INDEX

PROLOGUE

CHAPTER I: BASIC CONCEPTS

MUSICAL NOTATION

Note names

The Pentagram

The Notes

Chord symbols

Tablature

FUNDAMENTAL FREQUENCY, HARMONICS AND TIMBRE

MAJOR SCALE

Structure

Alterations in major scales

Key signature

Natural note

INTERVALS

Ascending intervals

Enharmonic intervals

Compound intervals

Descending intervals

Interval inversion

CYCLE OF FIFTHS

CHAPTER II: MAJOR KEY

TRIAD CHORDS

Diatonic chords

Note layouts

Chord inversion

SEVENTH CHORDS

Diatonic seventh chords

Tonal function of chords

Inversions

Chord m7b5

Chords with a sixth

Sus chords

The tritone and its resolution

The dominant chord

II-V MOVEMENT

DIATONIC TENSIONS

SCALE FORMULAS

MAJOR PENTATONIC SCALE

NON-DIATONIC CHORDS

Secondary dominants

Extended dominant and chain of dominants

Substitute dominants

Secondary seconds

Double tonal function

Diminished seventh chords

SUMMARY OF HARMONIC ANALYSIS

CHAPTER III: MINOR KEY

NATURAL MINOR SCALE

Tonal function of triad chords

Tonal function of seventh chords

HARMONIC MINOR SCALE

Tonal function of triad chords

Tonal function of seventh chords

Use of b9

MELODIC MINOR SCALE

Tonal function of chords

Tonal function of seventh chords

PENTATONIC MINOR SCALE

BLUES SCALE

SUMMARY OF THE MINOR MODE

HARMONIC ANALYSIS OF THE MINOR MODE

CHAPTER IV: SCALES AND MORE SCALES

SCALE-CHORD RELATIONSHIP

MODAL SCALES

Major chords and major modes

Minor chords and minor modes

Relative modal chords and scales

Parallel modal chords and scales

The characteristic note

How to play modal scales

RELATIVE SCALES IN THE MINOR MODE

Relative scales of the natural minor mode

Relative scales of the harmonic minor mode

Relative scales in the melodic minor mode

TETRACHORDS

Types of tetrachords

Modals

Minors

Other scales

SCALE OF THE MOMENT

ALTERED MIXOLYDIAN SCALES

Mixolydian b9

Mixolydian b13

Mixolydian b9 b13

Lydian b7

Altered or Superlocrian scale

Symmetric diminished scale

Tonal scale

THE IDEAL SCALE (HARMONIC SCALE)

THE DIMINISHED SCALE

CHAPTER V: MELODY AND HARMONY

MELODIC ANALYSIS

Strong and weak notes

Main and secondary notes

Melodic movements

MUSICAL THEME

Phrase or question

Counterphrase or answer

Resolution

Part

Form

Climax

Signs for repetition

HARMONIC MOVEMENT

Harmonic rhythm

Using chord symbols

Cadences

Voice leading

More utilized movements

The bass line

HYBRID CHORDS

MODAL HARMONY

The chords

Harmonic progression

The melody

Modes, one by one

MODULATION

Neighboring tones

Distant tones

Direct modulation

Modulation by pivot

Modulation by transit

MODAL INTERCHANGE CHORDS

HARMONIZATION AND REHARMONIZATION OF MELODIES

Harmonization of melodies

Self-evaluation exercise

Reharmonization of melodies

PUBLISHED BOOKS BY THE AUTHOR

MODERN HARMONY STEP BY STEP

Chords, scales, improvisation and composition in modern music:

Jazz, Blues, Rock, Funk, Pop and more.

Ricky Schneider

Translated by Eduardo Castro y Sierra

VISIT

http://cgo-music-books.com

Readers of my books will have access to

Free  Harmony and Improvisation lessons

Your opinion matters, send me any douts or suggestions and consultations at:

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This book is registered in the “Intellectual property registry” throughout the word. Texts, graphics and sheet music may not be copied, sold, shared or distributed without the authors consent.

Thank you for respecting the intellectual property rights.

PROLOGUE

What is the reason for this book?

At first, the word harmony usually provokes some degree of panic. In my years as a professor, I have found a bit of resistance in my students when approaching this matter, generally with the erroneous idea that it is something very complex and boring, resting them time to learn how to play.

In truth, if you can count up to 12 you may learn harmony and profit from the great advantages that this knowledge will bring to you.

Once you have entered the world of music, there comes a point when it is no longer practical to keep learning things by heart, since you will lose much time and will not advance.

Harmony consists of understanding the origin of and the relationship between chords and scales and, thereby, to remember much better the themes, easily transport  them to other keys, find the scales for a good improvisation, enrich your compositions, and much more.

With this book, you may advance step by step from an initial basic level to a really advanced knowledge covering major and minor keys, every kind of chord and scale, improvisation, theme analysis, composition and arrangements.

The concepts we will deal with cover every type of harmony on which modern music is based and its different styles: blues, jazz, rock, pop, melodic, etc.

How to use this book.

Differing from other texts on harmony, information here is not grouped by topics, but rather set in an order which will allow you to advance page by page as if you were taking a course. If you follow the chapters in order, you will have no difficulty in advancing.

Certainly, you may not read this book as a novel. Each new topic will require your practicing on your instrument in order to assimilate everything and be able to continue.

Most examples are in the most commonly used keys, which are also the simplest, thus to enable their understanding. It will be very useful to transport the examples to other more complex keys, so that you may gain practice in the use of alterations, intervals, scales, and assemblage of chords.

Every rule of harmony we shall study here is not an absolute law and, therefore, may and “should be” broken. Great musicians, who changed history, have done so. But before this happens, it is better to know them and thus not to venture on inventing ideas which have existed for decades.

To rebel is an indispensable quality for an artist, but not a good excuse to keep us away from study.

CHAPTER I: BASIC CONCEPTS

MUSICAL NOTATION

First, we shall see basic notation, which will allow us to work with harmony, but not every detail of musical notation.

Note names

In the Anglo-Saxon countries, the name of the musical notes, wich were formerly: Do, Re, Mi, fa,Sol, La, Ti (or Si); have been replaced by the letters of the alphabet, starting with the note A = LA

The Pentagram

The pentagram is a set of 5 lines and 4 spaces (numbered from bottom to top) where notes are placed in either an ascending or a descending manner according to scale order. Notes are represented by a musical figure (full, minim, quarter-note, etc.) which determines its duration. We shall not go into details at this point, and will generally use the full note, with some exceptions requiring another subdivision. This pentagram is headed by a clef -in this case, the G clef- which will define the pitch (name and octave) of each note.

There are different clefs, each in accordance with the instrument one shall be writing for, i.e., a figure using the same placement will be one or another note depending on the clef at the top of the pentagram.

In this book, we shall work exclusively with the G clef written on the second line, since it is the one most commonly employed for various instruments. The G clef on the second line means that the note appearing on that line of the pentagram is a G. Whenever the pentagram should not be sufficient to write very high or very low notes more lines will be added on top of or below the former, exclusively for such notes (additional lines).

The Notes

In western music, we shall find 12 notes (chromatic scale) which will be repeated above or below in the same order (octaves) and be separated from each other by a semitone or half tone, which is the minimal distance between sounds.

These 12 notes may be divided into 2 different groups:

Natural notes: these are the 7 notes which we call the scale of C major : C, D, E, F, G, A, B and correspond to the white keys of the piano.

The distance between natural notes amounts to a tone, with the exception of E-F and B-C, where it is a semitone.

Altered notes: these are the notes at half a distance between natural notes (with the exception of the 2 cases previously mentioned), which coincide with the black keys of the piano. To name them, the symbol # (sharp) is added to the note below it or the symbol b (flat) added to the note above it, i.e., the same note may have 2 different names to represent it.

Further on, we shall see when and why one or another name is used. These notes, with identical sound but different name, are known as enharmonic notes.

In the note names, the symbols # or b are added, depending on which of the 2 should come after the letter.

To memorize notes seems an easy task: you look at them for 10 minutes and you appear to know them. But when you try to read them pell-mell then problems begin.

Thus, I will recommend to you a very useful practice: repeat the major scale in an ascending and a descending order starting from each note until you can do that without mistakes.

C D E …. C B A G … E F G A… E D C B … etc.

Next, memorize only those notes which are in the spaces: F A C E. Those in the lines will be the immediately upper or lower notes. Practice this reading any score without lending attention to the figures, i.e., read them all at the same tempo.

Chord symbols

The letters may also define chords. If preceded by a small letter, this means that the chord is in a minor key (sometimes we may see a “-“.) If not followed by any other symbol, it will be a major chord.

Tablature

The tablature is perhaps the most recent method for writing guitar or bass scores, as well as the simplest. It provides in detail, through several lines representing the strings, the fret, with an assigned number where we should play each. This is a practical method but a limited one in the amount of musical information it allows to transmit.

In order to have a clear picture of notes and fingering, we may combine all 3 methods:

In the following chapters, we shall be adding notation symbols as soon as we learn of their origin.

FUNDAMENTAL FREQUENCY, HARMONICS AND TIMBRE

When we listen to the same note, e.g., an A at 440 Hz, played by different instruments (piano, guitar or trumpet), our ear may easily differentiate what instrument is playing it. The frequency is the same (440 Hz) and, therefore, also the octave.

Which is the difference among these sounds?

Beyond differences in dynamics (attack, sustained sound and release) what allows us to clearly distinguish one instrument from another is the timbre. All natural sounds (i.e., those not generated by a simple synthesizer or a fingerboard) are made up of various frequencies sounding at the same time. The frequency with the greatest volume is the one we identify as the fundamental (F0), in this case, A at 440 Hz. The rest of frequencies sounding simultaneously with the fundamental are called harmonics. As mentioned before, harmonics will generally sound at a smaller volume than that of the fundamental, and always in the same order. This ordering of harmonics is what is known as the harmonic series.

The fundamental and its harmonics (intervals): F0, F0, 5, F0, 3, 5, b7, F0, 2, 3, #4, 5, b6, 7, b7, F0, etc.

The same ordering from A: A, A, E, A, C#, E, G, A, B, C#, D#, E, F, G#, G, A, etc.

The different volume relationships between these harmonics, in respect to F0, form what is called timbre, which is the set of characteristics allowing us to differentiate one instrument from another.

MAJOR SCALE

Structure

A musical scale is an orderly succession of sounds to arrive from a given note (the tonic) to its upper octave. In western music, this distance is divided into 12 semitones forming a chromatic scale. The different ways of grouping these 12 sounds into semitones and tones (2 semitones) give way to the different known scales.

The major scale divides this distance into 5 tones and 2 semitones, grouped in 2 identical structures of 4 notes, which we shall call tetrachords, and which are separated from each other by a tone. This scale is characterized by a distance of a semitone between the third and fourth notes, and between the seventh and eighth, or tonic. In the case of C major, these semitones are to be found between E and F and between B and C.

We shall call this structure (T-T-ST) a major tetrachord.

There are different types of “TETRACHORDS”: major, minor, Lydian, etc., and their different combinations give origin to diverse scales. We shall later on see in greater detail these tetrachords. Therefore, we shall say that: a major scale is formed by 2 major tetrachords separated from each other by a tone, beginning with a given note which we shall call tonic and which lends its name to the scale, in this case, C.

Each one of the notes of this scale is known as a degree and assigned a Roman numeral in accordance with its placement within this scale.

At the same time, each degree of the scale is named after the tension relationship which it generates with the tonic.

I (first degree): tonic

II (second degree): supertonic

III (third degree): mediant

IV (fourth degree): subdominant

V (fifth degree): dominant

VI (sixth degree): submediant

VII (seventh degree): sensitive (for major scales) or subtonic (for minor scales).

Definitions

We will summarize the definitions in order to be clear in the future what we are talking about.

Scale: orderly succession of notes in order to arrive from a given note (tonic) to its upper octave.

Tonic: name given to the first degree of a scale, on which tensions generated by the rest of the notes lie.

Fundamental (F0 or f): main note of a chord upon which the latter is assembled. This sound is distinguished as being the main tone of a harmonic set.

Key: a group of notes hierarchically ordered in reference to the tonic.

Degrees: each one of the notes in a scale, written with Roman numerals.

Diatonic notes: the notes belonging to a same scale.

Conjoint degrees: degrees immediately before or after a note on the scale.

Tetrachord: a group of 4 notes on a scale, ordered by conjoint degrees.

We should emphasize that on many occasions the concepts tonic and fundamental appear as synonyms. In reality, the proper use of tonic is to refer to the first degree of the scale, and of fundamental when speaking of the main note of a chord. The fundamental will only be the same as the tonic in a chord of I degree.

Alterations in major scales

If we begin by assembling a major scale from another tonic, e.g., D, we shall have to repeat the same structural distances as in the former case.

We can see in each tetrachord that going from the second to the third note, we must rise the latter by a semitone in order to respect established distances (E – F# = 1 tone, and B – C# = 1 tone). There now appear 2 “altered” (#) notes in the scale. We shall say that the scale of D major has 2 alterations: F# and C#. The same will happen with each other major scale, since we will have to “alter” one or more notes in order to build a relationship of distances defining a major scale.

If we repeat the structure from F, we shall see the following:

In this case, on reaching interval A – B, we must lower B a semitone to repeat the structure T-T-ST. Now, “flat” notes (b) appear. It is important to clear up that, excepting a few occasions, a scale may not include 2 notes with the same name. Thus, in the anterior example we have written Bb, and not A#, since the previous note is an A. We can, therefore, see that repetition of the structure of the major scale from different tonics is what originates the appearance of altered notes in the different keys.

Let us look at more examples:

E major scale

Bb major scale

Try assembling other major scales starting from different tonics (Eb, A, G, etc.)

Key signature

In a score, alterations of key are set near the clef in order not to have to write them every time the altered notes appear. This we will call the “clef armor”. It will also tell us which the key of each work is by only looking at the alterations near the clef. In the next example, there appear near the clef F# and C#. This indicates that all F and C notes appearing in the work will be F# and C#, respectively, and that this work will be in the key of D major.

The “sharp” (#) signs will be written near the clef in an ascending order of fifths, the “flat” (b) signs in the reversed order, i.e., descending order of fifths or ascending order of fourths.

This is logical: no major scale may have an alteration without having the preceding ones in this order. For example, if a scale carries a G# it will also have F# and C# (A major scale), or if it shows a Db, it will also have Bb, Eb and Ab (Ab major scale).

It is very important that you memorize the order in which the clef alterations are placed because starting from this we shall establish 2 memorizing rules which will help you to know every alteration of all major scales. These rules are:

# “The tonic is the note following the last clef alteration in the scale”

Example 1: the last clef alteration is C#, the note following C# is D, and the key is D major.

Example 2: the last clef alteration is D#, the note following D# is E, and the key is E major.

b “ The tonic is the penultimate clef b””

Example 1: the penultimate clef alteration is Bb, and the key is Bb major.

Example 2: the penultimate clef alteration is Eb, and the key is Eb major.

Let us try this out in every possible key.

Finally, we will say that:

Major scales whose tonic is a natural note (neither “sharp” nor “flat”) carry # alterations, with the exceptions of C major, with none, and F major, which has a Bb.

