple FM stack.

If you want to take this further, then increase the modulation depth level of the first modulator and bring in an envelope (an acoustic-like envelope). Balance the output level of the modulator and the sustain level of the envelope and you will find you can get almost a twangy bass. Twangy, but still full and rich.

Now try your own sounds. If you're not sure where to start, then take a simple FM stack that works well for you and add another modulator. Start with the new modulator pitched at the same level as the existing modulator and gently increase the modulation depth. Once you can hear the effect of the new modulator and understand its effect on the tone, then start playing with the pitch.

Other Sonic Twists

Every sound that we have talked about in this chapter has been created with a sine wave. With cascades we have been modulating with non-sine waves (since we are modulating modulation). In the next chapter we'll look at sonic components in some more detail and check out the options for creating sounds with different waves.

Chapter 6: Waves

So far, we've broadly looked at FM synthesis in the context of sounds created with sine waves.

You will get varying results by using different waveforms (as we'll see later in this chapter). However, even if you only use sine waves, there are issues in how you deploy those waves which can have a significant effect on the sound you create, especially when you are working with parallel operators and cascades.

Combining Operators

It's common when creating sounds using analog synthesis to use several oscillators to build the sound.

With FM synthesis, there are always several operators active in any sound, and it is the interaction of those operators that has a significant effect on the final sound created. Beyond that simple interaction there is also the issue of how operators that may not interact on one another, may still have an effect on the final sound.

Let me give you an example: set a simple parallel carrier algorithm—one modulator, two carriers, all pitched at the same level.

In an analog synth, if you slightly detune one of the oscillators, you will hear a thickening or fattening of the sound. In an FM sound, if you detune one of the carriers, the same principles apply, but the end result is perceived more as tremolo (in other words, wavering volume as the two carriers interact). So here we have an example of two operators—which do not interact on one another—but still have a significant effect on the end sound.

Let's have a look at some of these issues in a bit more detail.

Doubling Operators

With FM synthesis, you can double operators. The effect of the doubling depends on how the operators are applied:

If you double the carriers—in other words, if you go from a simple FM stack to a parallel carrier arrangement with the parameters of the two carriers precisely matching—then you will hear an increase in volume.

If you double the modulators—in other words, if you go from a simple FM stack to a parallel modulator arrangement with the parameters of the two modulators precisely matching—then you will hear a change in tone. The change in tone is equivalent to a doubling of the FM depth for a single modulator (so if you double the modulator, but halve the levels of the modulators, then the tone will remain the same).

If you detune one of the parallel operators, then, as noted above, the result is usually perceived as a tremolo effect.

You can, of course, duplicate the analog technique and subtly detune two separate algorithms in order to thicken and enrich the sound. However, as with analog synthesis, there is a balance to be struck—if the detuning goes too far then the resulting sound can sound out of tune.

Operator Phase

When we talk about the "phase" of an operator we generally mean the position in a wave's cycle (see Figure 6.1). With one operator, the phase matters little, however with two operators the effect of phase can be dramatic.

Figure 6.1 The phase of an operator. The blue sine wave has reversed polarity (when compared to the red sine wave) and the dotted gray triangle wave is 180 degrees out of phase.

If you have two waveforms that are totally in phase then you will get reinforcement of the signal. Reinforcement is perceived as an increase in volume. If your waves are out of phase then you will get interference and cancellation. The effect of the cancellation depends on the individual waves: if you have two sine waves that are 180 degrees out of phase (but are of the same polarity), then you will get total cancellation. Equally, two sine waves in phase but where one has its polarity inverted will result in total cancellation.

The phase of a wave can be synchronized with the start of a note (in other words, the key strike, hence this is often called key synchronization). This means that phase of every note from each oscillator will be consistent each time a key is struck—in other words, if you have set two waves to be slightly out of phase, the tone this creates will be consistent for each key strike.

Some synths allow you to engage key sync and adjust the precise phase of wave. Others simply allow you to determine whether the wave is in sync or not, and if it isn't in sync, then the phase is effectively random. FM8 allows you to switch of key synchronization and to invert the phase of the wave (see Figure 6.2).

Figure 6.2 The Waveform block for an operator in FM8 where you can set key synchronization and invert the polarity of the wave.

In the context of FM synthesis, the significance of sync and phase is particularly significant for modulators, especially when you have parallel modulators. For instance:

If you have two parallel modulators both with key sync engaged and both at the same pitch and level, but one has its polarity reversed, then there will be complete cancellation of the two modulators. With complete cancellation, all that will be heard in this situation is the carrier.

If you have two modulators (particularly if they are of the same pitch) and neither is key synchronized (in other words, the phases are free-running), then the phase cancellation of the modulators will give a different sonic result (since the modulator will effectively no longer be a sine wave, instead being a product of the two operators).

Parallel Modulators

Ignoring the issues of phase, when two operators are combined a third wave is created (unless the operators are of the same pitch in which case all the combination does is to increase the amplitude).

In the normal course of programming an FM sound, the parameters from each operator are set independently and so any interaction between the two modulators is usually insignificant. However, if you set a fairly static FM sound, then the interaction between the modulators is significant because instead of using sine waves, your modulation source effectively becomes the product of the two modulator waves. This is especially interesting, because by varying the level of each wave you can adjust the waveform of the modulator (which in turn will change the sound output from the carrier).

For a practical example, assume that there are two modulators, both sine waves, with one pitched above another. Figure 6.3 illustrates the result.

Figure 6.3 When a sine wave, and a sine wave pitched an octave higher than the first are added together, the result is a wholly new wave.

This applies for any wave combinations, for instance at Figure 6.4 shows a sawtooth wave and a square (both of the same pitch) being combined.

Figure 6.4 When a sawtooth wave and a square wave are added together, the result looks like a combination of the two.

The significance of the results is that the modulator is changed.

Using Non-Sine Waves

In my opinion, the sine wave will always be the first choice wave for FM synthesis. However, that doesn't mean you shouldn't consider other waves, and there are two main reasons for using different waves:

First, and most obviously, you will be able to access an even broader array of timbres by using different wave combinations.

Second, efficiency. Many of the tones created by different waves can also be created (at least approximately) using FM techniques—it is much faster and can use much less computer CPU horsepower to simply pick a different wave. Equally, you can often use one modulator rather than two.

As you would expect, there are down sides to using other waves:

The loss of controllability. Sounds created by FM techniques are infinitely variable and completely controllable whereas sounds created by an alternative wave are available on a take-or-leave-it basis.

The tendency to noise. With the increased harmonic overtones (which I'll discuss later in this chapter) there is a tendency to create noise (and to create noise at lower levels of FM depth).

We looked at algorithms in the last chapter and you will have realized that if you're going to start considering alternative waves, then there are choices for how these are deployed:

Sine to sine. This is the conventional simple FM stack that we are used to. The advantage is that it is controllable and comparatively predictable.

Sine to alternate. The first change you can make is to set a different wave as the carrier, retaining a sine wave as the modulator. The effect of this (when the modulation depth is increased) is often to enrich the sound of the carrier. With caution, and depending on the chosen wave, this sound can be quite controllable.

Alternate to sine. The second change you can make is to set a different wave as the modulator, retaining a sine wave as the carrier. The effect of this (when the modulation depth is increased) is to significantly change the tone. This sound can be controllable, but gives far less predictable results.

Alternate to alternate. The final basic set up is to choose two non-sine waves (which may be different from one another). Depending on how harmonically rich each wave is, you may get quite wild and unpredictable results. However, if you're using a pair of triangle waves, then you may find the results quite pleasing and just a bit brighter than if you had used sine waves.

In order to understand some of the sonic results when non-sine waves are employed, we should first analyze the composition of individual waves.

Basic Wave Shapes

There are some wave shapes which are common to virtually every synthesizer that has ever been produced.

There are two ways to look at a wave:

First, you can view its plot on an oscilloscope. This will show us the general shape of the wave and is often how waves have been given their name.

Second, we can consider how waves are created. Each wave can be broken down into a combination of sine waves—by adjusting the respective level of sine waves at different harmonics (in other words at octave intervals above the first harmonic or fundamental) different wave shapes can be created.

The second approach—looking at the component harmonics—is a much more useful way to think about waves in the context of FM sound. Instead of thinking of one wave modulating another, we can think of a group of separate sine waves acting as a modulator or carrier (or both).

Sine Wave

The sine wave (see Figure 6.5) is perhaps the most basic element in a sound. It is the purest form of tone you can have—it consists of the fundamental note and has no overtones.

Figure 6.5 A sine wave.

When we look at the components of a sine wave (see Figure 6.6), there is only the fundamental.

Figure 6.6 The elements of a sine wave.

Triangle Wave

A triangle wave (see Figure 6.7) gives a sound that is slightly less reedy or perhaps less sharp than a square wave. If you want to stretch a point, you could alternatively think of the triangle wave as being like a sine wave but somewhat sharper in its output.

Figure 6.7 A triangle wave.