Major scales whose tonic is a “flat” note carry b alterations.

Scales whose tonic is “sharp” are little used; instead, an enharmonic equivalent is applied, G# = Ab, C# = Db, etc.

The least alterations in a key, the most common its use is.

With time, you will learn by heart the alterations of each scale, but it is important to know their origin.

Another tool of great usefulness when finding to know about scale alterations is the CYCLE OF FIFTHS.

Natural note

There are 2 ways of indicating that a note is to be altered (b or #):

Clef alteration: as we have seen, in the clef armor the note will be altered throughout the score.

Accidental alteration: if the alteration is not given by the clef, it will be put to the left of the note that is to be altered, centering the symbol on the place corresponding to the note (space or line). This alteration will affect the said note for the duration of the bar in which it is written, without need to repeat it again whenever the same note should appear.

In case this note must appear without alteration, the symbol “natural note” () will be used before it, and this symbol will affect the whole bar in which it may be found. If this note should have to appear altered again in the same bar, the alteration will be added once more, even though it can appear in the clef.

INTERVALS

An interval is the distance in tones and semitones between 2 notes that may sound simultaneously (harmonic intervals) or successively (melodic intervals).

Recognizing intervals is fundamental in learning any musical theory, since assemblage of scales, chords, arrangements or musical analysis, in general, is based on this relationship of distances.

Ascending intervals

The first step is very simple and consists of classifying intervals by degrees, and representing them by the corresponding number.

Following the order of the major scale, in the first case, E is the third note beginning from C, in the second G is the fifth, and, in the third, A is the second starting from G. In the scale of C major, the intervals of each note in reference to the tonic would be:

Intervals are classified in 2 groups: tonal and modal. At the same time, and taking into account the distance in tones and semitones existing between 2 notes of an interval, they may be divided into: perfect, major or minor, and augmented or diminished.

The tonal intervals are: unison, fourth, fifth and octave. They may be perfect, augmented or diminished. The perfect are named using only the number representing them, the diminished adding b before the number and the augmented adding # before the number.

The diminished interval is a semitone below the perfect; the augmented a semitone above the perfect.

The modal intervals are: second, third, sixth and seventh. They may be major, minor, augmented or diminished. The major are named with the number representing them, the minor adding b before the number, the diminished adding bb  before  the number (infrequent), and the augmented adding # before the number (very infrequent).

The minor is a semitone below the major.

The diminished is a semitone below the minor.

The augmented is a semitone above the major.

The last two are used very rarely.

Some examples

In the major scale, the intervals between the tonic and the rest of the notes are major or perfect, and none is minor, augmented or diminished.

Enharmonic intervals

The enharmonic intervals are those showing the same distance between their notes and, therefore, the same sound, but a different name due to their being formed by enharmonic notes. Further on, we shall see when these cases may appear and why.

In order to correctly classify an interval, we shall first write the number corresponding to the degree it represents, and then we shall define if it is perfect, major, minor, augmented or diminished according to the amount of tones and semitones separating both notes.

Compound intervals

These intervals are those surpassing the distance of an octave and are named adding 7 to the same interval when lying within the same octave.

Descending intervals

Descending intervals follow the same rules of the ascending insofar as degrees and distances are concerned, but counting downwards.

Interval inversion

Interval inversion consists of changing the octave of the note of reference and taking as reference the other. Having learned about ascending intervals, we may employ a rule for calculating their inversions:

“The sum of intervals will always be equal to 9 and the quality will be inversed: the major will be minor and the augmented will be diminished, and vice-versa. The perfect will remain perfect.”

CYCLE OF FIFTHS

The cycle, or circle, of fifths is a geometric representation of the 12 notes of the chromatic scale ordered by ascending fifths, clockwise, and descending fifths (or ascending fourths), counter clockwise. This geometric representation shows us the tight relationship maintained between tones and keys, and allows us to receive, in graphic form, much information on musical theory which will be of great usefulness as a tool for understanding harmony, musical composition, arrangements, etc.

SCALE ALTERATIONS AND KEY SIGNATURE

“Sharp” symbols (#): beginning from the note F, clockwise, we shall encounter the order in which the “sharp” symbols are written on the key signature of different scales: F – C – G – D – A – E – B.

“Flat” symbols (b): starting from the note Bb, counter clockwise, we shall find the order in which the “flat” symbols are written on the key signature of different scales, which is reverse to the previous: Bb – Eb – Ab – Db – Gb – Cb (B) – Fb (E).

Alterations of each scale: beginning from note C, in both directions, we shall find alterations belonging to each key of the major scale. Towards the right are the #’s and towards the left the b‘s. In the center is C, carrying no alterations, G follows with a “sharp” symbol, D is next with 2 “sharp” symbols, etc. In the opposite direction, F will carry one “flat” symbol, and Bb will be next with two b, etc.

CHAPTER II: MAJOR KEY

In our culture, major keys are the basis of practically all music. From it spring other keys and other concepts that will be more or less moving away from its center. We have already seen the starting point, i.e., the major scale, and we shall now see the different kinds of chords being formed from it (diatonic chords) and others (non-diatonic) which will incorporate some variants in their structure without entirely leaving the major keys.

These elements, and our understanding of them, will be our basic tools, so much for analyzing music as for composing it.

TRIAD CHORDS

A chord is a set of three (triad) or more notes sounding simultaneously or successively and constituting a harmonic unit.

The most common triad chords are formed by superposition of 2 thirds. Example: C major = C, E, G, where E is the third note of C, and G the third note of E. Consequently, if reckoned from the fundamental (C), E is its third, and G its fifth.

Triad chord = tonic + third + fifth.

One may see that due to its being a superposition of thirds, if the fundamental falls on a line of the pentagram, the third and the fifth will also do so, and the same will happen in a space. These chords carry as a main name that of the fundamental and are classified as major, minor, augmented or diminished, in accordance with the intervals of the said fundamental with the other notes forming it (3 and 5).

Thus, a chord will be major or minor if its third is major or minor, respectively, and maintaining the perfect fifth. The chord will be augmented if the fifth is augmented and the third major and it will be diminished if the fifth is diminished and the third minor.

Major        T        3        5

Minor        T        b3        5

Augmented        T        3        #5

Diminished        T        b3        b5

The nomenclature used in each case will be the following:

Diatonic chords

We shall call those chords diatonic which are formed by notes of the same scale (diatonic notes) taking as fundamental each of the notes (degrees) of the said scale.

In this example, we observe that the notes forming the different chords, fundamentals, thirds and fifths, are notes from the scale of C major, i.e., they do not appear as # or as b. These will be the diatonic chords in the key of C major and will be classified by degrees, which will be indicated by Roman numerals followed by the type of chord: I, IIm, IIIm, IV, etc. In every major key, diatonic chords will always follow this pattern, since, as we saw before, distances between notes of a same scale are always the same.

I  IIm  IIIm  IV  V  VIm  VIIº

Hence, we have 3 kinds of chords in diatonic triads: major, minor and diminished.

Let us see an example in E major:

From this information, it will become easy to recognize the key to which a chord progression belongs and to determine the scale that we may use to compose a melody or to improvise. This we shall call harmonic analysis. It will also be a very useful tool when taking our first steps in composing.

In example (1), there appears a very common progression in all types of songs. If we take into account, in reference to what we have previously seen, that F and G are conjoint degree and major chords, the only possibility is that they be IV and V, respectively, and, therefore, C will be the tonic, F the IV degree of C and G the V. In example (2) there are 2 conjoint degree chords, one major and the other minor (G and Am). Here, we find 2 possibilities:

1.- I and II (key of G major); in this case, D must be major because it is the V degree of G. right.

2.- V and VI (key of C major); in this case, D would have to be minor because it is the II degree, which it is not: wrong.

Surely, you will find other progressions of chords that momentarily cannot be analyzed with this information.

This is a first approach to harmonic analysis that we will be extending in the future as we study other types of chords and keys.

Note layouts

Note layout in a chord may vary in order, or even some of the notes be repeated. This is very common in string instruments, such as the guitar, where the distribution of notes on the different strings does not always allow our playing the chord in the order of thirds.

This does not alter the classification of a chord or its function, as long as the fundamental remain the lowest note (fundamental state), but it will be important to keep in mind what we shall call voice leading, as we shall see further on.

Chord inversion

When a specific layout forces the fundamental out from being the lowest note of the chord, we shall speak of an inversion. We shall then say that a chord is an inversion, or is inverted, when its lowest note is not the fundamental. In triad chords, there are 2 possible inversions:

The lowest note is the third (first inversion)

The lowest note is the fifth (second inversion)

Inversions are named with the same symbol as the original chord plus the note in the bass being preceded by a bar (/).

SEVENTH CHORDS

Continuing with the same progression of thirds that we used in forming triad chords, we will reach the point where we can form seventh chords, in which the new note will be the third of the fifth, i.e., the seventh of the fundamental. We are now meeting with a greater diversity of chords, since a seventh major (7) or minor (b7) may be added to each of the four options for the triad chords.

We shall symbolise them in the following manner:

When the seventh is minor, we shall only add a 7 to the triad chord symbol.

C7: C = major triad, 7 = minor seventh. C-E-G-Bb

Cm7: Cm = minor triad, 7 = minor seventh. Cm-Eb-G-Bb

C+7: C+ = augmented triad, 7 = minor seventh. C-E-G#-Bb

When the seventh is major, we shall add maj7.

Cmaj7: C = major triad, maj7 = major seventh. C-E-G-B

Cm maj7: Cm = minor triad, maj7 = major seventh. C-Eb-G-B

Exceptions

Cm7b5: The diminished triad with the minor seventh will be called minor 7 flat 5 (formerly called semi-diminished (Ø). C-Eb-Gb-Bb

C°7: The diminished triad with the diminished seventh will be called diminished 7. C-Eb-Gb-Bbb

Diatonic seventh chords

Repeating the concept of triads, diatonic chords in seventh chords will be the following:

Due to having 2 variants of seventh, we shall find 4 kinds of chords: major with major seventh (maj7), minor with minor seventh (m7), major with minor seventh (7) and minor with diminished fifth and minor seventh (m7b5), or semi-diminished.

Tonal function of chords

According to the function generated by each diatonic chord in respect to tonal center, they will be classified in 3 tonal groups: tonic, or resting, subdominant, or half tension, and dominant, or tension. This classification is related to the appearance of degrees IV and VII (tritone) within the notes making up a chord.

Tonic (T): these are stable or resting chords. They do not have the IV degree in their structure.

Imaj7    IIIm7    VIm7

Subdominant (SD): these have the IV degree in the chord.

IIm7    IVmaj7

Dominant (D): these have the IV and the VII degrees in the chord.

V7    VIIm7b5

In the triad chords, the tonal function of the chord of each degree will be the same as that in the seventh chords.

Tonic (T):    I    IIIm    VIm

Subdominant (SD):   IIm    IV

Dominant (D):    V    VIIº

In every musical composition, beyond the style it may belong to, the handling of tensions along the work will create different climaxes that will play with the attention of the listener, as in any type of “story”.

Generally, tension will progressively grow until reaching the climax, where the resolution will be abruptly produced.

Let us see some simple examples:

Depending on its tonal function, each type of chord will tend to move towards another, in accordance with how one would like to increase or resolve the tension of the story.

T: chords with a tonic function do not create the need for movement because they are resting, but, instead, to break the monotony of stability a T chord may move towards an SD or a D.

SD: it will try to go towards T to resolve the half tension, or towards D to increase it.

D: it will try to go towards T to resolve its maximum tension.

On rare occasions, for example, in Blues, one may see a D chord move towards an SD, that is, in order to decrease tension gradually.

Durations of resting times and of transitions towards tension, or towards its resolution, are subjective elements depending on each author’s manner of composing, and their duration will be related to the duration of each work or movement. Practicing such climaxes with your instrument is essential to thoroughly understand them, thus lending more power to expressivity and creativity when composing.

We shall summarize points seen so far in the next Table:

Inversions

In the same manner as triad chords, seventh chords may be inverted. In this case, there will be an additional inversion which will carry the 7 in the bass. It will be called the third inversion. The way to symbolize seventh inversions will be the same as in triad inversions.

Chord m7b5

The VII degree chord (VIIm7b5) is rarely used as a dominant chord in a progression. Generally, its function is that of the SD (II degree) in a minor key. We will go into it later on.

Chords with a sixth

In these chords, the 6 replaces the 7. In general, this option is chosen when the main melody is resolved in the fundamental of the chord. To prevent the dissonance generated by the half tone interval between the 7 of the major 7 chord and the fundamental of the melody, one will have to resort to the major 6 to form the seventh chord.

In other cases, one will look for the sound of the 6, especially, in a minor chord, because this is the characteristic sound of the mode one wants to stress (Dorian). This will be seen later in greater detail. It is not very common to find chords of b6 since the semitone interval with the 5 creates another dissonance.

Sus chords

In a chord, whenever the third is replaced by another note, the suffix “sus” is added. The most common example is when the 3 is replaced by the 4, forming a sus4 chord, or 7sus4. This chord works as a dominant, although generating less tension than the classic dominant, due to its having broken the tritone. Its sound is very characteristic, creating an atmosphere of expectation. In a lesser degree, the sus2 may be seen, working, in general, as a tonic.

The tritone and its resolution

The interval of #4 formed between the 4th and the 7th note is called the tritone in a major scale. Its name is due to the distance of 3 tones between both notes, whether in one or in the other direction: 4 - 7 or 7 - 4. In the key of C it is either F-B or B-F. This interval has the feature of provoking great tension, since the said notes lie half a tone away from the two main notes of the scale (the tonic and the 3). The passing of this musical tension to the resting state is called resolution.

The resolution of the tritone will then be by means of a semitone descending from the 4 to the 3, and ascending from the 7 to the tonic, thus resolving the tension and creating a feeling of rest or stability.

Tensions generated by the tritone will be a key element to understand future topics.

The dominant chord

The tritone will be the characteristic interval of a dominant chord (V7 or VIIm7b 5), V7 being the most frequently used. In this case, where the tritone resolves from the dominant chord of V degree to the tonic, we shall speak of the dominant resolving by a fourth leap (G-C), which is the distance between the fundamentals of the chords.

We can see that the notes of the tritone correspond to the 3 and the b7 of the dominant chord: the 3 will resolve to the tonic and the b7 to the third. In harmonic analysis, resolution of a dominant chord by a fourth leap will be marked with an arrow going from that dominant chord to the resolution chord.

II-V MOVEMENT

Among progressions of chords increasing in tension until being resolved in the tonic, the most usual ones are IV - V - I and II - V - I, both following the criterion SD - D - T. The former is commonly seen in styles such as Pop and Rock, while the latter is more present in melodic styles, such as Bolero, Jazz, Bossa Nova, etc.)

Reviewing what we have already seen, we ascertain that both SD chords carry just one note from the tritone, the 4, while the dominant has both. This is what triggers an increment in tension (I - II - V) and its abrupt resolution (V - I). In harmonic analysis, the II - V movement is indicated by a bracket going from the II to the V.

It is worth mentioning that this II - V movement is by fourth leaps, same as in the V - I movement.