A triangle wave is created by adding odd harmonics (sine waves spaced at octave intervals) with decreasing amplitude in the ratio 1/n^2. Therefore a triangle wave has the following harmonics:

The first harmonic at its full amplitude.

The third harmonic at one-ninth of its full value.

The fifth harmonic at one-twenty-fifth of its full value.

The seventh harmonic at one forty-ninth of its full value, and so on.

Figure 6.8 shows these harmonics plotted on a graph.

Figure 6.8 The first eight harmonics in a triangle wave. The fundamental is shown in red.

As you might imagine, since the triangle wave has few harmonics, and those that it does have are at a low level, the response from a triangle wave is similar to that of a sine wave in FM synthesis.

Square Wave

The square waveform (see Figure 6.9) has a hollow quality and is often used to create "woody" or "reedy" tones such as those found in woodwind instruments.

Figure 6.9 A square wave.

A square wave is created by adding odd harmonics with decreasing amplitude in the ratio 1/n. Therefore a square wave has the following harmonics:

The first harmonic at its full amplitude.

The third harmonic at one-third of its full value.

The fifth harmonic at one-fifth of its full value, and so on.

Figure 6.10 shows the harmonics of a square wave plotted on a graph.

Figure 6.10 The first eight harmonics in a square wave. The fundamental is shown in red.

If you look back to Figure 6.8, you will see that the triangle wave uses the same harmonics that are present in the square wave, however, in the square wave, those harmonics are at a higher level. When using the square wave in FM synthesis—particularly when using it as a modulator—the effect of these harmonics is much more noticeable giving a brighter sound.

You can recreate something that is sonically close to a square wave, but using FM techniques. Take a modulator and a carrier and pitch the modulator one octave above the carrier (so we have a C:M ratio of 1:2). If you then gently increase the modulation (on FM8, somewhere around 23 is good) you will get close to the sound. If you then add some feedback to the modulator (for me, setting it to 26 works well) the sound will give more of the brightness associated with a square wave.

While I will always advocate creating sounds with your ears, rather than with your eyes, in Figure 6.11 you can see the resulting waveform and the component spectrum in FM8 if you click on the Spect button (towards the bottom-left of the interface).

Figure 6.11 Creating a sound with the characteristics of a square wave using FM techniques.

Sawtooth Wave

The sawtooth wave (see Figure 6.12) is the closest that there is to general purpose wave in the analog synthesis world. It is bright and noisy.

Figure 6.12 A sawtooth wave. In this case, a rising sawtooth wave.

A sawtooth wave is created by adding both odd-numbered and even-numbered harmonics with decreasing amplitude in the ratio 1/n. Therefore a sawtooth wave has the following harmonics:

The first harmonic at its full amplitude.

The second harmonic at half its full value.

The third harmonic at one-third of its full value.

The fourth harmonic at one-quarter of its full value.

The fifth harmonic at one-fifth of its full value, and so on.

Figure 6.13 shows the harmonics of a square wave plotted on a graph.

Figure 6.13 The first sixteen harmonics in a sawtooth wave. The fundamental is shown in red.

If you look back to Figure 6.10, you will see that the square wave has harmonics at broadly the same amplitude, but the sawtooth wave has twice as many harmonics. When using the sawtooth wave for FM synthesis, twice as many harmonics means twice as bright.

In a similar manner to how you can create something like a square wave with FM techniques, you can also create a sound with a sawtooth-like character. To create this tone, take an operator and turn up the feedback—on FM8 when the feedback is set to around 43 I found a tone reminiscent of a sawtooth wave which, when filtered, behaved in a similar manner to a sawtooth wave. If you are going to create this sound, take care not to push the feedback too high—there is a fine line between a sawtooth-like sound and noise.

Non-Sine Waves in Practice

Many synthesizers offer a wide range of waves. Often these are great for analog-like sounds, having a harmonically rich content, but this harmonic richness makes these waves less suitable for FM synthesis (since, as we have seen, you are bringing many sine waves into play).

However, some synthesizers offer a range of more simple digital waves. FM8 is a good example—it has a range of waves created by adding two sine waves together. These digital waves may sound less interesting when heard on their own and may not give an interesting sound when pushed through a filter, but they form an excellent for sounds generated using FM techniques because they are more controllable.

Starting to Shape

This chapter has looked at a broader array of the raw sound sources that are available to you. Another way to shape sound is with filters which are discussed in the next chapter. When you look at filters, remember that complex waves are comprised of sine waves—all filters do is to reduce the amplitude of those additional sine waves.

Chapter 7: Filters

The original FM synthesizers did not have filters. However, most modern FM synthesizers offer some form of filter to shape the FM sounds. This inclusion also makes it possible to create hybrid FM/analog sounds taking advantage of both approaches.

Filters in Analog Synthesis

Analog synthesis is fairly straightforward. In essence a sound usually has three main elements present (see Figure 7.1):

the sound generator (an oscillator, or in our case, perhaps an algorithm)

the filter (to shape the tone), and

the volume control (to control the level of the sound over time).

Figure 7.1 The basic signal flow in an analog synthesizer.

Once the sound has been created, it is then "shaped" over time—both in terms of the tone and the volume. The tools to control the shaping through the filter and the amplifier are the same as for FM synthesis: primarily envelopes and LFOs, but a similarly wide range of modulators are available.

This type of synthesis—which is seen in every analog synthesizer and analog-emulating synthesizer—is usually called subtractive synthesis: the sound generator creates a sound and the filter "subtracts" elements to reach the final sound.

Subtractive synthesis has a different character to FM synthesis and filters offer sonic possibilities that cannot be created with FM techniques. For instance, with filters it is possible to get a "squelch" and the effect of filter sweeps—neither of these is readily accessible using FM techniques.

FM sound shaping by controlling the relationship between two or more operators gives a different sound to that created by using a filter to sculpt the sound—typically, but not always, the sound created with a filter will be less harmonically complex (the FM sound will generally be brighter and thinner). This can make FM and analog sounds the perfect complement for each other in a mix.

At its most basic you can think of the filter as being a tone control. A low-pass filter is like a treble control—turn it down and the sound gets "duller". There are different types of filters, but the most common is a low-pass filter, so we'll look at the workings of that type of filter first.

Filter Parameters

Filters have two main control parameters: cut-off frequency and resonance, see Figure 7.2.

Figure 7.2 A low-pass filter with a resonant peak.

Cut-Off Frequency

The cut-off frequency is the point at which the filter starts to have effect. So if you have a low-pass filter and set the cut-off frequency to 8kHz, the sound spectrum above 8kHz will be progressively reduced. If you are using a high-pass filter (which is discussed shortly), sounds below the 8kHz cut-off frequency will be reduced.

Resonance

Resonance adds some bite to a filter. It works by boosting the sound spectrum around the filter cut-off frequency as Figure 7.2 illustrates.

Used in moderation, the effect is subtle and can make a sound appear brighter and/or slightly thinner (or less fat if you prefer). When used to the extreme the effect is noticeable—most dance records use filter sweeps with high levels of resonance to exaggerate the effect of the filter sweep.

At very high resonance settings, some filters can exhibit quite extreme behavior, so take care with this parameter and turn down the output if you don't want to burn your ears off.

Filter Types

There are three main filter types that are usually found in FM synthesizers. There are other filter types, but these three are the most common.

Low-Pass

The low-pass filter (or if you prefer, high-cut filter) allows low frequencies to pass through it, see Figure 7.3.

Figure 7.3 A low-pass filter.

When a low-pass filter is fully open, all frequencies can pass through it.

As the filter is closed, it progressively allows less sound to pass through—you will hear this as the sound becoming duller as the higher frequency elements of the spectrum are filtered out. When the filter is nearly completely closed only the very lowest elements of the frequency spectrum can pass—this sound will be close to the sound of a very low-pitched sine wave.

The effect that the low-pass filter will have on a sound will vary depending on the waveform—brighter/sharper sounds (in other words, those with richer harmonic spectrums) will be affected more than those with simpler harmonic constructions.

High-Pass

The high-pass filter (or low-cut filter) is the reverse of the low-pass filter—it allows high frequencies to pass and progressively cuts out the lower frequencies, see Figure 7.4.

Figure 7.4 A high-pass filter.

Band-Pass

The band-pass filter acts like a combination of a low-pass filter and a high-pass filter by cutting the frequency spectrum at both ends to only allow a narrow band of sound to pass, see Figure 7.5.

Figure 7.5 A band-pass filter.

The cut-off frequency control determines the center frequency where the full signal is allowed to pass—from that point outwards, the spectrum of sound is progressively cut. The resonance control has the effect of boosting the signal around the cut-off frequency.

At extremes of frequency, the band-pass filter will sound similar to either a high-pass or a low-pass filter.

Band-Pass filters tend to take a lot of energy out of the signal so you may have to boost the level after the filter.

Filter Slopes

A low-pass filter progressively reduces the volume of a sound above the cut-off point. The rate at which the sound wave is reduced above the cut-off frequency is determined by the slope of the filter. The slope reflects how aggressively the filter attacks the sound it is filtering.

If you have a 6dB/octave filter (which is quite a subtle filter), it will reduce the level of the sound source by 6dB at one octave above the cut-off point, 12dB at two octaves above the cut-off frequency, 18dB at three octaves above the cut-off, and so on.

A 12dB/octave filter (sometimes called a 2-pole filter) will reduce the level of the sound wave's volume by 12dB for each octave above the cut-off point.

A 24dB/octave filter (sometimes called a 4-pole filter) will reduce the level of the sound wave's volume by 24dB for each octave above the cut-off point.

You will see some different filter slopes for a fixed cut-off frequency in Figure 7.6. This is an image drawn by hand and so is not to scale, however, you can see the differing result of the filter slopes. As you would expect, high-pass filters cut at the same rate, but below the cut-off frequency.

Figure 7.6 Different filter curves (note, these are not drawn to scale).

Filters in Practice

FM8 implements filters in an interesting way. There are three reasons why I use the word interesting:

First, the filter block is an operator. The effect of this is that (1) the whole audio signal does not need to pass through the filter and (2) the sound that has been processed through the filter can then be fed back into the audio chain (in other words you can use a filtered sound as a modulation source and change the filter parameters to change the effect of the modulation).

Second, instead of a high-pass or low-pass filter, there is a continuous filter. This sweeps from one extreme to the other, acting as a band-pass filter in between.

Third, there are two filters with flexible routing in order to give further sonic shaping possibilities.

Figure 7.7 shows the operator, and as you can see, like the other operators in FM8 it has its own dedicated modulation controls.

Figure 7.7 Operator Z, the filter block in FM8.

That's the easy stuff. Let me briefly point to some of the unique features. (These are not FM-specific, but I am noting them to highlight some of the tonal shaping functions of the featured synthesizer.)

In the Filter box you will see there are two rows of three knobs—that's one row per filter.

The cut-off and resonance knobs work as you would expect. The third knob is the Mode control which shifts between a low-pass filter (knob fully to the left), through a band-pass filter (knob vertical), to a high-pass filter (knob fully to the right). This is comparatively uncommon, but gives some interesting tonal shaping possibilities.

For the second filter, instead of having a cut-off knob, there is a spread knob. This adjusts the cut-off for the second filter by reference to the cut-off for the first filter. When set to zero, the two cut-off frequencies are the same.

The routing section gives further tone shaping options. Instead of having a parallel/series selector to arrange the audio flow through the two filters, there is a continuous control to mix between the two extremes. In addition there is a Mix 1/2 knob to balance between the filters. This works as a straightforward balance control when the filters are in parallel. When they are in series, the control works to send more of filter one directly to the output.

Using Filters with FM

When using a filter with FM sounds, it is important to approach the sound shaping with some care so that the delicate FM timbres are not lost. If you want to wipe out the FM timbres completely, then you might achieve better results with an analog synthesizer.

If you are using a filter to further shape your sound, the prime destination to control will be the filter cut-off frequency and the main modulation sources are the same as those we have already used:

Envelopes. Envelopes provide an ideal control source to modulate the filter cut-off over time. You can coordinate the filter cut-off envelope with the other operator envelopes (indeed, in FM8 you can link envelopes so their settings mirror).

Velocity. Velocity allows a filter to mimic the properties of natural instruments so that the sound gets brighter with more forceful playing. As well as allowing velocity to directly control the brightness, you can also set velocity to change the extent to which an envelope modulates the brightness (in other words, you can use envelopes and velocity together). You can also set velocity to scale your filter envelopes (so the envelope executes more slowly or more swiftly based on incoming MIDI velocity).

Key scaling. You may want to use key scaling when setting the filter to mimic the behavior of real instruments. If you are designing a patch to resemble the behavior of an acoustic instrument, a single cut-off point may be unnatural: the high notes would be too dull and the low notes to bright. To remedy this you can use key scaling with the filter: this will open the filter to a greater extent at higher frequencies and close it at lower frequencies giving a more natural response.

Adding Some FX

Now that we've looked at filters, let's look at some other non-FM techniques and focus on FX.

Chapter 8: FX

We've looked at the elements used to create a sound using frequency modulation synthesis techniques. Now we'll look at how to polish those sounds and how to extend your sonic palette further using effects units.

The FX units you find on today's synthesizers are generally used in several ways. One way is to use the FX as an integral part of the sound, for instance a distortion unit can help create a sound that is hard to create through synthesis techniques alone. However, to a certain extent in the context of FM synthesis, this approach can be problematic. The essence of FM synthesis is its detailed tones with constantly shifting colors. Slapping boat-loads of FX on top of these tones simply kills the tone.

The other way that FX is used is to enhance a sound, for instance, adding reverb to give a sound some space and depth. Within the context of FM synthesis this can maintain the sonic integrity (although with inappropriate application, the results can still smother).

For FM tones, FX works best when:

It is gently polishing the tone. For instance when overdrive is used to give a vintage vibe to a sound but the underlying quality of the sound still shines through.

It is smoothing the tone. For instance, a gentle amount of chorus can add brightness to a sound while removing unwanted thin sharpness.

It is adding another dimension to a sound. For instance, a small amount of echo can add a third dimension to a lively sound.

In deploying an FX you want to use as much care as you do when you create the underlying FM tone.

Deployment of FX

FX units are deployed in one of two ways: as insert FX units or as send FX units. There is a practical difference between the two.

Insert FX

With insert FX the whole of the audio signal passes through the FX unit (see Figure 8.1).

Figure 8.1 The signal flow through an insert FX unit.

If you want to add a distortion or overdrive effect, then you are likely to want the whole signal to be processed by the fuzz box. EQ and compression are other typical examples of insert FX.

Send FX

With send FX, you send part of your signal to the FX unit and then mix an effected signal back with the dry sound (see Figure 8.2).

Figure 8.2 The signal flow with a send FX unit.

Examples of FX units that are grouped under the send FX heading are modulation effects (chorus and so on), delays, and reverbs.

Other Routing Options

While there are only two configurations, there are other options—FM8 is a good example of a synthesizer which implements its FX units in a slightly different way.

FM8 puts the FX units at the end of the audio chain, immediately before the audio output, and the FX units are then effectively send FX which would seem to frustrate the option of having insert FX units. However, to allow for insert FX units, there is the facility to mix the clean and effected channels.

This means you can have a 100% effected sound, a 100% clean sound, or anything in between, so for instance, you could mix a signal 50% clean and 50% distorted.

If you set the signal to 100% effected, this means that all FX units are applied 100% which may not be appropriate for echo and reverb FX (as two examples). To address this issue, many of the FX units in FM8 have a dry/wet control so that the depth of the individual FX unit can be controlled.

There is only one minor downside to this approach. Say you want to add some distortion and a bit of reverb—perhaps you want to mix these 90% clean/10% distorted with some reverb. You can easily call up the Overdrive or Tube Amp settings and a Reverb unit. These units would be set on the FX audio chain.

However, the reverb would be applied to distorted signal. In this scenario there is no way to generate the reverb from the clean signal. So you might have a 90% clean sound, but any reverb would be 100% distorted.

This is an example from FM8: you may find other routing options in other synths.

Now we understand the routing options, let's have a look at the FX units that are available.

Overdrive and Distortion

Most people are used to hearing distortion used in an extreme way. However, depending on the amount of control you are given over the distortion, it can be used in a much more subtle manner. Typically, you should be able to squeeze the following spectrum of tone color from most overdrive and distortion units:

At very low levels, you are unlikely to hear much effect, but the overdrive can have the effect of warming up a sound and perhaps compressing it a bit.

With a touch more effect, you will often find that a sound can feel more "vintage" as the overdrive effect takes out some of the top end of the signal.

As the effect increases, the signal will start to break up—this might be a useful setting for sound effects.

The next step is to move into proper overdrive (start thinking of rock guitars and you will get the picture). This overdrive type effect can be quite controllable and quite musical, however, this is the point at which you start to lose the timbre of the underlying sound.

Finally you will get out-and-out distortion which may be hard to control or use with any subtlety.

If you use heavy amounts of distortion, since it has such a significant effect on the sound, you'll save a lot of time if you don't create a highly nuanced tone that will be lost is the processing.

When you use a distortion unit it is usually very easy to get a piercing sound which dominates the track, rather than a warm overdriven sound that may fit in context. If you are trying to recreate the sound of gently overdriven guitars, remember that all the rockers play their guitars through speakers—inefficient speakers that cut off most of the signal above 4kHz. To recreate this effect you may need to use a filter or some form of speaker simulator (which is offered in FM8).

Also, if you are looking for realism, then the distortion needs to be very controlled. Even heavily overdriven guitars can still sound clean (ish) if they are played very lightly. If possible, you can try to control the amount of distortion with MIDI velocity (by controlling the input level and the level of the carriers). To get more control and more gearing in the overdrive (that is to say a much greater range of overload), modulate the distortion depth with velocity as well as controlling the volume of the signal with velocity (if your synthesizer allows this).