DIATONIC TENSIONS

Tensions of chords: 9, 11 and 13, also called chord superstructure, do not make up a fundamental part of these chords, i.e., they do not modify their tonal function; they are added to provide an embellishment or to create a second melodic line moving below the main melody. Its employment is typical of certain musical styles, such as Jazz or Bossa Nova.

We shall see here a rule which is basic to know which of these tensions may be added to each of the diatonic chords, which we shall call available tensions, and which are not, or not available or not to be used chords.

Reviewing what we have already seen, we know that a triad chord is formed by superposition of two thirds: C major = C, E, G, where E is the third of C, and G, the third of E. Therefore, if seen from the fundamental (C), E is its third and G its fifth note. If we add another third (B), we will arrive at a seventh chord: C, E, G, B (Cmaj7).

Using this same criterion, when adding further thirds, the 9, the 11 and the 13 appear (which are the 2nd, the 4th and the 6th + an octave). These 3 notes are known as superstructure of the chord and classified either as available or as not available, or not to be used notes.

A tension is available when it forms an interval of 9 with one of the notes of the chord and not available when it forms one of b9.

In the former case, Cmaj7 in the key of C major, the F is a not available tension for the first degree chord, since it is the b9 of E; F is a semitone above E (b2) and, when rising it an octave, it becomes (b9).

D and A will be the available tensions, since D is the 9 of C and A the 9 of G (fundamental and fifth notes of the chord, respectively).

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Applying this formula, we will build a Table for each of the diatonic chords and their available tensions:

Notes in parentheses are the not available tensions.

Some rules to aid memory:

All minors take 11

All majors take 9 and 13

The IV is the only one with #11

The VII is the only one with b13

Exceptions

We can see that the second degree (Dm7) does not admit 13 (B) in spite of not being the b9 of A. This is because the tension would form a tritone with the 3rd of the chord (F - B), changing its tonal function from subdominant to dominant.

This rule on tensions or superstructure of the chord will not be applicable to dominant chords, especially in the minor mode, or to modal chords that we shall see further on, since many of the not available tensions are characteristic of these particular chords.

As we have seen before, when a note in a seventh chord is replaced by notes from the superstructure, it will not be considered a tension and, therefore, it is named an octave below: 6, sus4, sus2, etc.

Use of tensions

Applying these criteria, we may add any possible tension to any chord. Its use will be purely esthetic, or of style, as when a painter chooses his colors. As mentioned before, this will create a second melodic line below the main one. In general, the tension will be voice-leading (that is, the highest note of the chord).

A couple of examples on II V I

Here, the leading voice descends by conjoint degrees: F in Dm7, E in G7 13 and D in Cmaj7 9.

In this case, the leading voice is a pedal note (E); 9 in Dm7 9, 13 in G7 13 and 3 in Cmaj7. The name pedal note is given to a prolonged sound over which different chords progress.

SCALE FORMULAS

Once we have understood and remembered this, we will exploit it to build scalar formulas, in which every note will be denoted by the chord degree or tension it represents; if it should be a not available tension, it will be named 1 octave below, setting before it the letter “d” (a diatonic note, not part of the seventh or of an available tension). Further on, we shall see the usefulness of the scalar formulas in order to understand the SCALE - CHORD RELATIONSHIP.

Major scale: (f or 1), 9, 3, d4, 5, 13, 7

MAJOR PENTATONIC SCALE

In spite of the pentatonic scale having a simple structure and being much in use today, we have waited until this moment to speak about it so that we may better understand some key points, now that we are in control of several concepts.

As we saw before, the tritone (IV and VII degrees of the major scale) generates a strong tension in the scale due to each of its notes being a semitone away from the 3 and the tonic of the scale. If we eliminate those 2 notes from the major scale, we will obtain a scale with a “softer” sonority since, due to its lacking semitone intervals, tensions produced are of a lesser nature. The resulting scale is the major pentatonic scale.

MAJOR SCALE - TRITONE = MAJOR PENTATONIC SCALE

We have also seen that tensions of 9 and 13 (2nd and 6th) are tensions common to major diatonic chords (I, IV and V). If we eliminate these 2 tensions from the major pentatonic scale, we shall reach the chord triad.

MAJOR PENTATONIC SCALE – 9 AND 13 = MAJOR TRIAD

Inversely, we shall see that starting from the triad, which is the basis of major sound, and adding each time stronger tensions, we shall arrive first to the major pentatonic scale, and then to the major scale.

MAJOR TRIAD + 9 AND 13 = MAJOR PENTATONIC SCALE

MAJOR PENTATONIC SCALE + TRITONE = MAJOR SCALE

This is a concept applicable to various structures, which will be of great usefulness when improvising or composing in order to play with chromatic changes within the same scale, according to how we may “administer” the appearance of tensions.

As a reference, we may say that the major scale corresponds to the white keys of the piano (C major beginning from C) and the pentatonic to the black keys (major pentatonic of C# beginning from C#). The characteristic sound of this scale is present in many musical styles from the 5 continents, and we shall quickly identify it as Chinese music, Country, Jazz, etc.

NON-DIATONIC CHORDS

Until now, we have spoken of progressions of diatonic chords, that is, chords made up of only the seven notes of the same scale. To increase the possibilities in the handling of tensions, we may incorporate chords including some non-diatonic notes, without changing the key by including them (modulation). The use of these chords will also allow us to incorporate these non-diatonic notes to the melodies, thereby enriching their color.

In many cases, these non-diatonic chords are used to prepare the listener for the arrival of a new chord, while playing with the tensions that lead to its resolution in the newcomer. These non-diatonic chords, due to their having one or more notes alien to the tonality, will take a scale particular to each case we shall be seeing and analyzing along this book. For the moment, we will limit ourselves to classifying them as: : Secondary dominant, Dominant by extension, Chain of dominants, Substitute dominant, Secondary second and Diminished.

Secondary dominants

Definition: these are dominant chords resolved by a leap of a perfect 4th in a diatonic chord, whose tonic is also a diatonic note.

The tension generated by the tritone of these dominants, and their marked instability, herald the arrival of a diatonic chord on which they will resolve, thus creating a brief sensation of a pitch change, but which, by its brief duration, is not quite perceived as a modulation. For this reason, it may also be considered a temporal modulation.

In harmonic analysis of a progression, these chords will be marked with the symbol V7 (which defines them as a fifth degree dominant) followed by a slash and the indication of the diatonic degree which they will resolve will precede them.

Thus, there will be 5 secondary dominants:

V7/II  -  V7/III  -  V7/IV  -  V7/V  -  V7/VI

The following will not be secondary dominant:

The V7 of I since it is a diatonic chord, i.e., the natural dominant of the key.

The V7 of VII since its fundamental is not diatonic.

Resolution of a secondary dominant (by a leap of a fourth) is also marked by a bent arrow which goes from the said dominant to the chord on which it resolves.

Let us see the following cadence fragments in the key of C:

Extended dominant and chain of dominants

Whenever a second dominant resolves on another secondary dominant, it is called an extended dominants.

When such an extension includes more than 2 chords, it is called chain of dominants or chain of secondary dominants. This chain generates an atonal passage, that is, a momentary suspension and loss of the tonal center due to linkage of the tritones which will not resolve on diatonic chords. For this reason, on many occasions, they are used as tools for modulation (change of key). In such cases, it is not necessary to mark on each dominant chord its tonal function.

Substitute dominants

Definition: these are dominant chords since they have the same tritone and can be substituted by each other. Their tonics are b5 away, and their resolution, when functioning as substitutes, is by a descending semitone.

As we previously saw, a tritone is an interval three tones away in either direction or inverted (F - B or B - F). Therefore, it may function as such in 2 different keys, and resolve in different directions.

In this example, we can see the tritone F - B in key of C and the same tritone inverted, with an enharmonic note due to its belonging to the key of Db.

In the first case, F resolves by a descending semitone and B by an ascending one (E - C). In the second case, both resolutions are inverted: F ascending to Gb and Cb (B) descending to Bb. We can see that the same tritone may be present in 2 dominant chords: G7 and Db7 (the V degree in each one of these keys) since both notes are the 3 and the b7, or b7 and 3, of these 2 dominant chords.

For this reason, we may substitute a dominant chord by another including the same tritone, since the tension characterizing them is the same. The tonics of these dominants will also be 3 tones away but be symbolized as b5 instead of 4# (G7 – Db7).

This substitute dominant will resolve by a descending semitone and be marked by an arrow, the same as the dominants for the leap of fourths, but with a dotted line. We must also explain which dominant is being substituted with the label sub V7/V (substitute of the dominant of the V degree).

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Tensions generated in regard to the original dominant will be b9 and #11.

Secondary seconds

Secondary dominants, or their substitutes, may be preceded by a chord of minor II degree in respect to the chord they will resolve generating a typical movement II - V which we have already seen. These will be marked with a bracket without need of adding another kind of indication. In this way, a gradual increment of tension will be generated until its resolution is reached.

In the case of dominant substitutes, the secondary second may be working as a II for the chord to be resolved, or in a relationship of a fourth with the substituted dominant, generating 4 possibilities.

If the relationship between the II and the V is not of a leap of a fourth, the bracket will be included in the dotted line.

Whenever the resolution is in a minor chord, the secondary second will also be an m7b5 chord.  We shall see an explanation for this when we visit the minor keys.

Double tonal function

In some cases, the secondary second may coincide with a diatonic chord. We will say then that it has a double tonal function or double harmonic analysis. The corresponding bracket and diatonic degree must be provided.

In most cases, the sonority of these chords within the progression defines them more as a secondary second than as another diatonic chord.

In the following Table, we shall summarize non-diatonic chords in C major key seen so far, building different combinations between secondary seconds: m7 or m7b5 for those for minor chords, and both possibilities for the substitutes.

Diminished seventh chords

The diminished seventh chord (T, b3, b5, bb7) is a chord stemming from the VII degree of the HARMONIC MINOR SCALE, which shows several peculiarities:

- Its structure is a succession of minor thirds, which makes it a symmetric chord and, therefore, without inversions, since each inversion will form a new diminished chord with the same note, but also with another fundamental.

- We may also look upon it as a chord with an indeterminate fundamental, since each of its notes could be the fundamental.

- Based on this, we may say that there will only be 3 diminished chords: Cº7, C#º7 and Dº7, since the rest will be equivalent to some of them.

- It includes 2 tritones: T - b5 and b3 - bb7, a reason for its being very unstable and creating 4 possibilities for its resolution, since, as we saw before, a tritone has 2 possible resolutions.

- Therefore, it works in substitution of dominant chords (those containing these tritones) and resolving by ascending semitones.

In this case, Eº7 substitutes for C7, which is the V7/II because it includes the same tritone. Its notes (E, G, Bb and Db) are 3, 5, b7 and b9 of the chord of C7b9 without the fundamental (C). Tension of b9 is typical for a dominant resolving in a minor chord, as we shall see further on.

We may summarize the use of these chords in 3 cases:

By ascending semitone: as we have already seen, they work as dominants and are usually chromatically interspersed between 2 chords in an ascending manner. Most frequently used are: #Iº7 (previous example), #IIº7 and #Vº7

By descending semitone: these do not function as dominants, and some of its voices may descend chromatically.) They are conducted chromatically in a descending way towards the next chord. The most frequently used one is bIIIº7. They may also be chromatically interspersed between 2 chords.

Auxiliary: these resolve a chord in the same tonic, generally, I or V. Their function is to retard resolution.

Due to some of these features, they are also called passage diminished. The ambiguous and particular sonority of these chords makes them extremely attractive for creating moments of suspension, modulation, chromatic movements between tonics, etc.

SUMMARY OF HARMONIC ANALYSIS

We shall now summarize the symbols seen thus far in harmonic analysis:

IIm7: the key degree and its corresponding seventh chord

T, SD o D: its tonal function

V7/X: secondary dominant, X= diatonic chord

Resolution of a dominant by a leap of a fourth 

Resolution of a dominant by a descending semitone (substitute)

Movement  II – V

Movement  II – V by a descending semitone

Sub V7/X: substitute dominant of another dominant chord (X)

The dotted line is used when movement is by a descending semitone and not by leap of a fourth.

In the following chapters, we shall be adding analytical symbols as soon as they are treated. In the same manner, we will mention other non-diatonic chords, such as those of modal interchange.

CHAPTER III: MINOR KEY

The world of minor keys is more complex than that of the major ones, since there are several scales from which to build harmonic cadences. These scales have followed one another through time and different cultures, processes which have defined their characteristic sound and made them easy to distinguish. In modern harmony, we have 3 different scales from which to build harmony, the natural minor, the harmonic minor and the melodic minor.

The main feature of every minor scale will be its minor third which will lead to a new structure of the tetrachord (T-ST-T), which we shall call minor tetrachord, and will be the first tetrachord of the scale. These 3 scales will be defined depending on how the structure of the second tetrachord varies (changing the 6th to the 7th). Taking as a base the major scale, we shall analyze each one of these scales. This is the reason for our needing a very sound grasp of concepts seen when studying the major keys: structure, intervals of that scale, diatonic chords, etc., before going into the same points regarding minor scales.

NATURAL MINOR SCALE

The natural minor scale, also called Aeolian mode, shares the same 7 notes of the major scale, but taking as the tonic the sixth degree, which is why it is also called the relative minor scale. Thus, the scale of natural minor A will have the same notes as the scale of C major, since A is the sixth degree of the C major scale. The note A will now be the tonic of the scale and, therefore, its degree I, B, will be the II, C the bIII (due to its being the minor third of A), etc.

In an inverse direction, every minor scale will have its relative major:

Natural Am = relative minor of C major.

C major = relative major of natural Am

If we look at the scale of natural C minor, its notes will agree with the scale of Eb major, due to C being the sixth degree of that scale.

When comparing the scale of C major with that of natural C minor, we shall see that there are 3 different degrees:  bIII, bVI, and bVII, and the key signature will also be the same as that of the relative major.

We shall also add the scale formula, reviewing which: this is the interval of each degree in reference to the tonic, defined using the following criterion: the tonic as T, the notes of the seventh chord in the first octave, the available tensions of the second octave and the not available tensions of the first octave, writing before them the letter “d” (diatonic note).

The seventh degree of the scale no longer has the function of sensitive due to its being 1 tone away from the following octave and, therefore, the tension it generates much less, i.e., it does not form a tritone. This will influence the tonal function of the chords which have it. In accordance with this, the diatonic chords will be the same ones as those of the relative major key, but the number representing the degree of each one will obviously change.

We shall now see the diatonic chords of the triad and the seventh chord, and their tonal functions.

Tonal function of triad chords

Minor tonic (T): they will have bIII but not bVI.

Im        bIII

Minor subdominant (SD): they will have bVI in the chord.

IIº        IVm        bVI        bVII

bVII will also be considered the SD due to its having the IV but not the bVI degree, in analogy to the major mode.

Dominant (D): due to its being the V degree, it is considered a dominant chord, although without the resolving force of the major, since it is a minor chord and, as we have seen, does not form a tritone.