The controls on most overdrive and distortion units are quite simple. Very often all you'll see are a drive control and a tone control (although some units offer more flexibility). Usually the quality of the drive is also affected by the level of the incoming signal (higher signals distort more quickly and have less dynamic range), so if you're trying to shape the sound, experiment with adjusting the levels of your carriers as well as playing with the drive knob.

Compression

Compressors were originally used to prevent an analog signal overloading an analog input, and indeed, compressors still are used for this purpose.

In essence, a compressor is an automatic gain control: when a signal gets to a certain level the compressor restricts how much louder the signal can get (see Figure 8.3).

Figure 8.3 A compressor controlling an input signal.

Most compressors allow you to control:

Threshold. The threshold is the level above which a signal is attenuated.

Ratio. The compression ratio controls the extent to which a signal above the threshold is allowed to increase in level. So for instance, with a 4:1 ratio if the input signal increases by 4dB above the threshold, the output signal will only increase by 1dB above the threshold.

Gain. When a signal has been compressed, it will be quieter than the input signal. The make-up gain allows the output level to be rebalanced to an appropriate volume.

In practice, you may want to use the compressor as a volume control to pull in some of the peaks. You can also use it as an effect where it can help to:

make a sound fatter and/or smoother

enhance the perceived loudness of a sound, and

give the sound more punch.

The disadvantage of using a compressor is that the resulting sound can tend to dominate a mix. With more extreme compressor settings, the sound will usually have a more uniform level and sometimes the delicate harmonic shifts of a patch can be covered up as all of the harmonics take a similar level.

EQ

The purpose of equalization is to make certain elements of the sound spectrum louder and other elements quieter. You can use EQ creatively or surgically. However, remember that you still need to get your sound to sit in a mix, so go carefully with the EQ, and try not to use the effect to cover the faults of poor programming. Also, remember that you may not hear the full effect of any EQ tweaks unless you are using full-range speakers.

The most flexible form of EQ is the parametric EQ where you can set:

the frequency to be boosted or cut,

the amount of boost or cut, and

the bandwidth (or Q) of the boost or cut. The bandwidth determines how wide the boost or cut is, much like a constantly variable slope control for a filter.

A simplified form of EQ is the shelf EQ. A shelf EQ will cut or boost:

the whole signal above a specified frequency in the case of a high shelf, or

the whole signal below a specified frequency in the case of a low shelf.

Take a look at Figure 8.4 which shows a low shelf EQ (on the left), a high shelf EQ (on the right), and a parametric EQ in the middle.

Figure 8.4 A low shelf, parametric, and high shelf EQ.

EQ can be very effective in taming FM sounds, however, before you go too wild with the effect, it is worth taking some time to see whether the sound can be tamed at source. Often a bit of key level scaling will achieve the same effect but in a more natural manner.

Modulated Delay Effects

Modulated delay effects take many different forms (chorus/flanger/phaser, and so on) but they all do a similar thing: in essence they mix a delayed, pitch-modulated signal with the original signal to give a fuller/warmer/richer/whooshier (insert whatever description you want) sound. The delay time for the delayed signal is so short that you don't hear it as an echo, simply as a cohesive changed tone.

While the operating principles are the same, the sound the different units produce can be markedly different. Although the delays are so short the delayed signal cannot be separately identified, the delay time has a major effect on the sound.

Used sparingly, these effects can give an element of spark or richness to a sound. Used to excess and you will create a sound that quickly becomes passé.

Phaser/Flanger

Words cannot readily describe the difference between the sound produced by a phaser and the sound produced by a flanger, however, to my mind a phaser gives a more nasal sound where a flanger gives a more whooshy type sound. One of the reasons for the phaser sounding more nasal is that the delayed signal passes through a notch filter (which has its frequency modulated).

Flangers and phasers are often used on percussion sounds and with plucked-type sounds (such as guitars and electric pianos/clavinets). The sound is very distinctive and is hard to use in a subtle way, so you are likely not to want to use the effect too frequently. The sound also has a 1970s retro quality to it—whether you love or hate that era is likely to have an infulence on how you feel about phasing and flanging.

The main controls you are likely to find on a phaser or a flanger include:

Delay. The delay control will adjust the time of the delayed signal.

Feedback. The feedback control sets the number of times the delayed signal is repeated. This has an effect on the perception of depth of the effect.

Rate. The rate control adjusts the frequency of the low frequency oscillator modulating the pitch of the delayed signal.

Depth. The depth control adjusts the extent to which the low frequency oscillator modulates the pitch of the delayed signal.

Chorus

Chorus units also mix a delayed signal with the original signal, however, they use a longer delay than would be typical with a phaser or flanger. This delayed signal is then modulated by a low frequency oscillator.

The result can be a much more lush/smooth sound—at extremes however, it can sound like vibrato played too fast or just bad tuning.

Used in moderation, the effect can either add sparkle or thicken up a sound without noticeably changing the sound's characteristics. If you're cautious, you will also find that the chorus effect can smooth out some rough edges created in an FM tone.

The main controls you are likely to find on a chorus are similar to those on a phaser or a flanger and may include:

Delay. The delay control will adjust the time of the delayed signal.

Feedback. The feedback control sets the number of times the delayed signal is repeated. This has an effect on the perception of depth (or out-of-tuneness) of the effect.

Rate. The rate control adjusts the frequency of the low frequency oscillator modulating the pitch of the delayed signal.

Depth. The depth control adjusts the extent to which the low frequency oscillator modulates the pitch of the delayed signal.

Tone. The tone control will adjust the tone of the delayed, modulated signal to take away any harshness or metallic ringing.

Delay

Virtually every synthesizer with built-in effects will offer some sort of delay.

Usually there will be two ways to set the delay time:

The delay may be set as an absolute amount, usually defined in milliseconds.

Alternatively, the delay time may be linked to the tempo of the track, being defined as a fraction of the beat (for instance, with delay of 1/4, the signal is delayed by a quarter note).

Often several different types of delay unit are available—the most common are mono, stereo, and cross delay.

Mono Delay

A mono delay adds a simple delay to the input signal. A mono delay can be achieved in a stereo delay unit if the delay time is equal for both channels.

Stereo Delay

With a stereo delay, there are two separate delay lines which may (or may not) have different delay times. Conventionally these delay lines are hardwired left and right.

Cross Delay

Like a stereo delay, a cross delay has two channels. However, the output from the first delay is fed into the second and the output from the second is fed into the first. This can give the effect of spreading the delays across the stereo spectrum or ping-ponging the delays between the two channels.

Common Delay Controls

The most common controls that delay units have are:

Delay time. As noted, delay time is often (but not always) synchronized to the host's tempo and expressed in terms of beats.

Feedback. Feedback controls how many times each delay repeats (quite literally, it controls how much of the delayed signal is sent back to the input).

EQ, damping or a filter. EQ, damping, and a filter may be used to control the sound of the echo. Typically these controls will be used to cut the high frequency elements of the delayed signal to make the sound duller, resulting in a more natural sounding echo.

When adding delay, you need to consider what you are trying to achieve. If you are adding the slightest touch of slap-back just to give a bit of spark and a bit of space, then make sure you have done that. If you want to add a bit of echo, make sure that the delays are duller than the original source. If you are after an effect, then, as with the modulation effects, moderation is key.

Reverb

Reverb can give a sound some spatial context.

With reverb units, there is significant interaction between the controls, so even more than normal it is necessary to balance several parameters when shaping the sound. The most common controls offered by reverb units are:

Pre Delay. This controls the time between the original signal and the reverb taking effect. Smaller values give the perception of a smaller room while longer delays give the perception of larger rooms.

Size (or Room Size). This controls the size of the room being simulated by the reverb unit and has a direct effect on the decay time of the reverb (in other words, the time for which the reverberation effect sounds). Occasionally some units will offer a separate decay control to adjust the decay time.

Damp. Damping works by cutting the higher frequencies in the reverb signal. One of the reasons why electronic reverb sounds artificial (that is clangy and metallic) is because it has too much high frequency information. The damping control can help to create a more realistic simulation.

Width. If a width control is present, it will adjust the stereo width of the reverb.

Using FX in Your Own Sounds

We've now looked at the sonic elements and the FX units to polish and enhance our sounds, so it's time to move on and start creating sounds.

Chapter 9: Creating Sounds with Frequency Modulation Synthesis

When it comes to creating sounds using frequency modulation synthesis techniques, there are no hard-and-fast rules. Taste is more important than theory and your taste will almost certainly be different to mine. Accordingly, this chapter is intended only as an introduction to—a starting point for—FM sound design. You will notice that there are no patches accompanying this book—that is intentional, this chapter is all about using your ears and finding what sounds right to you rather than replicating what sounds good to me.

There is no magic formula to creating an FM sound. However, I would suggest a few basic steps before you jump in:

Understand the function of each control.

Understand the basic algorithms and the building blocks that are available, and how the interaction between modulators and carriers can create the basic tones.

Have a definite aim about the sound you're trying to program—don't just fiddle with the knobs and hope something useful comes along.

Once you have these basics sorted, I suggest a two stage approach:

Get something that is functional and reasonably close to where you want to end up. As long as you have a grasp on the basic building blocks (and if you don't go back to Chapter 5: Algorithms and Sonic Building Blocks), you should be able to get to this point quickly.

Then undertake the detailed tweaking. This is the time to make sure the patch is exactly right for your needs—and will be the time consuming part of the programming. This is where you can focus on getting the envelopes right, tweaking the key level scaling, and so on.

As a side note before we continue: many FM synths offer a high resolution mode to enhance the fidelity of the sound. This works by increasing the resolution of the internal computations and will chew up more CPU horsepower, but will give a much better—clearer, crisper—sonic result when you are creating sounds. So if you've got a high quality mode, engage it before reading on.

Deploying Your Building Blocks to Create Sounds

So how do you get from the basic building blocks to a sound?

Let's have a look at an example patch structure. This should give a context to how an FM patch may be constructed.

It is quite usual for an FM patch to include several elements. For instance, a classic electric piano type patch will have two main elements—the bell tone (heard when the key is struck) and the sustain sound. From this foundation the sound can then be developed (as Figure 9.1 shows).

Figure 9.1 An example of the structure of an FM piano.

In the figure you can see how the basic building blocks can be brought together:

A modulator/carrier pairing (modulator two/carrier four) creates the bell sound.

A modulator/carrier (modulator one/carrier one) creates the sustain sound. A second carrier (carrier two), also modulated by modulator one (creating a parallel carrier algorithm) doubles the sustain sound created by the first carrier, but at a different octave.

Carrier three (without a modulator) is used to thicken up the sound.

Six operators, three main blocks, and we have the basis of a sound.

Let me offer a few last thought before we look at creating sounds in a bit more detail.

Designed For Purpose

Any sounds you create should be created for a specific purpose (even if that purpose is just to have fun or to hear how something sounds). When you are creating sounds for a specific purpose—for instance, to work within the context of other parts—you stand a far better chance of getting the right sound which then fits in the mix.

Although you might have designed a sound for a specific purpose, that does not prevent you from using it in another context. Indeed, you may find that, for instance, a bass sound is a good start point for creating a stab sound, and so rather than starting from a plain sound you can simply tweak an existing sound.

Context of a Mix

It doesn't matter whether the sound you create is good or bad when you listen to it in isolation—it matters whether the sound works when you deploy it in context. In other words, it only matters how it sounds in the mix.

When you are looking at how sounds work within the context of a mix, ideally each sound will have its own place in the frequency spectrum, and will be clear and distinct. You may not always want that clarity, however, you will be more likely to have your mixes criticized for being "muddy" than for being "too sparse".

Choose the Right Tools

When you are programming take some time to make sure you choose the right tool.

While I would never discourage you from trying, there are some tools that are better suited to certain jobs, and sometimes, FM synthesis is not the right answer. For instance, although it is quite possible to create incredibly fat sounds using FM synthesis, I think you will get better and more consistent results by using analog synthesis techniques. Equally, if you want to recreate the sound of an acoustic piano, you might get something interesting, but you will probably get better results if you use a set of piano samples.

More importantly, choosing the right tool is also a function of having the knowledge to control that instrument. The only way to learn how to use a technique and an instrument is to keep using one instrument over a long time—don't keep buying new instruments, pick one synth then learn every aspect of its character and every aspect of FM sound creation.

Emulating Real Instruments

When it comes to creating sounds, a first step for many people is to attempt to recreate the sonic textures of real instruments.

It is possible to recreate some real instruments with FM techniques. However, just because you can recreate some, that does not mean you can recreate all instruments, nor that it is necessarily desirable thing to do.

While it is possible to recreate some instruments using FM techniques, there are several reasons not to. One main reason is that some FM sounds—for instance, the FM Rhodes piano sound—have become so ubiquitous, that people have forgotten what the real things sound like, so trying to recreate the original will give you a sound that is "wrong" for many listeners.

There are other reasons not to try to recreate real instruments. Perhaps the most simple reason is that there are better options. If you want to create a piece that uses real instruments, then there are two options if you want to something that will not be noticeable to the listener:

Use real instruments. If you want the nuance of a piano, then using a piano will give you the best sound—there's no way that a synthesizer will sound better than the real thing if your goal is a real piano. If your goal is a super-real (or enhanced) sound, then an FM synthesized sound may be better.

If the real thing is impractical, then use a set of high quality samples.

Another reason for not trying to replicate real instruments with synthesis is that it is impractically difficult. With a real instrument the musician has a virtually limitless tone palette. While FM synthesizers have an incredibly wide tone palette, you can realistically only create one sound at any one time (or if you use some modulation, a limited range of sounds). What you cannot readily do with a synthesizer is replicate the choices that are open to a player—for instance, you cannot replicate a simple change from a bowed note to a plucked note as a violin player may make. The only way to create these ranges of tones is to synthesize each one separately... and that is where using a synthesizer becomes less practical, especially if you are trying to synthesize a whole performance.

A correlation to the range of tones that any one instrument creates is that real sounds are usually created by a range of instruments. If you look at an orchestra, there isn't a single "string" instrument. Instead, there are a range of violins, violas, cellos, and basses, each one of which has its own unique range of tones. It is the combination of these tones that gives the final sound that we hear as "strings".

While I'm not an advocate of reproducing real instruments, for descriptive purposes, it's often very useful to reference real instruments, and the characteristics of real instruments, when trying to describe sounds, and so I will make these references (as you will read).

Playability

Finally, any sound has to be highly playable. The playability of the sound is one aspect that separates the average sound from the professional. Use your knowledge of how the sound will be deployed to set the modulation sources.

For instance, if the sound is going to be played by a live musician, then you might ensure that velocity has an effect and that the modulation wheel and expression pedal both offer a wide range of control.

Sounds in Practice

The sounds I'm going to describe can be recreated with any synthesizer. Where I'm quoting settings, these are the settings I am using in FM8. They are not meant as a direction but rather as an indication of the sort of settings that might work for you.

Building Basses

Let's start by looking at some bass sounds.

Simple FM Bass Sounds

It's surprisingly easy to make effective, deep, playable bass sounds using FM techniques. It's also surprisingly easy to bring a lot of control and nuance.

You can create an effective bass sound with a simple FM stack, however, when you add a second modulator to create a cascade you introduce many more sonic options. Let me step through the fundamentals of a basic bass, starting with a single carrier and ending with four operators.

As a first step, open a carrier and set an acoustic-like envelope with the sustain level set about halfway.

Clearly this won't be the most interesting sound you've ever heard—it's a simple sine wave—so call up a modulator. Drop the pitch of the modulator by an octave (C:M ratio 2:1), set the modulation depth to a reasonable level (66 sounds good to me), and adjust the envelope—an organ envelope with a slowed attack can give just enough quack to be interesting (too slow and you'll get too much quack and lose some of the immediacy of the tone).

At this point, the sound might be a bit too bright/thin, especially as we move up the keyboard. To remedy this, set some velocity tracking in the modulator (something around 65 sounds good to me). This gives up a spectrum of tone control and at medium velocities, fattens the sound up a bit.

However, as the sound moves up the keyboard, it becomes a bit too shrill for my taste (remember this is meant to be a bass sound—we're not worried about the top end of the frequency range). To counter this shrillness, some pitch key scaling helps—to my taste, the full level can be kept from C-2 to C3, but above C3, the level should drop reaching zero at the top of the range. In other words, the level of this operator will progressively drop from the middle of the keyboard and at the top of the range this modulator will have no effect.

So far, we've got quite an interesting sound, but we can add some roundness and fullness, as well as some more richness to the tone. Bring up a second modulator, this time modulating the first modulator (so that we've got a cascade). Drop the pitch to an octave below the modulator (C:M ratio 2:1 which in respect of the carrier which is an octave above the first modulator the C:M ratio is effectively 4:1), set the modulation depth to a low level (somewhere around 12), and set an acoustic-like envelope.

If you set up this second modulation, you will probably hear a deeper thicker tone that gives the sound a smoother response to changing MIDI velocity. You'll probably hear an engine-like tone at higher velocities which becomes particularly noticeable if a note sustains. Some of that engine-like tone can be smoothed (but not removed completely) and more thickness added if you route this new modulator to also modulate the carrier (so the carrier is modulated by both modulators, one of which is also modulated by the other). If you increase the level of this new modulation to somewhere in the range of 30 to 50 you should find a pleasant thickening and rounding of the tone.