Vm

Tonal function of seventh chords

Minor tonic (T): Im7, bIII maj7

Minor subdominant (SD): IIm7b5, IVm7, bVImaj7, bVII 7

bVII7 is considered a subdominant chord even though it has the structure of a dominant, because it is not the V degree of the tonic.

Dominant (D): Vm7

In the same way as in the Vm7 triad, it is considered the dominant for reminding one of a major mode in the V-I leap although, due to its lacking the tritone, it does not have a clearly resolving effect.

HARMONIC MINOR SCALE

As we have seen, the lack of a sensitive (major VII) in the natural minor scale prevents generating in harmonic cadences clear tensions, as happens with the major mode, therefore progressions of chords are flatter and do not generate sharpness in movements.

Looking for how to resolve this lack, a new minor scale is built rising a semitone the VII degree (bVII to VII) and carrying it to a sensitive degree. Thus, we will arrive at the harmonic minor scale, also called Arabic scale for its characteristic interval of a tone and a half between bVI and VII.

Tonal function of triad chords

Diatonic chords which will change (in parentheses) in reference to the natural minor, will be those including the VII of the scale in  their structure, as the fundamental, third or fifth, in the case of triads, and as the seventh, in seventh chords, while the rest remains the same:

Minor tonic (T): Im, (bIII+)

Minor subdominant (SD): IIº, IVm, bVI

Dominant (D): (V), (VIIº)

Tonal function of seventh chords

Minor tonic (T): (Im maj7), (bIII+ maj7)

Minor subdominant (SD): IIm7b5, IVm7, bVI maj7

Dominant (D): (V7), (VIIº 7)

I degree maintains its tonic function, although, in the case of the seventh chord (Im maj7), the major 7 gives it a particular and somehow unstable sonority.

bIII, due to its including the #5, generates a certain instability, which makes it, according to the context, work as a T or as an SD.

The II, IV and bVI chords do not change and, therefore, their tonal function does not either.

The VII degree is now the dominant chord, due to its having a tritone, and even more so in the case of the seventh chord (VII°7) due to its having 2 tritones.

The V degree is clearly a dominant chord because it now has the sensitive of the scale, and the tritone, in the case of the seventh chord.

Use of b9

In spite of including now a clearly dominant chord of the V degree, resolution of the tritone is not as strong as in the major mode, since the 4th degree of the scale (b7 of the dominant) does not resolve by descending semitones, but by descending tones, because the third of the tonic chord is now minor.

To compensate for this weaker resolution, one usually adds to the dominant chord of minor keys, the tension of b9. Now one has a new tritone, formed by the 5 and the b9. This tritone will resolve by an ascending semitone from the 5 to the  b3 , and by a descending semitone from the b9 to the 5 of the tonic chord. This dominant, with 2 tritones, will be a more unstable chord and generate a strong tension towards the minor chord of the tonic.

In some cases, one may alter the 9 in an upward direction (#9), in spite of this not being a note of the scale. The function of adding this note will be to break the interval of a semitone (Ab- B, in this case), preventing the Arabic sonority. Thus, an artificial scale will be created which will be seen in the next chapter MIXOLYDIAN b⁹ b¹³.

This V7#9 chord will generate a characteristic sonority due to its including the major and the minor third (enharmonic of #9). It is typically used as V degree in minor Blues.

To conclude, we shall say that the dominant chord of the V degree with b9 is considered typical of minor keys and that the chord symbol of a dominant chord with b9 takes into consideration using, both in chords and in scales, the #9.

MELODIC MINOR SCALE

With the intention of looking for a minor scale with the sensitive and also preventing the Arabic sound, that is, to make it resemble western music, the VI degree is raised half a tone preventing the tone and a half interval of the VII. Thus, one reaches the melodic minor scale.

We observe that this is a scale practically like the major scale but with b3, which is what makes it a minor scale. Now, the chords affected by this new change will be those having the VI degree of the scale in their structure, with 3 or 5 as tonic in the case of triads, and 7 as tonic in that of seventh chords, i.e., the I, the II, the IV and the VII chords, and the rest will remain the same

Tonal function of chords

One rarely finds a context with the melodic minor keys: chords stemming from this scale may be found playing a specific role within a certain context which will not necessarily be melodic, as we shall see further on. The triad chords do not usually associate with this minor mode because they happen with other minor modes, or even major, as in the case of IIm, IIm7 and IV.

Tonal function of seventh chords

Minor tonic (T): (Im6), bIII+ maj7

Minor subdominant (SD): (IIm7), (IV7)

Dominant (D): V7

VIm7b5 and VIIm7b5 are not used as a tonal function of the minor mode; as we shall see further on, they have other applications.

Im6 is a more stable chord than Im maj7, making it more frequently used. Here, the 6 will replace the 7 and, therefore, in the scale formula, it appears as a note of the seventh chord and not as a tension.

IV7, called the Blues IV7, is a dominant chord but behaves as a function of the dominant due to its not resolving the leap of a fourth.

V7 is clearly a dominant chord but, in comparison with the harmonic mode, will not have the b9. The only tension which characterizes it is b13 (also available in the harmonic mode) but without a resolving character on the tonic chord since it coincides with the b3 of this chord. Therefore, the V7b13 chord, although typical of the minor mode, does not provide any other tension of a resolving character beyond the tritone.

The melodic minor scale is very much employed in Jazz and other improvising styles derived from this style, whose relative scales are adequate to create melodies or improvise on secondary or altered dominants, minor chords or even m7b5.  It is also a resource to leave the corresponding diatonic context.

PENTATONIC MINOR SCALE

In a manner similar to that of the natural minor scale, or Aeolian, being relative to the major scale, the minor pentatonic scale is relative to the major pentatonic. Thus, the minor pentatonic of A will be formed by the same notes as the major pentatonic of C, but beginning in A.

Similarly to what we have done in the major mode, we may pass from an arpeggio of Am towards the minor pentatonic and then to the minor natural adding tensions. Here, we shall not play with the tritone because, as we have seen, It is not a dominant of I degree.

We shall first include 2 tensions common to minor diatonic chords (IIm, IIIm and VIm degree) which are the b7 and the 11

MINOR TRIAD + b7 AND 11 = MINOR PENTATONIC SCALE

Next, we shall add to the minor pentatonic the 2 tensions of 9 and b13.

MINOR PENTATONIC SCALE + 9 + b13 = MINOR NATURAL SCALE

And the same with all minor relative keys.

BLUES SCALE

The scale typically used in Blues is nothing more than the minor pentatonic scale to which an extra note is added, called the blue note. This Blues note is the b5. It is therefore considered to be within the group of hexatonic scales (six notes). At present, this scale is typical of the styles: Blues, Rock and Roll, Fusion and Jazz.

SUMMARY OF THE MINOR MODE

Let us compare the 4 scales, the degrees differentiating them and their diatonic chords.

In a minor key, the chords employed in progressions may stem from any of the 3 scales, the same as the melodies or the solos we may build.

In the following Table we shall summarize the diatonic chords of the major scale and the 3 minor scales, and we shall label in black those chords used less in minor progressions. This does not leave out that, with the intention of exploring uncommon sonorities, one may utilize any of the chords reviewed.

HARMONIC ANALYSIS OF THE MINOR MODE

The harmonic analysis of the minor mode will follow the same rules of the major mode. Each degree will be identified with its corresponding Roman numeral and the kind of chord it forms, and the dominants will be labeled with an arrow. It must be considered that the second degree will now be m7b5, stemming from the natural, or harmonic, mode.

In the first line of the example, we shall see a movement characteristic of various minor themes, where the tonic descends chromatically to reach the bVImaj7 (this movement may be transferred to the bass, generating third inversions.) In this case, we may interchange various minor scales we have seen, keeping in mind the presence of the major or the minor 7 or 6 of each chord.

CHAPTER IV: SCALES AND MORE SCALES

SCALE-CHORD RELATIONSHIP

We have seen the structure of the chord (triad or seventh) and the superstructure (tensions 9, 11 and 13). If we place these seven notes by conjoint degrees, we shall arrive to a scale.

The type of scale we obtain will depend on the type of chord (kind) and the tensions available for it, in accordance with the corresponding diatonic degree. 

Classification of each degree of the scale in respect to that chord (scale formula) will provide a spectrum of tensions characteristic of the mode corresponding to each case. This we shall call the scale-chord relationship.                                  

In the example, we see the chord Cmaj7 as a function of the tonic (I degree), and the corresponding scale -in this case, major or Ionian mode scale- will be composed of 4 notes of the seventh arpeggio: T, 3, 5 and 7, the available tensions 9 and 13, and the not-available tension d4. The available notes may be included in the chord (Cmaj7 9, C6, etc.) or in the resulting melody of the composition or improvisation. The not available notes, in this case, d4, will be in the corresponding scale but sounding as a note of passage. We shall see the application of this point in greater detail in the section MELODIC ANALYSIS.

In this way, we shall integrate harmony and melody within the same harmonic concept, which will define the corresponding mode to each chord.

It is important to clarify that the scale-chord relationship is an independent analysis established for each chord and its corresponding scale at that moment, without relating that scale to the remaining chords making up the progression. It is, therefore, also called Momentary Scale. The resulting scale may be diatonic at the key of the theme (modal scales), if the chord is diatonic, or non-diatonic if the corresponding chord is not, as we have seen in the section NON-DIATONIC CHORDS.

MODAL SCALES

Modal scales have always created doubts about what they are not, and how to achieve the aimed at sonority for each. In order to understand what a modal scale is, the first point that may be explained to us is that each one of them -IONIAN (major), DORIAN, PHRYGIAN, MIXOLYDIAN, AEOLIAN (natural minor) and LOCRIAN- stems from playing the major scale beginning from each one of the degrees, respectively. This we shall call relative modal scales.

The Ionian scale is the major scale starting from the first degree of that scale (C), the Dorian from the second (D), the Phrygian from the third (D), etc. In other words, these are scales “relative” to a major scale (C major, in this case) but with another tonic (D, E, F, etc.). The sixth degree, or Aeolian mode, is the minor natural scale, as we have already seen in the previous chapter. Although this is right, and the simplest way to understand how scales are derived, it poses us the first doubts:

Am I always playing the same scale?

Do I always have to start in the same note? (tonic of each mode)

If I begin with another note, am I playing in another mode?

A plainer way to understand the modal concept is to look at each mode from the same tonic (C). This we shall call parallel modal scales. We shall also go into the formula for each scale with greater detail.

By keeping the tonic in C, we shall see how some of the notes of each mode are altered, since in the Dorian mode C will be the II degree of the scale of Bb, in the Phrygian the III of Ab, in the Lydian the IV of G, etc. This means that each modal scale of C will be relative to different major scales.

In the formula for each scale, we shall distinguish which degrees are changing in each mode.

We have already seen how to each note of the major scale corresponds a specific chord (diatonic chords); now, we see that to each also corresponds a modal scale. Since some of these chords may coincide in their kind, the relationship scale to chord will define more precisely the corresponding mode of each chord. Let us now group chords and scales according to their kind: major or minor.

Major chords and major modes

Diatonic Major chords: I, IV y V degree.

In C major key:

C,F y G in triads.

Cmaj7, Fmaj7 y G7 in sevenths chords.

Major modes: Ionian, Lydian, Mixolydian (I, IV and V degree), respectively.

Minor chords and minor modes

Diatonic Minor chords: (II, III y VI degree) The  VII will be considered an exceptional minor mode since it includes the diminished m7b5

In C major key:

Dm, Em y Am in triads y Bº

Dm7, Em7 y Am7 in sevenths chords y Bm7b5

Minor Modes: Dorian, Phrygian y Aeolian (II, III y VI degree) y Locrian (VII degree) respectively.

We can see the former, relatively and in parallel, in the scale-chord relationship.

Relative modal chords and scales

Parallel modal chords and scales

In the last example, we can see what the momentary scale for each kind of chord may be:

For a Cmaj7 chord, we may use 2 scales: Ionian or Lydian.

For a Cm7 chord, we may use 3 scales: Dorian, Phrygian or Aeolian.

For a C7 chord, we may use only 1 scale: Mixolydian.

For a Cm7b5 chord, we may use only 1 scale: Locrian.

The function of a chord within a diatonic major progression defines each corresponding modal scale.

Here, the momentary scale is very obvious, even though it will be more difficult to distinguish modes separately, because major keys will always pull us to their center in spite of sounding in each chord in its corresponding mode.

We may find more ambiguous progressions where the modal concept sounds more plainly.

In this case, we clearly see a progression of chords in D minor key, but when want to establish its relative major key, we meet with 2 possibilities:                                                            

1.- Aeolian or natural minor mode: As we have seen, Dm7 will be the minor relative mode to F major (the VI degree), and Am7, in this case, the IIIm7.

Considering that now the key is D minor, Dm7 will be the I degree and Am7 the V. Modal scales, for each case, are the following:

2.- Dorian mode: We could look at the same progression as relative to C major, where Dm7 will be the IIm7 and Am7 the VIm7. In each case, modal scales will be the following:

Dm7 will continue being the I degree because it is the tonic of the progression and Am7 the V, but within a Dorian modal environment. We shall broaden the concept in the section MODAL HARMONY.

If we built a progression on only one chord, m7, we shall meet with one more possibility of its being the Phrygian mode, since there will not be any other chord conditioning its mode, and any of the remaining 3 alternatives, Dorian, Phrygian or Aeolian, may apply.

The characteristic note

If one analyzes the formulas of each modal scale according to its kind (major or minor), we shall see that each scale has a particular degree which does not appear in the others. This note will be called characteristic, and it is the one giving the typical sonority to each mode. In some modes or chords, it is necessary to draw on a second note in order for the sonority to be wholly defined. This note is known as the “secondary characteristic” and makes up, together with the characteristic note, the tritone present in each modal scale.

Let us now look at which are the characteristic notes of each mode (the secondary characteristic note being in parentheses).

Major modes

Ionian: 4 (7)

Lydian: #11 (T)

Mixolydian: b7 (3)

Minor modes

Dorian: 6 (b3)

Phrygian: b9 (5)

Aeolian: b6 (9)

Locrian: b5 (T)

- These characteristic notes will have to be present in the melody or the chord to define the mode.

- In most cases, the characteristic note agrees with the not-available tensions within the major keys.

- Pentatonic scales, major as well as minor, do not have a characteristic note, which creates a softer sound, that is, with little tension. We can see this in the 3 parallel modal minor scales in pitch of C.                             

- A good exercise to listen for the appearance of the modal sound on a chord is to play first the pentatonic and next the modal scale, stressing the characteristic note.

You will clearly hear a new sonority, which in some cases may seem a bit strange if you are not used to it, but you shall soon notice how your ear has become accustomed to it and recognizes the note.

How to play modal scales

We shall begin with the simplest example, a chord of C7, to which only one modal scale corresponds: the Mixolydian.

Always, when one starts studying something new it is convenient to lean on what one already knows in order to modify it. This choice is very important since it will help one quickly reach the right scale. The most common situation is to consider a modal scale as relative of a major one, as we have observed, and thus be able to find the scale and its corresponding digitation. In this case, the Mixolydian scale of C, will be  a major scale of F with a new tonic (C). This is not advisable because we will be thinking of another pitch (F), and then we will have to look for a new tonic (C), which will, take time and risk sounding in the key of F instead of in that of C.

Hence, we shall look for a method which will provide us with a correct scale-chord relationship more appropriate in its sonority.

As we have done before, we shall divide the modal scale according to kind (major or minor) and, in each kind, start from the corresponding pentatonic scale (major or minor) and then add the tritone notes (characteristic notes) to finally arrive at one or another modal scale. In this way, we shall profit from what we already know and, making a slight change in one of these two notes, reach from one mode to another.

We shall look at this process first in the major and next in the minor modes:

As a first step, and starting from the major triad, we shall build the major pentatonic scale to which we shall add two tensions common to the major modes (9 and 13). These 5 notes will be shared by the 3 major modes. Next, adding the major scale tritone notes (F and B in this case), we shall build the Ionian mode. Lastly, by altering one of these two notes, as corresponds to the major relative mode, we shall define the other two modes, Lydian (#11 and 7) and Mixolydian (d4 and b7).

In the case of the minor modes, we shall depart from the minor pentatonic scale, made up of the minor triad, to which we shall add the tensions common to minor modes (11 and b7). These five notes will be common to the three minor modes. Once more, adding the notes of the relative major tritone (Eb) Ab-D, we shall arrive at the Aeolian mode and, by inserting alterations as applicable (9 and 6 for the Dorian, and b9 and b6 for the Phrygian), we shall build the other two minor modes. 

RELATIVE SCALES IN THE MINOR MODE

Similar to the major mode with its relative scales -the modal scales we have just seen- the three minor scales also generate other relative scales built by starting from each of the degrees of the latter and following the same criteria as those used with the modals. These scales have a very particular sonority and are applied in specific situations as secondary dominants, or particular musical styles, such as Flamenco, Jazz, Modal themes, etc. Other scales are very seldom used due to their strange sonority. The name given to each stems from the modal scale most closely resembling the scale in regard to its application, and the degrees which have been altered are stressed. We shall see the name of each one of them and their formulas, and will analyze in detail those scales most frequently used.

Relative scales of the natural minor mode

Here, there are no changes in regard to the major key: since the notes are the same, the relative scales will be the modal scales we have already seen, but beginning with the Aeolian mode, as I degree.

I degree: minor natural scale or Aeolian mode

In modern music, this mode is very popular in Rock and Pop and, to a lesser degree, in Jazz, on the chord of the I degree of a minor key (Im or Im7), although. as we have seen with other degrees, particularly the V, one must draw on other chords and scales stemming from the minor scales, which we shall now see.

II degree: Locrian scale

This is the scale typically used when the m7b5 chord works as a second degree in a progression in the minor mode IIm7b5 - V7 - Im7

Relative scales of the harmonic minor mode

As we have seen before, this scale has a typically Arabic sound due to its interval of a tone and a half. Its relative scales also have the latter and, therefore, its main uses are related to the Spanish, or Flamenco, sonority and to some styles of Rock and Heavy metal.

I degree: Harmonic minor scale

It is used on the Im chord, Im maj7. However, it is an infrequent chord due to its instability.

V degree: Spanish Phrygian scale

Also known as the major Phrygian, it is very much employed in Flamenco on the chord of the V degree, with the function of tonic. When applied on V7/III and V7/VI, it is known as MIXOLYDIAN b⁹ b¹³.

Relative scales in the melodic minor mode

These scales are those most frequently used when improvising with Jazz and other associated styles.

I degree: Melodic minor scale

Very often, it is used on tonic chords Im, Im6 and Im maj7, playing with the sonority of the 6 and the major 7.

VI degree: Locrian 9 scale

Very much in use to improvise on chord m7b5, since it does not have any not-available tensions due to its having the natural 9. We shall speak of this at THE IDEAL SCALE.

The following scales are described in the section on ALTERED MIXOLYDIAN SCALES: IV degree Lydian b7, V degree Mixolydian b13, VII degree Altered or Superlocrian scale.

TETRACHORDS

Up till now, we have seen two types of tetrachords, the major (T-T-ST) and the minor (T-ST-T), but there are three more stemming from some modal scales. Combining these 5 tetrachords, we shall be able to build all the scales we have seen and others derived from them.

Types of tetrachords

MAJOR: T – T – ST

MINOR: T – ST - T

PHRYGIAN: ST – T - T

LYDIAN: T – T - T

HARMONIC or ARABIC: ST – T and 1/2 T -  ST

Different combinations of 2 of these tetrachords will give as a result the following scales, which we have already seen:

Modals

IONIAN or MAJOR  =  MAJOR + MAJOR

DORIAN  =  MINOR + MINOR

PHRYGIAN  =  PHRYGIAN + PHRYGIAN

LYDIAN  =  LYDIAN + MAJOR        

MIXOLYDIAN  =  MAJOR + MINOR

AEOLIAN  =  MINOR + PHRYGIAN

LOCRIAN  =  PHRYGIAN + LYDIAN

Minors

NATURAL  =  MINOR + PHRYGIAN

HARMONIC  =  MINOR + ARABIC      

MELODIC  =  MINOR + MAJOR

Other scales

LYDIAN b7  =  LYDIAN + MINOR

LOCRIAN 9  =  MINOR + LYDIAN        

MIXOLYDIAN b13  =  MAJOR + PHRYGIAN

SPANISH PHRYGIAN  =  ARABIC + PHRYGIAN

ARABIC  =  ARABIC + ARABIC

Identification of tetrachords will not only be of usefulness in understanding the structures of the different scales, but to a great degree also in practicing auditory recognition of scales to achieve mastery of them in a gradual manner.

SCALE OF THE MOMENT

As we have seen in the first part of this chapter, we shall call scale of the moment that modal scale or scale relative to the chord on which it is sounding, taking into account the arpeggio notes and the superstructure deriving from it. We shall thus define the modal or the relative scale corresponding individually to each chord in a progression, beyond the fact that the chords and their corresponding scales be diatonic to a common scale or not.

When we face a non-diatonic chord, the simplest way to determine the corresponding scale for building a melody or a solo is to apply the concept of scale of the moment following the steps:

1.- Determine the key of the chord progression (harmonic analysis).

2.- Write the scale of that key beginning from the tonic of the chord in question (modal scale).

3.- Substitute in the resulting scale for the non-diatonic degrees of that chord.

Let us look at an example:

We shall look for the corresponding scale for A7, which is the non-diatonic chord:

1.- The key is C major.

2.- Build the scale of C major starting from A (Aeolian mode).

3.- Replace the note C of the scale by C#, which is the non-diatonic note of A7 (the 3 of the chord).

With this method, the resulting scales will have the same name of the most similar modal scale in reference to its structure and the tonal function of the chord, plus an indication of altered tensions further appearing.

In the same example, A7 will be a secondary dominant (V7/II) and, as a dominant chord, the corresponding scale will be the Mixolydian.

As may be seen, in the momentary scale, b13 (F) appears instead of 13 (F#), as in the Mixolydian scale. Therefore we call this scale Mixolydian b13, as simple as that.

If we pay attention to the 7 notes of the resulting scale, we shall notice that these notes coincide with those of the melodic minor scale of D minor, but starting from the V degree (A). This is what we have seen before with the relative scale of the V degree of the melodic minor.

Therefore, we shall say about this example that the Mixolydian scale b13 in the scale-chord relationship will correspond to the V7/II, and is relative to the melodic minor scale from the V degree. Using the same criterion, we shall analyze all altered Mixolydian scales in the next section.

ALTERED MIXOLYDIAN SCALES

The Myxolydian scale is characteristic of the dominant V degree and, therefore, generates more tension. Besides the typical tension of the tritone that, as we know, resolves by a semitone towards the tonic and the third of the first degree chord, we may play with other tensions resulting from the altered 9, 11 and 13, which may also resolve by an ascending or descending semitone.

These altered tensions proceed from:

- The tonal function of the chord: momentary scale (secondary dominants, substitutes, etc.).

- Scales relative to another major or minor scale.

- Increments in the tension of the chord altering the notes in the superstructure. These scales may, in some cases, not be a momentary scale and not be relative to others. They are employed depending on the points of view of the composer or the soloist.

We shall see these scales, one by one, analyzing their origin and/or their relative scale.

Important: the b9 tension in a Mixolydian scale establishes an interval of a tone and a half with the third which generates a typically Arabic or harmonic sonority. To prevent this sound, in certain musical styles, such as Jazz, the #9 is usually inserted, which is the other alteration possible for this tension, leading to a scale of 8 notes; that is to say, when we see the indication b9 in a scale, we shall take for granted that the #9 will also be present.

Due to their diatonic origin in the minor scales, the Mixolydian scales with b9 or b13 usually resolve in minor chords and, in the same manner, those having these no altered tensions, will also tend to resolve in major chords, unless one is looking for an unexpected non-diatonic resolution.

Mixolydian b9

This scale is very little used, although one finds it mentioned in some textbooks since it has the b9, which is the alteration typical of the dominants resolving in a minor, as we have seen. It does not stem from any momentary scale nor is it relative to any other.

Mixolydian b13

Scale-chord relationship: V7/II.

Relative scale: melodic from the V degree.

We have already mentioned that b13 is a tension typical of a dominant resolving in a minor chord, but let us remember that this tension is the same note as the third of the chord on which it resolves, which is the reason for its not generating the sensation of resolution.

Mixolydian b9 b13

Scale-chord relationship: V7/III y V7/VI.

Relative scale: harmonic from the V degree. We insert the #9, as we have already mentioned.

This is a typical scale resolving on a minor chord.

Lydian b7

Scale-chord relationship: IV7 y and substitute dominants.

Relative scale: melodic from the IV degree.

IV7: Due to its being a major scale built on the IV degree, it receives the name of Lydian but with an altered 7, although from its functioning as dominant we could also look upon it as a Mixolydian with #11.

Substitute dominants: Regarding these chords, we could find different altered tension possibilities, depending on the type of dominant which it is substituting. To simplify matters, this scale has been established as a standard of substitute dominants, since tension #11 is equivalent to the fundamental of the substituted dominant.

It is worth mentioning that this scale agrees with the altered scale of the substitute dominant. In the example, the Lydian b7 on C7 agrees with the altered scale on F#7, the dominant which it would substitute.

Altered or Superlocrian scale

Relative scale: melodic from the VII degree.

I have written 2 ways of looking at this scale: as a melodic of Db from the VII degree, and with enharmonic notes in respect to C. In this manner, the tensions may be more clearly observed. This momentary scale does not exactly derive from any of the dominant chords we have studied until now. Its peculiarity is that all its tensions are altered, which is the reason for its being the scale generating the greatest tension on a dominant chord, which is generally labeled V7 alt., when one wants to apply this scale.

If we apply it on a chord with altered fifths, the tensions will be b9, #9, b5 and #5 (first example). If we apply it on a V7, the tensions will be: b9, #9, #11 and b13 (second example).

Symmetric diminished scale

Its structure derives from the diminished scale, which we shall explain in the next section, where all its particular features are given in detail. The difference in structure is that it carries alternating intervals of ST-T-ST-T… type inversely from the diminished. It is considered an artificial scale due to its not stemming from any relative mode, and the tensions which it alters are b9, #9 and #11. It is particularly applied to dominant chords with b9 acting as a MODAL INTERCHANGE in a major progression.

We may see in its formula that the 9s are altered, as in minor modes, but the 13 is not, as in major modes. Hence, this scale generates an ambiguous sonority, which makes it very interesting for use with dominants that resolve either towards a major chord or a minor chord. It must be carefully tested and listened to notice how each of its tensions resolves.

Tonal scale

This is also a symmetric and artificial scale, whose structure is T-T-T-T… resulting in a hexatonic scale (six tones).

Peculiarities:

- The structure of the scale will be a symmetric progression: T-T-T-T… 

- This is an artificial scale and, therefore non-diatonic.

- The result is a scale of 6 notes (hexatonic).

- It does not generate any consonant chord.

- Beginning from any note in order of thirds, we shall generate an augmented triad chord (C+) or C7+ if we add the b7.

- As seen in point 1, the structure of the scale repeats itself by tones, the reason for each of these notes being able to function as tonic.

- Thus, there will only be 2 tonal scales possible (for example, C and C#), and the cycle then repeats itself.

- Due to having 2 alterations of the V degree, it is very frequently applied on chords with an altered fifth (C+, C7+ or C7b5). If it should be applied on a dominant chord with the perfect 5, these two alterations could then be considered as #11 and b13. The result would be a Mixolydian b13 with the #11, but its use is less frequent. We usually see the same scale but with enharmonic tensions.

Summary

In order to create a memorizing rule, we may group these 8 Mixolydian scales in 2 groups of four. The first four would be named Mixolydian, with their corresponding alterations. These will always have the perfect 4 as characteristic in this scale.

The other four will result from altering the 4 (#11) into one of the four previous ones. Their name does not include the term Mixolydian. This rule will be very useful to study their fingerings starting from other scales, as in the case of the modal scales.

THE IDEAL SCALE (HARMONIC SCALE)

As previously mentioned, the tensions available for a chord are those which lie at a distance of a tone (or 9) from each of the notes of the seventh chord arpeggio. If we build a scale with this criterion, the notes of a chord and all possible tensions, we shall achieve an “ideal scale” since there will not be any not-available note.

We can also find this scale as “Harmonic scale” because all of its notes are or can be part of the chord. But it must not be confused with “Harmonic minor scale”.

In this manner, we shall be in the presence of scales exclusively thought for in function of the chord (momentary scale), beyond a tonal situation generating the progression in which it stands. Therefore, on many occasions, we may arrive at non-diatonic scales in regard to that progression.

This is the first consideration we may take into account in what is known as “outside” improvisation, since we will be able to employ, for example, a Dorian scale on an m7 chord without its being in function of the II degree or of modal tonic.

Let us look at some examples on the more frequently used chords.

THE DIMINISHED SCALE

See DIMINISHED CHORDS for a review.

As we previously saw, the diminished chord comes from the VII degree of the harmonic minor scale. Therefore, its corresponding scale is the relative stemming from this (harmonic minor from the VII degree). But, to prevent this clearly Arabic sonority, a new scale is built starting from a superstructure a tone away from the notes of the chord, as we saw in the previous paragraph (ideal scale). We thus arrive at the diminished scale.

Peculiarities

- The structure of the scale will be a symmetric progression: T-ST-T-ST…

- This is an artificial scale and, therefore, non-diatonic.

- The result is a scale of 8 notes (octatonic).

- It has four tritones.

- The interspersed tensions a tone away generate another diminished 7 arpeggio also a tone away from the original. This means that their structure has two diminished 7chord arpeggios inserted. 

- Apparently, at step 1, the structure of the scale is repeated by minor thirds (the same as the chord), the reason for each of its notes being able to function as a tonic.

- Thus there will only be 3 diminished scales possible (for example, C, C# and D), and the cycle will repeat itself.

Use of all these scales will be according to the judgment of the composer or improviser. This means that beyond their corresponding origin and diatonic application, they may be used to create greater tensions on the chords “breaking” the rules we have seen.