We can smooth the tone and add more weight with another operator, pitched an octave below the first carrier (in other words, set at the same pitch as the first modulator). Set up a simple acoustic-like envelope with the sustain level fairly high (around three-quarters) and attach the operator to the output (making it a carrier) with its level set to around 70.

This adds some more weight, but is a bit dominant. To control the presence of this element, set its velocity response (to 100). This means the full weight of the operator is only heard which MIDI velocity reaches the maximum.

To tweak the tone of this new element, set the second modulator (in other words, the first modulator in the cascade, which is pitched an octave below this carrier) to modulate this carrier. Somewhere in the range of 30 to 50 sounded good to me.

As you can hear, this gives a pretty thick sound which is responsive, playable, and still quite nimble.

As you have heard (I hope you're trying these sounds on a synth—there's little point in just reading about them)—by adding modulators (and a second carrier) we have thickened up the tone. MIDI velocity gives the player some tone control and the sound can also be adjusted by tweaking the modulation depth. Of course, there are other options, for instance, either (or both) of the modulators could be attached to the output.

Now you have a basic bass sound, go and play. See if you can find the limits of the tones that are available.

Bass with Attack

The Simple FM Bass Sound gives a good bass, but in some ways it lacks character in the attack of the note. So let's create an interesting attack portion and then make it into a bass sound.

First, call up an operator to act as the carrier.

Call up modulator one, set the pitch an octave up (C:M ratio 1:2), set an impulse envelope, and set a moderate level of modulation depth. This should give quite a pleasant wooden tone. Now mute this operator and call up a second modulator.

Set the second modulator to modulate the carrier (so we have a parallel modulator arrangement). This time, push the pitch of the modulator to set a C:M ratio of 3:20 (in FM8, with the carrier ratio set at 1, you can achieve the appropriate ratio by setting the modulator ratio at 6.6667). Again set an impulse envelope and a moderate amount of modulation depth. This C:M ratio is the basis of a chime, but in this sound it gives a pleasant metallic tone.

With this second modulator, push the velocity setting to the maximum. Now, at low velocity levels, this modulator will have no effect and so a sine wave can be heard, but at high levels its effect can be clearly heard.

Return to the first modulator and unmute it. Set the velocity setting, but this time to the negative maximum so that the modulator has effect at lower velocities but not at higher velocities. In this way, we have a highly velocity-sensitive set up that allows us to cross-fade between the two tones created by the different modulators.

So far we only have the attack portion of the note. To change this to a bass sound, call up another modulator, drop its pitch by an octave (C:M ratio 2:1), and adjust the modulation depth to suit.

This gives a very 1980s bass sound, but with a very controllable tone.

You will notice that there has been no effort to shape the carrier or the modulator creating the bass tone and I haven't looked at key level scaling. I'll leave these to your taste.

Sub-Oscillators

With analog synthesis a sub-oscillator is often employed.

A sub-oscillator is an additional oscillator added (usually) one, although sometimes two, octaves below the main oscillator (or oscillators). They perform two main functions:

First, they change the tone of the sound, usually giving it more thickness.

Second, they add more weight to the sound. This can be a subtle addition to the solidity of a note or it can be massive sub-sonic floor-shaking bass.

These two changes are usually mutually inclusive, so you will add weight and change the tone of the sound by adding a sub-oscillator. The analog synthesis technique is easy to use in FM synthesis (since you will often have a spare operator which can be called into service) and indeed, we did something fairly similar in the Simple FM Bass Sound. However, the technique can be applied in many situations, for instance, to round-out a piano-like sound.

An operator acting as a sub-oscillator can create a new sound; however, that is not necessarily the aim:

If your aim is simply to create a more solid bass (or other) sound without altering the tone to too great an extent, then try an operator without modulation as your sub-oscillator. This will simply add a sine wave which shouldn't change the tone too much.

If your aim is to create a deeper and richer sound, and you can accept some change in the timbre, then modulate the carrier acting as the sub-oscillator.

Both options will give a change in tone—the choice of whether to modulate, and if so by how much—affects how much the tone changes.

The other factor affecting the tone change is the level of the sub-oscillator: at lower volumes the sub-oscillator will be less noticeable (and will therefore not add as much weight).

One point to remember when you're adding sub-oscillators: speakers. Listen through full range speakers, otherwise the sound you will end up with will be far too bass-heavy.

Bass FX

Personally, I'm not a big fan of FX on bass sounds—they tend to make the sound mushy and the whole mix becomes flabby. However—and slightly counter-intuitively—adding some subtle chorus will often brighten up a bass sound and give it more presence, while not portraying much of the chorusing effect. This brighter sound will, of course, be more dominant and take up more space in the mix.

A word of caution before you add too much chorus... Bass sounds created with FM synthesis tend to be brighter than bass sounds created with analog techniques or sample-based synthesis. Accordingly, you need to be more sparing in your use of chorus if you are adding it to an FM bass sound and you don't want that sound to become a feature.

Anyway, that's enough bass. Let's move on to brass.

Building Brass Sounds

Real brass instruments create a very brash and harsh sound. What people often perceive as brass is a much softer, more restrained tone. As well as being harsh, real brass instrument tend to sound much thinner than many people expect—often people associate brass with a fat sound because they are used to hearing brass as a section with several instruments covering a wide range of the tonal spectrum.

However, if you want to create something with a moderately realistic brass tone and character, FM synthesis is a great tool.

Basic Brass

A basic FM brass sound is quite simple: all you need is three operators, each with a acoustic-like envelope, set in a parallel modulator configuration.

Take the carrier and adjust the sustain level to around 60%. In this sound much of the shaping can be achieved through the modulators.

With the first modulator, keep the pitch at the same level as the carrier (C:M ratio 1:1), set the modulation depth quite high (around 70, perhaps), and drop the sustain level in the envelope to around 45. This will give a thin brass-like tone.

You might want to mute the first modulator when you set up the second one (but don't forget to turn the first back on). With the second modulator, drop the pitch by an octave (C:M ratio 2:1), set the envelope sustain level to around 35, and push the modulation depth to around 50. This will give you another brass tone, but slightly less strained than is created with the other modulator.

On their own each modulator/carrier combination gives a clean brass sound. Together they give a much rawer, rougher brass sound. Once you have the basic tone, there are some tweaks to enhance the tone:

First, slow the attack time in the modulator envelopes slightly. This will give a slight spit at the start of each note. Ideally set the two envelopes to have different attack times (the lower pitched modulator being slower). This difference will ensure the tone has some movement.

Set some velocity scaling in the modulators so that MIDI velocity gives some tone control. You don't want anything too radical here—just enough to give you some feel.

Once you have these sound set up, you need to balance the modulation depths, the sustain levels (of the modulators), and the velocity response in order to tweak your tone.

This sound will play over a reasonable key range. You might want to use some key level scaling. However, when the tone becomes very unnatural, that is probably a symptom that the whole sound is out of an appropriate range rather than a case of elements needing to be tweaked.

When you're happy with your sound, think about doubling this algorithm, possibly at a different octave, to give more weight.

As an alternative, you can also try a parallel carrier arrangement. Keep the carriers at the same pitch and drop the modulator by an octave (C:M ratio 2:1), set different levels of modulation depth, detune one of the carriers by a few Hz, and you'll get a variation on the brass them that doubles well with the brass tone we've already created.

Cheating...

There are several ways you can fatten up the basic brass sound. I've already mentioned doubling the algorithm and I'm sure you've thought about adding a sub-oscillator. Let me add another thought.

Analog.

It is very easy to create brass-like sounds using analog synthesis—essentially you run a sawtooth wave through a low-pass filter. While this is probably technically cheating to make a suggestion like this in a book about frequency modulation synthesis, you might want to think about adding a filtered sawtooth in addition to the FM algorithm in order to create a best-of-both-worlds type sound.

You might also want to think about adding a very discrete amount of overdrive/distortion to roughen the sound up a bit, especially if you add some conventional analog elements.

Deploying Brass Sounds

Going back to the notion that much of what we hear as brass is actually a brass section—in other words, a group of individual instruments, each different, playing together—if you create a brass-like sound and play a few chords, you may not achieve satisfactory results since you won't get the effect of individual instruments playing together.

There are several approaches you can adopt to achieve greater realism (or rather, to reduce the unrealistic result that comes from having one brass patch), perhaps the most effective is to create a number of individual patches and play each as a separate part. This replicates how real instrument sections are created. Given the permutations and ranges of tones that are readily accessible with FM, this is a good way to create realistic performances.

Building Bell-Like Tones

For many people, the first time they really become aware of frequency modulation sounds in a track was when they heard FM bells. And once you notice those bells, then you'll start noticing them popping up all over the place.

Creating a convincing bell- or chime-like tone using FM techniques can be quite a challenge... until you've got it right once. And after that, it almost becomes too easy to create these tones.

I want to look at two bell-like tones. The first, will be a less-than-classic sound, but the second will be much more what you expect to hear.

Grindy Bell

The idea behind Grindy Bell is to get something that is definitely a bell, but maybe not as musical as might be expected. This sound works best in lower registers—towards the top end of the keyboard, it gives something of a conventional FM bell sound.

The basis of this sound is a parallel carrier arrangement.

Set the first carrier with an impact envelope, but set the decay time from strike to zero sound to around 10 seconds.

Put a similar setting into the second carrier, but with a slight tweak—for instance, make the decay time shorter and change the decay slope.

Pan the two slightly left and slightly right, and slightly detune one of the carriers to give a gentle tremolo effect. This tremolo will translate as ringing when we get the bell tone.

To create the bell tone, set the pitch of the modulator 21 semitones above the carriers (C:M ratio 3:10) and set quite a sharp impact envelope with a decay time of under a second. Once set, push the modulation depth to get a bell-like tone.

So far, the sound is pretty clean, so we should rough things up a bit.

Call up another modulator and set it to modulate the two carriers, but set the modulation depth to a very low level. Then drop the pitch to give a C:M ratio of 3:1. As long as you keep the modulation depth low, you can use an organ envelope here.

This new modulator adds a bit of darkness, but let's add some more. Call up a new simple FM stack:

Set the pitch of the modulator at the same pitch as the two existing carriers, set an impulse envelope with a decay time of around seven seconds, and set the modulation depth to around 60.

Set the pitch of the carrier one octave below the pitch of the modulator (C:M ratio 1:2) and set an envelope similar to that of the modulator.

On its own, this simple FM stack doesn't sound very interesting, but if you mix it at a low level with the other elements in the sound, it gives a darkening/detuning to the bell sound (when played over the lower keyboard ranges).

In the higher ranges, the brighter elements dominate to greater extent and so you might want to use same key level scaling to tame the tone if you want to play it across the keyboard.

Classic Bell

This is a simple straightforward bell sound—nothing grindy here. It is designed for single bells—it probably won't sound at its best if you try playing chords.

The basis of this sound is a parallel modulator set-up:

The C:M ratio for the first modulator should be set to 3:10.

The C:M ratio for the second modulator should be set to 3:20.

For each of the three operators, set an impact envelope. The carrier should have a decay time of around 7 seconds and the lower pitched modulator a similar decay time (but longer also works). The higher pitched operator envelope should have a shorter decay time (perhaps around 4 seconds).

In the carrier and the lower-pitched modulator, a release section needs to be included otherwise the sound will unnaturally stop if a key is released. The release section should last around three seconds. The carrier should decay to zero whereas the modulator should remain at its level—this setting will mean that the volume decays but the tone remains consistent.

The modulation depth should be set to taste. To my ear the lower pitched modulator can have a higher modulation depth (around 50 to 60) where a lower figure (around 35) is appropriate for the higher modulator. Balancing the two modulation depths will give you a range of tonal options.

This is the basic bell sound. As you can hear, it is clean, fairly accurate, and also not very interesting. There's a lot we can do to make the sound more interesting and richer:

First duplicate the carrier. Set the two modulators to modulate this carrier, but with different modulation depths (so you get a different tone). Tweak the carrier envelope so that it is not a perfect match for the other carrier, and slightly offset the pitch for this carrier. The pitch offset will give a tremolo effect which is perceived as the bell having more "ring". Once you have the sound nailed, pan the two carriers slightly to the left and slightly to the right of the stereo panorama.

You can add a third carrier if you want to give another dimension, however, this may not make a significant change to the tone. If you do add a third carrier, consider messing with its pitch (for instance drop it an octave below the pitch of the other carriers or raise it by an octave).

To add some more body, but without changing the tone too much, think about adding an operator without modulation. Set this operator one octave or one octave plus seven semitones below the two main modulators and increase the level slowly until it gives body without changing the tone.

As with the other sounds, we started this bell-tone with a basic element and built. The end result is a rich bell sound, however, it may be too rich. If this is the case, then scale back on some of the elements.

This sound plays over most of the keyboard range, however at the very top of the keyboard you might find it gets a bit sharp. If this is the case for your ears, then use some key level scaling to tame some of the elements.

Bell FX

You can use quite a lot of FX without the processing becoming too noticeable. The most natural sounding processors are chorus, reverb, and echo.

Chorus will add some thickness and a lot of sparkle to the sound. You can turn the depth (of the LFO modulation) up quite high, but the speed (of the LFO modulation source) should be kept fairly slow.

A short delay time with a low amount of feedback will give some life to the sound and brighten up your bell-like tones.

A small amount of reverb will often help to smooth the sound, giving a more natural bell or chime-like tone.

Building Key-Based Sounds

Many key-based sounds share a construction that is similar to bell-tones and so you will not be surprised that piano-type sounds are another strength of FM synthesis.

Clavinet/Harpsichord

You can probably figure out a clavinet/harpsichord sound very easily, but as this is the first key-based sound, here's an idea or two to get you started:

Set up a cascade with each operator having an impulse envelope.

In the carrier, set the decay time of the envelope to around five seconds.

In the modulator attached to the carrier, set the C:M ratio to 1:10, the decay time to around 1.5 seconds, and push the modulation depth to around 25.

In the first modulator (the one attached to the middle modulator), set the C:M ratio (or should that be modulator to modulator ratio?) to 10:7, the decay time to about 0.5 seconds, and move the modulation depth to adjust the tone—somewhere short of 50 sounded good to me.

It is that quick and easy to get this sort of sound.

Electric Piano

There are many similarities between the electric piano sound and bell sounds. However, there are significant differences:

The piano sound is more controlled—there is no bell-tone as such, just a hammer strike.

The piano sound also has a longer sustain sound with no ringing—just a gently decaying timbre.

There are many ways to create an FM piano—this sound is going to have three elements:

A bright hammer strike.

A moderately bright tone to give character to the sound.

A duller sustaining sound to give warmth and fullness to the sound.

Let's look at the three elements—each of which starts from a basic FM stack—and see how they work together.

The hammer strike gives a very thin metallic tone. Set the algorithm with a C:M ratio of 1:12 and a reasonable modulation depth (around 50). This gives a very bright sound, but that is pulled in by using an impact envelope on the carrier so that only the strike sounds—there is no sustain.

For the bright character tone, set the carrier at the same pitch as the other carriers and raise the modulator to give a C:M ratio of 1:3, with the modulation depth set to around 50. Envelopes on both operators are impact envelopes with a decay time of around three seconds.

For the sustain tone, both the carrier and the modulator should be set to the pitch of the other two carriers (so there is a C:M ratio of 1:1) and a with modulation depth of around 60 to 65. With two acoustic envelopes, the modulator should reach the sustain level (which is around 25%) after about half a second, and the carrier reach its sustain level (set around 40%) after three seconds.

Set the sustain tone to the maximum level, the bright tone to about 65, and the hammer strike to around 35 and these three elements together will give an electric piano-ish sound. Of course, this is the point where we can get tweaking and looking at tonal variations:

For a tonal change, go straight to the modulator in the bright character section. If you drop the modulator from a C:M ratio of 1:3 to a C:M ratio of 1:2, you will get a much more wooden tone. By contrast if you raise the modulator to give a C:M ratio of 1:4, or even 1:5, you will get a brighter, more metallic character to the sound.

If you want to add more bite, then set the hammer modulator to modulate the bright character stack's carrier. This setting won't change the tone too radically (unless you really push the modulation), but it will change the character of the sound.

To get some tonal response, with the hammer modulator attached to the second carrier, push up the velocity response on the modulator. This gives a very responsive feel to the patch.

As you can hear, even if you don't like the initial tone, this sound is very tweakable and with a few minor adjustments it is easy to shape the tone in a number of different directions.

Organ

Perhaps the ultimate parallel carrier FM sound is an organ emulation. There are many variations that you can call up, but let me give you a quick example.

Call up five carriers, attach them to the audio output with a moderate volume level (around 50), and tune them as follows:

Operator one, ratio: 0.5 (one octave below fundamental)

Operator two, ratio: 1 (fundamental)

Operator three, ratio: 2 (one octave above fundamental)

Operator four, ratio: 3 (one octave and seven semitones, a major fifth, above fundamental)

Operator five, ratio: 4 (two octaves above fundamental)

This is a basic organ set-up. At the moment, all we are doing is creating an organ sound with sine waves.

You will hear that as you increase or decrease the level for each operator, the tone changes. Effectively the level changes shift the composition of the sine waves creating a new wave (think back to the composition of waves that we looked at in Chapter 6: Waves.

If you slightly shift the pitch of each operator, you will get an organ-like vibrato, but the tone is still not compelling. However, it gets far more interesting when we bring in a modulator.

Call up the last operator, set its ratio to 1 and then set it to modulate the carriers (add one carrier at a time and keep the modulation depth low, around 5 to 25). You will hear that as the modulation depth changes, the organ tone changes.

This set-up gives us three ways to sculpt the tone:

The first option is to change the level of the carriers.

The second option is to change the amount by which each individual carrier is modulated.

The third option is to change the pitch of the modulator.