CHAPTER V: MELODY AND HARMONY

MELODIC ANALYSIS

Analysis of a melody, its composition and harmonization, holds a close relationship to the chords accompanying it; in fact, they are “the same thing”. Pianists see this more clearly because their instrument allows them to play at the same time melody, chords and bass line. In spite of the fact that we use to separate all these concepts when studying harmony, one must remember they form a unit. In an orchestral arrangement, the chords are usually divided into diverse melodic lines which the different instruments or sections will play. Here, it becomes clear to us that chord movement is, in reality, the sum of different melodies (voices), each one moving according to a certain criterion. What we recognize as the main melody is that which stands out from the others due to its pitch (generally, the highest one or leading voice, its volume and/or its timbre).

Similarly, the melody may be seen as a voice standing out from within a chord and, therefore, complying with the rules we have seen until now for construction of chords. This concept is important to keep in mind all along the present chapter, where we shall analyze the construction of melodies and harmonic sequences. It is worth clearing up that when we speak of melody we are also speaking of improvising, as an idea for impromptu composing. Melodic analysis will consist of classification of notes of a melody with a number indicating interval distance in reference to the fundamental of the chord, as we have done with the momentary scale. We shall look at the criteria to follow when using this classification of notes.

Strong and weak notes

In a couple of rhythmically equal figures, stress will naturally fall on uneven times, more so the first than the third.  In accordance with this, we shall consider the first note strong (s), the third semi-strong (ss) and the second and the fourth weak (w).

If we combine the subdivisions of times, the criterion will remain the same.

In ternary bars, the first note will be strong and the other two weak.

Main and secondary notes

Within a melody, we shall classify each one of the notes as either main (m) or secondary (se).

Main notes: these will be the ones with greater harmonic “weight” in relation to the chord and, therefore, will have to satisfy certain rules regarding this.)

Main notes will be:

- Those in either a strong or a semi-strong time.

- Those of long duration.

- Notes of short duration that take a leap, i.e., do not move by conjoint degrees.

According to those criteria we have already seen, main notes will be one or more of the notes of the seventh or available chord tensions on which they are sounding, from which they will take their name in melodic analysis. That is, they will be represented with the number indicating interval distance in respect to the fundamental of the chord. In the case of available tensions, they will be labeled to lie in the secondary octave, same as those in the momentary scale.

f = chord fundamental, T = tonic

Rhythmic anticipation: this results from anticipating with a note of short duration (quaver or semiquaver) the attack of the main note which should be in a strong time and generally linked to the latter. This advanced note will be analyzed as if it had fallen in this strong time, that is, as the main note of the figure which it anticipates and, therefore, of the following chord, even if the latter were a silence.

Secondary: these are basically notes for transit between a main note and another. Hence, they do not have a harmonic “commitment” to the chord.

Secondary notes will be:

- Those falling in a weak time and of short duration.

- Those moving by conjoint degrees or semitones towards a main note.

In addition to these features, secondary notes may be any note, whether diatonic or not, and according to this we shall divide them in diatonic and chromatic.

Diatonic: these are notes within a momentary scale, be they available or not-available notes. One shall write a “d” before their interval number and they are always labeled to be within the first octave.

Chromatic: these are notes moving by chromatic approximation (semitone) and do not belong to the momentary scale. They are labeled with a “c”.

According to the type of movement, the secondary notes will be classified as: passing notes, bordure, not prepared or embellishments, even though this classification is not noted on the melodic analysis.

Passing note: this moves by conjoint degrees of a note from one chord to the next.

Bordure: a passing note by conjoint degree or chromaticism, inserted at the repetition of note of the chord.

Not prepared: this is a passing note preceded by a leap or a silence.

Embellishments: these are notes of very brief duration preceding a main note, generally an upper or a lower diatonic. In former times, they were written a size smaller than that of normal figures, not being added to the total sum of figures of each bar. Its execution rests value to the anterior or posterior figures. The most commonly used are: trill, mordent, appoggiatura, etc.

Melodic movements

Each degree of the scale corresponding to the key of the theme and/or the momentary scale will be, as previously seen, more or less stable. Unstable notes will tend to move easily to the most stable neighboring note in either an upward or a downward direction or to an ever more unstable note to increase tension.

Classification, in order of stability, is the following:

Stable: I, V, III

Unstable: VI, II, IV, VII and non-diatonic notes.

Conjoint degrees and leaps

Movement between 2 stable notes by conjoint degrees and in the same direction (scale) is a natural tendency for our ear, and it usually resolves by a leap in the reverse direction. This leap will be greater the greater the length of the scale preceding it. When movement is produced abruptly by a leap, our ear requires listening to the conjoint degrees included in this leap, with the exception of the leap being towards the tonic. These intermediate notes will sound in a direction opposite to the leap. Its omission or delay in appearing in the melody will create either a greater or a lesser tension.

Beginning of a phrase

The beginning of a phrase may be of three type

Anacruse: melody begins before the theme, in way of an introduction.

Acephalous: the melody begins with a silence.

Thetic: the melody begins with the theme.

MUSICAL THEME

Development of a musical theme is a passage between stages of repose and tension, where we may also insert moments of half tension.

This “story” will maintain an intimate relationship with the listener, captivating his attention with clear ideas (phrases) which will gradually build a global concept of the theme (form).

The ability that we shall develop in the interplay of tensions will succeed in captivating that attention thanks to its need to be led to a point of rest.

Same as with a novel, a film, etc., a too lengthy situation of rest will lead to boredom and a too prolonged tension to discomfort. We must learn to know how to “minister” our resources to alternate between the 2 states until arriving at a moment of maximal tension (climax) where the denouement of the story (resolution) is produced.

On carrying out melodic movements, we will have to take into account their relationship to harmonic movements (scale-chord relationship), or vice versa, considering them as a whole moving in the same direction. Thus, the same melody may have different harmonizations, which change its character. It is very important that movement and harmonic rhythm be adequate for the melody. We shall see this point in further detail later on.

From lesser to greater, the subdivision is:

A group of notes builds a phrase

A group of phrases builds a part

A group of parts builds a musical theme which will have a form

Phrase or question

A phrase, also called a motif, has a binary duration, in most cases of two bars. This will have to be a clearly graspable idea for the listener, so much as regards its melodic concept as its rhythmic one and will have at least two stable notes and their corresponding transit.

Counterphrase or answer

When improvising, it is very common to hear speaking about “question and answer”, comparing building melodies with a conversation.

The phrase, or motif, is the question and the counterphrase, or counter-motif, the answer. If the question is clear and defined, the answer will be easier to build and the dialog attractive for the listener.

The counterphrase will have the same duration as the phrase, generally two bars, and thus begin on the third bar and occupy as much as the fourth. It may be a new motif, the same or a variation of the phrase.

As variations, we will have several alternatives:

- Repeat the rhythmic idea and change the melody.

- Repeat the melody and change the rhythm.

- Begin with an identical idea and change the ending or the resolution.

After the answer is found, another question will appear, a new phrase or motif usually the same as the first phrase, or a variation of the same (generally placed on the fifth and the sixth bar), but clearly different.

Resolution

Finally, on the seventh bar, a resolution of tensions being generated in the three former phrases comes about and reaches a rest. The eighth bar may continue in the state of rest creating the end of the part or generate a new tension giving way to a new part or a repetition of the same.

Part

Summarizing the previous statements, a part will have the following structure:

The square part is formed by eight bars and is the most frequently used in modern music. In some styles, such as Blues, this structure consists of twelve bars. To a lesser degree, we may also find parts with less or more bars and an even structure (ten bars) or an odd structure (seven or nine).These will be “not square” structures.

Form

Form is the general vision of a theme which will contain one or more parts, each part being designated with a capital letter by order of appearance and of the alphabet. Depending on the structure of this form, we shall classify it as:

Strophe: an identical part which repeats, A  or  A A

Binary: two different or similar parts, A B  or  A A´

Ternary: three different or similar parts, A B C  or  A A´ B

Rondo: a theme is repeated with insertion of others (strophes). This repetitive theme is called a refrain. A B A B A   or    A B A C A

Repetition or re-exposition of a part may be:

Identical: exactly equal.

Variation: melodic, harmonic or rhythmic alteration in which the original idea may be recognized.

Imitation: identical or a variation played by another instrument or other instruments.

Development: re-elaboration on an original idea, generally more complex in melody and/or arrangement.

Cases 2, 3 and 4 are re-expositions (variants of the same idea). In order to differentiate them, the new parts will be designated with the same letter as the original, and accompanied by the symbol “ ´ ”, as many times as there should be re-expositions: A, A´, A´´, etc. These main parts may be accompanied by others acting as a preparation (introduction), a link (interlude or bridge) or a final resolution (coda).

Each part integrating the form will end with a simple double line marking bar ending, to signal the beginning of a new part. So much the part as well as the form do not depend exclusively on melodic movements. They will also depend on harmonic movements which we shall see in the next section.

Climax

We shall say that the climax is the moment of greatest tension within a theme and precedes the resolution, which is usually a step towards rest or stability.  Depending on the form or the complexity, there may be more than one climax within the same theme, which will generally be in different parts.

Signs for repetition

Since a form usually repeats parts or phrases of a theme, there are several ways of indicating this without the need of rewriting these repetitions and thus preventing extensive scores which look like sheets.

Repetition bars

If the part or the theme must be repeated in its entirety, this is indicated by two letters DC, i.e., “da capo”, or from the beginning.

This may also be indicated with two periods at the left of the final bar.

If only a fragment should be repeated, the two repetition bars (opening and closure) will be put at the beginning and the end of the same.

Repetition box

Repetition boxes indicate how many times a fragment must be repeated but with a different ending.

Each final variation will be included in the bars spanned by the bracket and a number indicating the order in which they must be played. At the beginning of a part, a repetition opening bar will be put, and at the end of the original phrase a bar marking closure of repetition which will indicate a return to the beginning.

On arriving at box 1, there will be a leap to box 2. In the following repetition, on arriving at box 1, there will be another leap to box 3, and so on.

In this case, the fragment or the piece is repeated on arriving at the end of box 1, and when arriving at the beginning of the same, this will not be played and one continues to box 2.

Coda

A coda is a fragment of the original idea of the theme appearing at the end as an “epilog”. Its degree of simplicity or complexity and duration will be related to the development achieved with the theme. It will be indicated with a symbol which will be put wherever the coda is played. As the coda is usually a fragment of the theme already played, one usually adds to the symbol one of different clarifying options:

DC to coda: da capo (from the beginning) to the coda.

Segno to coda: at the place of the score where the original idea is found which must be repeated and setting a double bar at the end of the theme, which is generally explained with the word fin or fine (from the Italian, “the end” or “ending”).

In the example, the work will be played continuously until reaching the double bar (4th bar), return to the segno (sign) and repeat till the coda (2nd and 3rd), leap to the coda (5th) and the coda will be played to the end (fine).

HARMONIC MOVEMENT

Harmonic rhythm

As we have seen with groups of four figures, groups of four chords will have a stress that may be strong, semi-strong or weak using identical criteria.

The most stable chords (T: I, III and VI) will be placed on strong bars, while the unstable ones (SD: II and IV) (D: V and VII) on weak ones. One will have to take into account the complexity of the progression to adequately place the different types of chords depending on certain concepts:

Chords duration: chord with a prolonged duration increases its stability, what on many occasions may change its tonal function from SD or D to T. This situation may be a resource for creating modulation effects.

In the example, we see how a V degree chord will happen to have the function of a tonic, which may be either a temporal or a definitive modulation towards a Mixolydian mode.

Place of the bar: within the same bar, we shall also have strong or weak stresses and, as we saw with melodies, anticipations, too.

Progression: anterior and posterior chords will influence the definition of a chord being either strong or weak, creating more or less resolving movements and, therefore, more or less stable, be they diatonic or not.

Relation to the melody: strong notes in a melody, which do not belong to the arpeggio of the chord, may define the mode of the same, as we have seen with modal scales calling them “characteristic” notes.

In conclusion, the distribution of chords is extremely important for defining their degree of stability, since a wrong placement may change their function. Something which in many cases may also be seen as erroneous, in others will be a resource for composing.

Progressions, together with the melody, will label the direction of movement, which may be predictable, according to what is more habitual, or create “surprise” in the listener, if the movement is unexpected.

Using chord symbols

In present-day modern music, use of chord symbols is a practical way to write accompaniment and define harmony.

If we undertake a correct analysis by tonal degrees and functions, we may understand: the harmony of the theme or movement, the scales we may use in improvising, more easily remember the progressions or transport the key.

Notation by chord symbols allows more or less freedom to the player in accordance with the indications provided so much in rhythm as in placement of the notes of each chord.

We shall find out, step by step, how to enrich notation. We indicate the chord symbols and the amount of chords by bar with oblique lines marking the time unit.

At the beginning of each part, we shall define the style that will label rhythm in free form .

We shall define a rhythmic pattern with flat-headed figures and add the word “simile” which will enable doing variations on the same idea.

We shall write all the rhythms. We may include the leading voice of the chord (the highest note) to define timbre.

Cadences

By harmonic cadence, we understand a chained series of chords giving resolving character to a phrase. According to the type of resolution, they are classified as: conclusive (authentic and plagal) and suspensive (semi-cadence, imperfect and broken).

Conclusive

Authentic: The cadence which resolves from a dominant chord of V degree on a tonic chord of I degree.

Plagal: The cadence which resolves from a subdominant chord of IV degree on a tonic chord of I degree.

Suspensive

Broken: The cadence which resolves on a chord with tonic function which is not of I degree.

Imperfect: A cadence which resolves on a tonic chord in a weak or inverted time.

Semi-cadence: Production of a momentary rest on a chord which is not tonic. It is most commonly seen at the end of a phrase on a dominant of V degree which will repeat from the beginning, where it resolves.

Voice leading

When one thinks of a chord progression, one pinpoints it as an accompaniment, leaving the melody and the bass aside, where as when our instrument registers a greater range of pitches, such as the piano, one tends to integrate these concepts in only one movement, from which an arrangement may later develop.

Placing all the voices within the same system allows one to visualize the intimate relationship existing among voices, even though one may later “open up” the arrangement for other instruments, assigning one or more voices to each one.

An arrangement written with the same system is called leading or conductor.

A chord is a set of voices moving in a certain direction and resolving tensions formed between intervals, created between those voices, by a tone or a semitone.

These intervals are considered consonant (4, 5, 8, 3 and 6) and dissonant (2, 7, #5, b5, etc.) As we have seen, these movements will tend to resolve situations of tension (dissonances) towards rest (consonances). The more voices remaining without any movement during these cadences, the more this resolution of tension will be perceived as coming from the voices in movement.

In other words, “voice leading” Is nothing else but treatment of the intervals produced between those voices involved in chords and their movement towards a new chord.

The study of voice leading is what is known as counterpoint. It is not a topic of this book to go into the wide world of counterpoint and its rules, which would produce several volumes devoted to its study. We shall explain the basic points affecting the building up of progressions of chords.

It is important to clear up that when we study the movement of voices treatment of the bass becomes a special topic.