And, of course, these three option interact.

See how many different textures you can find and then try changing the pitch of the carriers.

Building Pads

Building pads with FM techniques is a fairly straightforward process—choose a building block and build from there using the techniques we have looked at so far.

In some ways FM pads are that simple, however, this approach can easily lead to static tones and sounds that fill too much of the sonic spectrum. To counteract these issues, there are a few techniques you might want to think about:

Double up and slightly detune two elements. In essence, treat the sound source much as you would if you were creating a sound in an analog synthesizer.

Employ sophisticated envelopes to keep the sound subtly shifting, and if that doesn't work, apply an LFO to certain operators to ensure the sound moves.

Add some user control, for instance, control the modulation depth in some of the algorithms with aftertouch so the player can subtly shift the tone.

Use a subtle amount of FX.

Call up a filter (ideally a high pass filter) to take out any flabbiness.

Bring in some rhythmic elements...

Rhythmic Pads

If you have patience and dedication, then rhythmic pads are for you...

This is the ultimate parallel modulator sound and requires that you have a synth with flexible envelopes:

Start with a carrier with an organ envelope.

Call up a modulator and set any C:M ratio at a reasonable depth.

Go to the modulator envelope and engage tempo sync (if available), then with the envelope, create a sustain section (typically lasting a bar), and in this section create a rhythmic envelope (see Figure 9.2) so that beyond simply changing tone, there is a rhythm created with the modulation.

Figure 9.2 An example of a rhythmic envelope created in FM8.

Call up a second modulator and set a different C:M ratio.

In the second modulator, create a different, but complementary envelope rhythm.

As far as rhythms go, to start with I suggest you employ simple beats to get a feel for this technique. Most significantly, listen for what you don't create directly—in particular, listen to how the various modulators interact. If you set the beats at different levels, then you'll find a range of tones which will create more interest in the pad.

And once you have two modulators working, add a third... and then a fourth...

Building Your Own Sounds

That should be enough sounds to get you started, so go and grab your synthesizer of choice and start making your own noise.

If you're wondering where to find out more about making sounds with synthesizers, then check out the next section, Further Resources, which points you to a range of further materials (including free downloadable books and free sound design videos).

Further Resources

I hope you have found this book interesting and useful. If you want to know more about sound design and making music with synthesizers, then I suggest you head over to my website (noisesculpture.com) and check out my music-related books and videos. If you're browsing the site, I suggest you look at the following books and videos first.

How to Make a Noise Series of Books

There are five books in the How to Make a Noise series (this one, plus the four others listed here). Each book looks at a different aspect of synthesis, focusing on the particular strengths of that technique.

While each book is separate, there is (as you would expect) some overlap (for instance, a filter will always act like a filter, whatever the synthesizer—but the way that the filter is used will vary).

How to Make a Noise: Analog Synthesis

(published by Coombe Hill Publishing, ISBN: 978-0955495502, available in electronic format only, noisesculpture.com/analog)

How to Make a Noise: Analog Synthesis looks at creating sounds using analog synthesis techniques.

Analog synthesis works by taking a sound source and shaping it with a filter. This is a simple but powerful technique which allows you to create the warm, rich, energetic, and commanding sounds, and with some care you will find tones with detail, complexity, and delicacy.

These are the techniques used to create the sounds that you associate with many classic synthesizers such as the Moogs (Mini Moog, Moog Modular, Taurus, Little Phatty), the Oberheim synths (OB-8, OB-X), the Rolands (SH-1000, Juno-6, Jupiter-4, and Jupiter-8), Prophet-5 from Sequential Circuits, and the ARPs (ARP 2500, Arp 2600).

You will have heard these techniques used on many recordings and will immediately recognize the sounds they produce. After reading the book you will be able to create and control these classic sounds when you apply the techniques to hardware or software synthesizers.

How to Make a Noise: Sample-Based Synthesis

(published by Coombe Hill Publishing, ISBN: 978-0955495502, available in electronic format only, noisesculpture.com/sample)

Sample-based synthesizers can be used to create the sound of a full orchestra or individual instruments. They can replicate the sound of a full drum kit, delicate vintage gear, and specialist instruments. Samplers allow one musician to play the bagpipes, a harp, a lute, and a whole orchestra, all at the push of a button.

As well as offering the facility to recreate the sound of real instruments with a high degree of sonic fidelity, sample-based synthesis also allows real sounds to be used as the basis for new sounds. These sounds can then be manipulated and mangled to create unimagined sounds with genuine complexity and depth.

How to Make a Noise: Sample-Based Synthesis looks at how to create and control sounds—both realistic recreations of real instrument and creative warped tones—and the tools and techniques that are available to help shape your sounds.

How to Make a Noise: iPad Synthesizers Edition

(published by Coombe Hill Publishing, ISBN: 978-0955495502, available in electronic format only, noisesculpture.com/ipad)

The fourth book in the series, How to Make a Noise: iPad Synthesizers Edition doesn't focus on a particular technique, but instead, looks at creating sounds on five synthesizers that are available for the iPad (BassLine, iMS20, iELECTRIBE, ReBirth, and NLogSynth Pro).

Many of the techniques discussed in the other books are covered in iPad Synthesizers Edition, but with particular focus to their application to the five featured iPad synthesizers.

How to Make a Noise: A Comprehensive Guide to Synthesizer Programming

(published by Coombe Hill Publishing, ISBN: 978-0955495502, noisesculpture.com/comprehensive)

There is another book in the How to Make a Noise series—the original hard copy (paper) book. The four electronic-only books are parallel editions to this existing book.

How to Make a Noise: A Comprehensive Guide to Synthesizer Programming was first published in 2005 and revised in 2007 and so is now past its first flush of youth. However, it is perhaps the most widely read book about synthesizer programming (and there's a free downloadable PDF version, too).

This book focuses on building sounds (over 300 sounds are built) and looks at building these sounds with six synthesizers (Cameleon 5000, Rhino 2, Surge, Vanguard, Wusikstation, and Z3TA+) which were on the cutting edge when the book was first published, but (in most cases) have now been superseded.

However, the techniques outlined are still applicable and the book also sets out other synthesis options, such as additive synthesis and wave-sequencing (which are not covered in any of the other publications).

Jumpstart Your Music Career

(published by Course Technology PTR, ISBN: 978-1435459526, noisesculpture.com/jump)

You will have noticed that this is not a book about synthesis. However, once you can make sounds, then might to want to make some money from your music, and this is where Jumpstart Your Music Career comes in. This book is for every musician who wants to earn a living—and to sustain a long-term career—making music.

It has never been so easy to have a career in music: the barriers to entry have never been lower, the access to and ways to find fans have never been more straightforward, and the options to generate income have never been more plentiful.

The hard part is developing a strategy that's right for you and then executing it. Jumpstart Your Music Career looks at how you can build and sustain a successful career. It is the book that should be on every musician's bookshelf.

Cakewalk Synthesizers: From Presets to Power User, second edition

(published by Course Technology PTR, ISBN: 978-1435455641, noisesculpture.com/cakewalk-synthesizers)

Cakewalk Synthesizers: From Presets to Power User, second edition is the ultimate guide to understanding and using all of Cakewalk's synthesizers and learning about synthesizer programming.

The book features the complete range of Cakewalk (and rgc:audio) synthesizers, including Rapture, Rapture LE, Dimension Pro, Dimension LE, Beatscape, Session Drummer 2 and Session Drummer 3, Z3TA+, and Pentagon I.

There is also a package of downloadable material to accompany this book. This package includes additional chapters and is available for free to everyone (you don't need to have bought the book). This package also includes sound design master classes from several leading synthesizer programmers and so is well worth checking out.

Becoming a Synthesizer Wizard: From Presets to Power User

(published by Course Technology PTR, ISBN: 978-1598635508, noisesculpture.com/becoming-a-synthesizer-wizard)

Becoming a Synthesizer Wizard: From Presets to Power User is for:

People who are new to synthesis and who want to understand the basics and take their first steps in creating and controlling sounds with synthesizers.

Musicians who are familiar with synthesis, but who want to solidify or expand their knowledge so they can use their tools more fully.

Anyone who wants to build, share, and perhaps sell their own synthesizers.

The book looks at synthesis from first principles. It focuses on the elements of synthesis and the building blocks, and it highlights its examples using four leading modular synthesizers (Zebra 2, KarmaFX Synth Modular, VAZ Modular, and SynthEdit). From these building blocks, the book looks at a range of sound building techniques that can be used with the featured synthesizers, or can be readily applied to any other synthesizer.

The book is also a great introduction to SynthEdit for anyone who wants to create—and then share or sell—their own synthesizers.

Synthesizer Boot Camp

(noisesculpture.com/synthesizer-boot-camp)

Synthesizer Boot Camp is a series of videos which looks at specific synthesizer techniques that can be applied in creating sounds. All of these videos are freely available on my website and can also be accessed on the Noise Sculpture YouTube channel.