A cadence of four voices will mean use of chords, where the bass is generally the fundamental of the chord which will be duplicated in one of the higher voices. Voices will be numbered according to pitch, the highest one being the 1st voice (melody or leading voice. In reference to choral arrangements, an arrangement for four voices will be:

1st voice: soprano

2nd voice: contralto

3rd voice: tenor

4th voice: bass

This nomenclature considers pitches within a system of two pentagrams (F clef and G clef).

We shall treat movement of voices in the G clef classifying them according to voice number in order of their pitch without taking into account the above range.

Position, disposition and inversion: position of a chord may be closed (the voices will all be within the same octave) or open (the voices will be in more than one octave), without considering the lowest, or bass.

Disposition is the order in which the voices of the chord appear: fundamental as first voice, third as first voice or fifth as first voice.

One must not mix up the concept of disposition with that of inversion. In disposition changes, we refer to the placement of higher voices without minding the bass. We already know that if the bass is the fundamental of the chord, we will be referring to a chord in root position, whereas when it is the 3, the 5 or the 7, it will be an inversion.

Inversions will be exceptional cases used when one would like to give preference to a specific bass movement for a particular reason.

Movement between fundamentals: : some movements between fundamentals of chords (the lowest note, or bass line) will sound stronger than others. This is due to the lowest frequencies being more difficult to distinguish by ear and, therefore, the first notes of the HARMONIC SERIES will be more easily perceived and thus sound stronger.

Strong: 4 or 5

Semistrong: 3 or 6

Weak: 2 or 7

Harmonic continuity:

As we have mentioned, resolution of intervals in a cadence becomes more evident when the rest of the notes of a chord remain in the same place or move the least possible. This we shall call harmonic continuity. Its principles are:

- The interval between notes of a chord must not go above the 8, excepting the bass.

- All notes shared between chords will remain in the same voice.

- If there were not any shared notes, the voices will move to the closest note in an ascending or a descending manner but in closed position.

- The sharp notes (#) will move in an ascending manner and the flat notes (b) will move in a descending manner .

- In order of preference and in function of availabilities, movements will be: to maintain a note in common and to move by chromaticism, by tone or by third.

- On occasions, a change of disposition of chords will contribute to good harmonic continuity.

In the more common movements between fundamentals, we shall have the following notes in common:

Triads

4th or 5th: 1 note in common

3rd or 6th: 2 notes in common

2nd or 7th: no note in common

Sevenths Chords

4th or 5th: 2 notes in common

3rd or 6th: 3 notes in common

2nd or 7th: 1 note in common

The general tendency of harmonic continuity is that not common, voices descend. Based on this, when the pitch of the chords becomes too low, an octave leap will be taken upwards to restore continuity. This leap will preferably be taken within the same stable chord of long duration.

More utilized movements

According to concepts seen so far, we find some cadences or chord progressions which are very much in use in modern music because they summarize some concepts favorable for the listener (type of movement between fundamentals, resolution of tensions, etc.)

Cadences

V  -  I

IV  -  V  -  I

II  -  V  -  I

Progressions

I  -  VI  -  II  -  V7

I  -  V7/II  -  II  -  V

I  -  V7/IV  -  IVmaj7  -  IVm

The bass line

Bass movements, which may be considered the second most important voice after the melody, will be determining in harmonic progression.  That is, harmonic progression may be in function of bass movement, or vice versa. One way or another, the bass line will have a motif generally created from patterns of movement (by fourths, fifths, ascending or descending semitone, etc.).

Notes commonly used as a reference for each chord are the tonic and the fifth, inserting other notes rhythmically defined by the style of the theme.

The bass may move in parallel to the melody (both either ascending or descending) or in opposite directions (if the melody raises the bass, or vice versa). Very commonly, chromatic notes are inserted in the bass to reach from one tonic to the next, enclosing the next tonic to be reached with ascending or descending semitones. This resource, also utilized in improvising, is known as target tones, or chromatic approach.

This movement, generally in black notes, is what is called a walking bass, typical of Jazz or Blues. Let us look at an example.

Walking is usually improvised, trying to prevent patterns of movement that may result monotonous. In other styles, the bass follows an established pattern which, once understood, will be very easy to apply and, as we have seen, will simply be pointed out for the bass player without writing it in detail note by note. The bass arrangement may develop a much more varied harmony if we consider the use of chord inversion or of hybrid chords.

HYBRID CHORDS

We shall call a hybrid chord one formed by a triad or a seventh and a bass not forming part of the same, for example, Bb/C.

In spite of chord symbol being Bb, the bass will define the fundamental of the chord, i.e., we shall analyze it as a chord of C, with certain peculiarities. The fact that they are symbolized this way is for convenience in reading, because, as we shall see, the true coding of such chords would be unnecessarily complex.

Its main feature is the omission of the 3, what makes it very indefinite and tending to create a suspended situation which may be more or less stable depending on previous or later movements.

We shall see some examples of the different kinds of chords of C and analyze their function.

The prefix “omit” will make clear which note of the triad is not present.

In these two cases, we see how the same hybrid chord may have a different function, which will depend on the context in which it is found.

In the following example, it will be as a dominant:

In the following example, it will be as a minor:

Other examples of hybrid chords:

As we may see, the use of hybrid chords is very frequent in modal harmonies, which we shall see in the next segment, where we shall analyze them in greater depth.

MODAL HARMONY

Modal music may be comprehended as a kind of music whose tonal center, or key, is in one of the Greek modes (modal scales). Therefore, the melody will be made up of one of the modal scales which we have seen and the harmony with the diatonic chords stemming from it.

Among these seven modes, the Ionian is taken as the major mode, or key, and the Aeolian, with its harmonic and melodic variants, as the minor. Thus, the tendency is to speak of modal harmony when the themes or passages have their tonal center in the five remaining modal scales: Dorian, Phrygian, Lydian, Mixolydian and Locrian. Among these modes, there will be some more sonorous than others and, therefore, more commonly found.

The Ionian mode, or major, has been the most frequently used in western music due to the regular structure of its scale, the balance of its tensions and the natural tendency to resolve them (tritone). In this way, our ear has become used to it and to its forms, which makes us look for similar structures and resolutions when we pretend to change to other modes.

As we have seen with the minor mode, this auditory need to recognize habitual tensions is not always possible and the use of certain additional “tools” is necessary to achieve it.

We must also consider that the seven notes, and their respective diatonic chords in a modal key, are the same as those in their relative mode (Ionian), by merely changing the degree which corresponds to each one. Hence, when creating a harmonic-melodic modal structure, one must consider several factors in order that our ear will feel like searching for that tonal center in that mode and not for its relative major, to which it has become accustomed.

We must not mix up the use of a modal scale inside a cadence or major progression, for example, a Mixolydian scale on a V7/I (momentary scale), with the concept of modal harmony. If we are looking to build a theme in Mixolydian mode, that seventh chord will serve by functioning as a tonic in the progression (I degree) where it shall find a rest, and the Mixolydian scale will now be the scale of the key.

The lesser stability of these modal tonal centers makes it necessary to apply certain resources to achieve a state of rest when using them: the tonic chord is usually repeated more than is typical, and one does not draw upon secondary dominants, substitute or secondary seconds, since these harmonic resources would lead our ears away from a weaker tonal center.

This limited variety of harmonic resources makes progressions a little monotonous. Therefore, to create different parts of a theme, the mode is usually changed (modulation) in those parts, repeating on many occasions the same idea but in a new key.

We shall see the resources available to us and some rules to achieve these tonal centers.

The chords

We shall begin by drawing a chart with the diatonic chords of each mode.

Kinds by degrees

In the key of C (relative modes)

As previously mentioned, the seven chords of each mode are always the same, with differences in the degree representing them.

We shall classify diatonic chords in Tonic, Cadential and Preventable.

Tonic: chords making up the I degree of each mode.

Cadential: chords containing the main characteristic note of the mode. Reviewing what we have already seen, main and secondary characteristic notes (in brackets) will be:

Major modes

Ionian: 4 (7)

Lydian: #11 (T)

Mixolydian: b7 (3)

Minor modes

Dorian: 6 (b3)

Phrygian: b9 (5)

Aeolian: b6 (9)

Locrian: b5 (T)

Preventable: chords which tend to resolve on the relative major chord, especially those including a tritone and if one of the notes of that tritone is the fundamental of the chord.

The remaining chords are neither representative of a mode nor preventable.

We shall see an example in the Ionian mode; the rest will be seen afterwards, when analyzing each mode.

The characteristic note is the IV degree (F) and, thus, chords including this will be cadential (C = II, IV and V). The chord to be prevented (P) is the VII degree since it has the tritone (B-F) and B is the tonic. The I degree will be the tonic chord (T)

Use of triad chords simplifies harmonic progression due to their lacking the 7. In some cases, the sound will be more ambiguous and the presence of more chords or of the characteristic note in the melody will be a requisite for defining the mode. This is a very frequently employed resource when looking for delaying the definition of the mode, in this manner creating surprise in the listener.

Determinant chords

These are those tonic chords containing characteristic notes and, hence, defining the mode without need of recurring to other chords or certain notes in the melody.

Hybrid chords

Each mode will have certain characteristic hybrid chords which, due to their indefinite or incomplete character, will help creating progressions maintaining modal sonority.

We shall see some examples in the key of C and their possible functions.

Apparent hybrids

These are inversions of chords in which, in a modal context, the bass sounds as chord fundamental. It is a very frequently used resource to keep the sonority of the tonic by creating progressions of several chords.

Chords by fourths

Creation of chords by intervals of fourths, instead of thirds, as is usual, generates an ambiguous sound which will also contribute to hold us away from the relative major mode. Chords to be prevented (P) will be those including the tritone of the key. These chords may be created in either triads or sevenths. We shall see examples of both in the Ionian mode of C.

Chords by fourths in triads

Chords by fourths in sevenths: fourth note may be another interval of a fourth or of a third.

In the same manner, these chords may be built in the other modes.

Chords symbols are not quite defined, the more utilized forms are:

- Indicate the tonic of the chord attaching the number 4: C4, D4, etc.

- Add to the previous indication that the mode one finds oneself in will define the type of corresponding fourth or third: C4 dor., G4/F dor., etc.

In both cases, the coding will provide freedom to build chords with different dispositions or different structures stemming from the same mode.

Harmonic progression

Considering the concepts of harmonic rhythm we have seen, we shall succeed in having a chord define the tonal center when:

- It is found in strong bars

- Its duration is prolonged

- The tonic is held in the bass employing, besides the tonic chord, inversions and hybrid chords.

With these concepts, we shall achieve the desired tonal center preventing the tendency towards a relative major.

Superstructure

As we have seen, chord superstructure (tensions 9, 11 and 13) is also a progression of thirds and, therefore, the structure of another triad or seventh chord, if we should be repeating the tonic in its next octave. The sum of these two chords (I and II degree) will include the seven notes of the modal scale and, hence, define the mode. The same occurs with every mode when combining chords of I and II degree. .

This means that the sole presence of these two chords will be enough to define modal harmony with the presence of all the notes of the scale. Of course, one must utilize one of the resources we have seen so that one of them sound as a tonal center. As examples of this: holding the bass in the looked-for tonic, playing a chord in strong bars or providing a longer length to one than to the other.

Combination of the two arpeggios of these chords will also be a very often used resource for improvising. Other combinations with chords containing a characteristic note (cadential chords) will also define a mode, even though not all the notes of the scale appear: Dm7 - Cmaj7, Dm7 - G7, etc.

The melody

The melody usually gyres around the tonic and the characteristic note, trying to prevent the sensitive from the Ionian, which tends to resolve on the tonic of that mode. Appearance of the characteristic note in the melody will define the mode without need of the note being present in the chord.

Melodic ideas are typically simple and clear. In the following example, we see a Dorian theme where the characteristic note (B) is present in the melody in the first three bars and in the fourth in the chord of second degree (cadential).

Modes, one by one

We shall see all characteristics described in each mode, leaving aside the Ionian and the Aeolian, of which we have written enough in the chapters on major and minor keys. We shall indicate the following:

DC: Determinant chord, T: tonic, C: cadential chords, P: chords to be prevented, CN: characteristic note and hybrid chords used with tonic function.

Dorian mode

Scale formula and tetrachords

This is the most frequently used mode within modal themes. The structure of the scale is symmetric due to its possessing two similar tetrachords (minor). Although the VI degree is a note to be prevented in a major environment, in the modal one it is the characteristic note, frequently replacing the diatonic chord m7 by m6.

Diatonic chords by degrees and kinds

Superstructure

As we have seen, the VI major degree is the characteristic note, which differentiates this mode from the natural minor, where we shall find the bVI.

The superstructure of the scale will form an arpeggio of the chord of the II degree (in this case, Em or Em7).

Hybrid chords and apparent hybrids (the bass falls always on the tonic)

Phrygian mode

The Phrygian mode is characteristic of traditional Spanish music.

Scale formula and tetrachords

Diatonic chords by degrees and kinds

Superstructure

The bII degree is the characteristic note, which is what differentiates this mode in natural minor. This note, used as b9 tension, which would be a note to be prevented in a chord of IIIm7 in a major environment, in modal harmony, defines the sound of the mode. The bVI, however, will continue being a note to be prevented. The superstructure of the scale will form the arpeggio of the chord of II degree (F or Fmaj7, in this case).

Hybrid chords and apparent chords (the bass falls always on the tonic)

Lydian Mode

Due to having an augmented IV degree, which is its characteristic note, this is a mode previously not very much in use. In modern music, it is more frequently employed to create a sonority producing a greater feeling of “suspense” in major keys.

Formula of the scale and tetrachords

Diatonic chords by degrees and kinds

Superstructure

As we have seen, the #IV degree is the characteristic note, differentiating this mode from the Ionian, or major. The superstructure of the scale forms the arpeggio of the chord of the II degree (G or G7, in this case).

Hybrid chords and apparent chords (the bass falls always on the tonic)

Mixolidian Mode

This mode is typical of Blues, and other styles deriving from it. Due to its I degree being a dominant chord (in this case, G7), one must keep in mind that the chord now performs as the tonic, a reason for preventing resolution of its tritone now becoming indispensable.

The Mixolydian scale generates a very different sonority in the scale of Blues, mainly because of opposition of 3 major against b3 of this scale, and appearance of the 6 and the 9.

Many times, one inserts a Blue note as a note of passage in the Mixolydian scale in order to wink at the style.

Scale formula and tetrachords

Diatonic chords by degrees and kinds)

The chord of the I degree in a seventh is, at the same time, the determinant chord due to b7 being the characteristic note.

Superstructure

Hybrid chords and apparent chords (the bass falls always on the tonic)

Locrian mode

The Locrian mode is not used in modal harmony since its I degree chord is extremely unstable due to its having the tritone and the b5. As we have seen, use of this scale is, in most cases, applicable to II degree chords in a minor key.

We shall see some examples of modal harmony in accordance to what we have explained.

In this example, we see a Lydian theme with its characteristic note in the chords of the tonic and in a hybrid chord in the 4th bar (Em/G = G6). In the 3rd bar, there are two cadential chords, the first a hybrid one, A/G.

Now, here we have a Phrygian example; a combination of the I degree in strong bars with the II is enough to define the mode.

MODULATION

With modulation, we are referring to a change of key within the same theme and in a prolonged manner. As we have seen, on many occasions, chords or non-diatonic scales may appear without this meaning that a permanent change in key will be produced. In modulation, one must clearly distinguish the sensation of rest in a new chord or tonal center, which is different from the original.

This modulation may spread to neighboring or to distant tones.

Neighboring tones

These are those keys which have in their clef armor either one or no alteration differentiating them from the key preceding them. There will not be any difference in the armor when modulating from a major key (Ionian) to its relative minor (Aeolian), and vice versa.

For example, tones neighboring a C will be: Am, G, Em, F and Dm.

Neighboring a Cm, these will be; Eb, Fm, Gm, Ab and Bb.

Notes being altered on changing the armor are considered characteristic of the modulation and their presence in the harmonic progression or the melody will be decisive for noticing the change.

In some cases modulating towards neighboring tones, the change of tone becomes more ambiguous depending on the treatment of the progression or the melody. This may be looked as a resource or an error in treatment of the notes.

The most frequent modulations to neighboring tones are by a leap of 4 or 5 to major tones or their relative minor (VI degree).

Very commonly, one finds themes in major mode, which in their part B modulate to their relative minor, or vice versa. Part C, or final, may continue in relative tone or return to the original.

Distant tones

These are those tones with more than one alteration in their clef differentiating them from those of the tone preceding them.

Very frequently, there will be a tonic movement similar to those in neighboring tones but changing the mode from major to minor, or vice versa. For example, modulation of C to: Fm, Eb, Gm, Bb, or from Cm to: Am, Dm, G, etc.)

In Pop music, modulation has been frequently done by tone or ascending semitone at the moment of repeating the theme, or a part of the same, to give the sensation of greater gloss or force.

According to treatment of harmony in the passage from one key to another, we shall classify modulations in: Direct, Pivot or Transit. Direct modulation will not be prepared and the other two prepared.

Direct modulation

The change of tone is suddenly produced creating a surprise sensation with some determined goal, as the one we cited previously for Pop music by an ascending semitone. Here, modulation will have to be clear, that is, not include neighboring tones or, if intended, plainly mark the characteristic note in the melody and/or chords.

The indication in harmonic analysis will be as follows.

T1 will be the original key and T2 the modulation key and the keys will be indicated below those symbols.

Modulation by pivot

This happens when a chord or group of chords belong to both keys. The sensation of modulation will be produced when leaving the last common chord, which is the one named pivot. Therefore, only one chord be considered a pivot.

Use of many common chords, which is what happens in neighboring keys, creates a sense of confusion.

In case the pivot chord should change from momentary scale to modular, the corresponding scale will be T1.

Modulation by transit

In modulation by transit, a group of chords generates a sensation of ambiguity or lack of a tonal center which will serve to connect one key with another. This is usually accomplished with chains of chords as dominants by extension or sequences of II-V. These chains will have to include a clear scheme whereby the repetitive idea is set in evidence which will begin with a strong bar.

Transit is indicated with a dotted line going from the beginning to the end of the cadence.

To summarize, we shall define towards which tone we plan to modulate (neighboring or distant), and how we are going to go about it (direct, pivot or transit), always keeping in mind the harmonic rhythm. It will be convenient for the new key to appear in a strong bar, better still at the beginning of a new phrase (group of 4 bars or their multiples).

Beyond all theoretical considerations, our ear will be the one to determine if it perceives a new tonal center, and when.

MODAL INTERCHANGE CHORDS

Given a progression in a certain major key, chords of modal interchange are those diatonic chords proceeding from a parallel mode (same tonic, different mode), generally minor.

Even though the more common tendency is to employ the most utilized chords in the Aeolian mode and apply them to the Ionian, there are other interesting possibilities.

In this case, we see a IV degree minor 7 (Aeolian mode) in place of the IVmaj7.

These chords may proceed from any one of the modes we have seen: modal scales, natural harmonic or melodic minor scale.

It will be convenient to keep them in mind in each case. We shall mark in black those most used ones.

Tonal function of these chords is as SD and momentary scales applied to each one are defined by kinds.

maj7: Lydian

m7: Dorian

7: Lydian b7 (except alterations indicated on the chord)

m7b5: Locrian or Locrian 9 (of VI degree of the melodic scale)

It may turn out that, depending on source of a chord, its momentary scale will be another, but these are used by convention, which does not limit us from making our own choice.

Even though modal interchange is usually done from the major mode (Ionian) with parallel chords of the other already mentioned modes, we shall not have to take this as a limitation at the time of building our progressions.

In harmonic analysis, the degree corresponding to the kind of chord (for example IVm7) will be used. If you want to go into further details, one may prefix the letters mi (modal interchange) and the mode of from which the chord comes.

We shall see several examples, their analysis and their scales.

Example 1

In the 2nd bar, the modal interchange is a II - V movement from the minor mode; the II stems from the Aeolian mode with a Locrian scale and the V from the harmonic with a diminished symmetric scale, which alters the 9 and the 11 (b9, #9 and #11) but not the 13.

In the 4th bar, a minor IV comes from the Aeolian mode, as m7 or m6, and will go, in both cases, to the Dorian scale. The IVm6 may be seen as a first inversion of IIm7b5, performing the same function of minor SD.

Example 2

An interesting sequence of maj7 chords. Bbmaj7 comes from the Mixolydian mode (bVIImaj7) and Abmaj7 from the Aeolian (bVImaj7). As we have seen, both take the Lydian scale.

Bbmaj7 could also derive from the Dorian mode: in such cases, the closest mode is chosen, i.e., the one with least difference alterations. In this example, the Mixolydian mode will only have an alteration differing from the Ionian mode, whereas the Dorian will have two.

Example 3

In the 3rd bar, the #IVm7b5 (from the Lydian) connects between the IV and the V with a chromatic bass. Its scale will be Locrian.

Example 4

In the 2nd bar, two chords stemming from the Aeolian mode, the IVm7 and the bVII7, take the Dorian and the Lydian scales, respectively. Although these chords form a II - V, both carry the function of minor SD, since the dominant does not resolve by a leap of a fourth or by a descending semitone.

In the 4rd bar, the Dbmaj7 coming from the Phrygian mode (bIImaj7) creates the effect of a delay in the resolution of the dominant, and its voices descend chromatically towards the Imaj7. Its scale will be Lydian.

HARMONIZATION AND REHARMONIZATION OF MELODIES

Harmonization of melodies

For a given melody in a certain key, the process of harmonization will consist of chord progressions which we may build to “accompany” it.

The first step will be to recognize such notes in the scale-chord relationship of progressions we shall build.

We shall pose an exercise for practicing this.

Self-evaluation exercise

The following exercise will serve as a review and a self-evaluation to determine how much we have learned from this book and its applications. We shall take any note (for example, F), consider it the main note of a melody and place it in a major key (for example, C).

We shall look for every chord we have seen where this note may appear as: part of a seventh, or available tension, in the following order: diatonic chords, secondary dominants, secondary seconds and substitute dominants.

We shall create a chart from this where we shall describe: the degree in the chord (f (fundamental), 3, 5, 7), tension (9, 11, 13), and whether it is available or not, name and kind of chord, tonal function (T, SD, D, V7/X, etc.), momentary scale and its formula.

Let us look at the example: note F in C major key:

We see with this exercise that a note may be harmonized with a great amount of chords in accordance with the relationship it may have with almost each one of them. One should also bear in mind that a group of notes may be harmonized with the same chord, or the same note may be harmonized with various chords.

We could extend this exercise by adding chords: secondary seconds of the substitutes, diminished by a step, chords of modal interchange or repeat them in a minor key, modal keys or modulate them.

This is simply a practical exercise which will be of great usefulness for the correct choice of chords in the following steps when looking for a harmonization:

1- Determine the structure of the melody, phrase, counterphrase, part and form.

2- Establish a key

3- Begin with a simple progression: few chords in strong bars determining a first harmonic movement to which we want to steer and the moments of rest, tension and climax (T, SD, D). Here, it will be critical to keep in mind the concept of rhythm we have already seen.

4- The bass line: this may be before the first progression, establishing a movement of the basses on which we shall later determine the chords..

5- Insert chords and/or cadences. In the next step, we shall see this as a reharmonization of melodies.

6- Arrange movement of voices from the chords.

In the examples to follow, we shall apply these concepts together with others.

Reharmonization of melodies

The concept of reharmonization is based on restructuring of harmonic movements, either to enrich their variations or to create a new arrangement of the original theme, with full respect of the melody.

This change in harmony could lead us more or less away from the original theme, depending on our intention, using three resources: replacement, elimination or addition of chords or cadences which, in their turn, could be diatonic or non-diatonic.

One will, always have to consider the new scale-chord relationship which will establish the melody with new chords to be added or replaced, in accordance with the rules of melodic analysis.

We shall go from the simplest to the more complex based on the same fragment of an original theme with a simple harmony, describing the harmonic and the melodic analyses of each case.

Original theme

The rest is on a chord of I degree tonic (C) which transits to a medium tension (IV degree SD: F), returns to rest and becomes more tense with the typical movement IV - V (SD - D: F - G).

Replacement by diatonic chords with the same tonal function

In this case, the relationships of rest and tension are maintained but changing the “chroma” of harmony, since the new chords belong to another kind.

In the second line, the chords of a triad have been replaced by those of a seventh. The I degree (C) has been substituted by two chords with the function of a tonic (IIIm7 and VIm7: Em7 and Am7) and the IV degree SD by the IIm7 (Dm7) with the same function, inserting a typical cadence (III - VI - II – V), whose tonics move by leaps of a fourth.

Inserting non-diatonic chords

Once some chords have been established as an “objective” (the IV degree in first and second lines: Fmaj7), chords are inserted with certain tensions, which may be diatonic or non-diatonic, to mark the transit towards those chords.

In the first line, we shall insert dominants by extension (V7 and V7/IV) to transit towards the IV degree (Fmaj7), delaying movement between tritones (G7 - C7) with insertion of a secondary second (Gm7), while in the 4th bar a II -V (Bm7b5 - E7) movement in search of the VI degree will begin a chain of dominants by leaps of fourths resolving on IVmaj7 (Fmaj7). In the last bar, a IVm6 (Fm6), acting as a typical modal interchange with the Aeolian mode, will create a tension which will again resolve on the I.

Change of tonal center

This reharmonization is more distant because it plainly proposes a change of key. A detailed analysis of the melody will allow us to know towards which new tonal center we may conduct ourselves, surely a neighboring tone. In this case from C to F (a modulation by a fourth) will be convenient, since the characteristic note of modulation (Bb) is not present in the melody, which will provide us with new scale-chord relationships.

In the first line, the passage of the I to the IV (Fmaj7 towards Bbmaj7), is preceded by a VI degree which keeps sounding as a tonic chord whose bass descends by conjoint degrees to search for the Bb. In the last bar, two minor SDs (IVm7 and bVII7; Bbm7 and Eb7 of the Aeolian mode), in II - V order, mark the tendency of a return to the I degree. In this case, these two chords do not function as II - V since the dominant does not resolve the tritone, and therefore both are considered minor SDs.

In the second line, the first two bars copy the same movement (maj7 in three times, 7 in one). In the first case, the V7/IV (F7) looks for the IV (Bbmaj7) and, in the second bar, the IV7 of Blues (Bb7, stemming from the melodic scale) resolves on the bVII7 (Eb7: Aeolian mode) which may also be considered a substitute of A7. From there, a chain of dominants, inserting substitutes, produces a chromatic movement in the basses until arriving at V7 (C7) which will resolve on the I.

In the way of Blues

In spite of the structure not being typical of Blues (12 bars), reharmonization will try, in this case, to imitate that style, using the typical chords I7, IV7 and V7 (C7, F7 and G7) closing the reprise with a turn around which will return to I.

As we have seen, the possibilities of reharmonization are very ample and all may be correct if we apply the criteria employed in this chapter, originally and with a clear sense.

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PUBLISHED BOOKS BY THE AUTHOR

MODERN HARMONY STEP BY STEP is a book devoted to the study and understanding of modern harmony and its different musical styles, including Jazz, Blues, Rock, Funk, Pop among others.

All topics are oriented to improvisation, composition, arrangements and the analysis of this styles.

This book is divided into five chapters which are organized to help you progress step by step, as if you were taking a course.

Hundreds of examples illustrate the different concepts explained in each section, providing a practical way to bring theory to your musical instrument.

Major and minor scales - Modals and artificial scales - Diatonic and non diatonic chords, your tensions and your scales - Composition tools, Modern music analysis - Improvisation, and more.

Available in both printed and ebook format in Amazon

Modern Harmony, EXERCISES I This first exercise book is based on the first three chapters of Modern Harmony Step by Step: Basic concepts, Major key and Minor key.

You can practice in different keys and chords progressions all the modern harmony concepts:

Intervals, major and minor scales, its alterations; triads and 7th chords, tonal functions, secondary dominants, chain of dominants, substitute dominants, harmonic analysis, themes and melodies reharmonization, etc.

Ever since I wrote Modern Harmony Step by Step I had in mind to complete this work with an exercise book. Many readers also wrote me asking for it to put into practice all the theory I advanced in this first publication.

The main need was to practice the concepts in different keys, note combinations, chords, etc . Also to analyze different chord progressions and reharmonize them, chord substitution practice, resolutions, etc.

Available in both printed and ebook format in Amazon

Modern Harmony, EXERCISES II In this second harmony exercise book we will transit the path that will lead as from calculation to creativity, both composing or arranging music, searching scales in order to compose or improvise melodic lines, and interchange harmonies to comping them.

You can practice in different keys and progressions:

Scales: modals, relative to the minor modes, Diminished, Mixolydians with

their alterations, Harmonics, etc.

Harmonic and melodic analysis, modal harmony, hybrid chords, modulation, modal interchange and reharmonization.

Analyzing themes or creating your own cadences and progressions to apply these points.

Available in both printed and ebook format in Amazon

HOW TO IMPROVISE IN MODERN MUSIC is a book oriented towards learning and practice of musically improvising on any instrument in every style of modern music: Jazz, Blues, Rock, etc.

The examples and exercises in this book are accompanied by 44 tracks in mp3 format which will help you understand every concept and transfer it to your instrument.

Application of these tools for the development of phrases and solos are grouped in 5 chapters where we shall work on the elements indispensable for a creative musical development.

In each chapter, information will be ordered by degree of difficulty, accompanied by theoretical concepts which will help you understand their application.

IMPROVISATION: To play or to study? Creativity. How to use this book? The “Diary of practices.”

FORM: Recognizing the parts of the themes.

EAR: Recognizing notes, scales and chords.

RHYTHM: Phrasing beyond scales employed.

NOTES AND SCALES: Different scales and the tensions they generate on the chords.

CADENCES: Melodic lines chords.The solo.

You may work, independently, on those points you may consider necessary to develop from any level, creating your own diary of practices: Scales (pentatonic, modal, Mixolydian, artificial, chromatic, etc.), arpeggios and their combinations, tensions and resolutions, guide notes, target tones, modulation, Swing, Blues, Turnarounds, “The Solo” and its guidelines, etc.

Available in both printed and ebook format in Amazon