Jazzology: The Encyclopedia of Jazz Theory for All Musicians

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CHAPTER 1 INTERVALS

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The next-to-smallest interval is the tone, or whole step. This is the distance between notes that are two keys apart on the piano. For instance, from C to D is a whole step. The semitone and tone form the basis for measurement of larger intervals.

Interval measurements have two parts: quantity and quality. The quantity, or numeric value, is determined by the musical alphabet: C D E F G A B. For example, the interval formed by the notes C and G will always be some type of 5th, regardless of the quality of C or G (flat or sharp).

Major and Perfect Intervals

The quality of an interval is determined by comparison with the intervals found in the major scale. When compared with a major scale, a whole step is found to be equal to the distance from the first to the second note, giving us yet another name for it: the major second.

It should be committed to memory that any major scale contains half steps (h) between scale degrees 3-4 and 7-8, and whole steps (W) between all other pairs of notes. The half steps in any scale can be indicated with a wedge-shaped mark, or caret symbol (^). Here’s the major scale in the key of C.

The distance from the root to the various pitches in the major scale form the basic intervals against which all others are measured. These eight intervals are divided into two basic types, perfect or major.

Perfect: unisons, 4ths, 5ths, octaves

Major: 2nds, 3rds, 6ths, 7ths

Minor, Diminished, and Augmented Intervals

A chromatic half step ), while a diatonic half step –A). The appearance on the staff may be different, but the interval is the same.

Major and perfect intervals may be augmented (increased in size) or diminished (reduced in size) by either type of half step to change their qualities.

Major and perfect intervals become augmented when the upper note is raised by a half step, or the lower note is lowered by a half step. The process may be referred to as augmentation.

before the lower note.

An augmented interval becomes doubly augmented when the upper note is raised by a half step, or the lower note is lowered by a half step.

When a major interval is diminished by a half step it becomes minor.

before the lower note.

Through diminution, minor and perfect intervals become diminished.

A diminished interval becomes doubly diminished when the upper note is lowered by a half step or the lower note is raised by a half step.

This illustration will help you remember the order of changing interval qualities. Notice that perfect intervals jump directly to diminished; there is no such interval as a minor 5th!

) are referred to as enharmonic equivalents.

When an interval is inverted (the order of the notes is changed, i.e. C to D becomes D to C) you’ll find its complementary partner. For instance, an inverted major 2nd is equal to a minor 7th, an inverted major 3rd is a minor 6th, and so on. Notice that inverted major intervals are minor (and vice versa) while inverted perfect intervals are still perfect. These interval pairs should also be memorized, to facilitate further study.

Inversions of Major Scale Intervals

Interval Abbreviations

Intervals are used so often in describing chords and scales that they are sometimes named in an extremely abbreviated way. Learn to recognize these variations in interval names.

Perfect and major intervals are implied by no mention of their quality at all: 5 for P5 (perfect 5th), 7 for M7 (major 7th), etc.

) is often used instead of augmented (or its abbreviations, aug or +).

) is often used instead of min or "m."

) instead of dim or d, or the diminished symbol (°).

instead of min or m, 2 instead of m2.

) instead of dim 7 instead of dim7 or d7.

3 is minor, 5 is diminished.

7, etc. (When naming notes, .)

The augmented 4th/diminished 5th intervals are also called the tritone, abbreviated TT. A tritone equals three whole steps.

The charts below list all the intervals up to the 13th, as they are most commonly named in the jazz idiom. (Not all possible augmented and diminished names are listed.)

Intervals smaller than an octave are called simple intervals.

Intervals larger than an octave are called compound intervals. They may be analyzed as a simple interval raised by an octave.

Consonant Intervals and Dissonant Intervals

A harmonic interval results if the notes are played at the same time, while a melodic interval occurs when the notes are played successively. The method of measuring intervals is the same for both harmonic and melodic intervals.

Harmonic intervals may be either consonant or dissonant.

Consonant intervals occur when two pitches that are sounded together produce an agreeable sound. Consonance gives the impression of unity, cohesion, and stability.

Dissonant intervals, on the other hand, occur when two pitches that are sounded together produce a sound that seems to require modification or resolution. Dissonance gives the impression of instability, tension, and the need to resolve to a consonance.

Consonant intervals are subdivided into three types:

Enharmonically equivalent intervals usually appear in different contexts and thus should not be considered the same as their counterparts, i.e. while a minor 3rd is consonant, an augmented 2nd is dissonant.

The consonance or dissonance of the perfect 4th interval also depends on the context in which it occurs. If it stands alone on the root of a key center, it is dissonant. It may be consonant if it occurs over other notes as part of a chord.

This is a simplification of the traditional rules of consonance and dissonance that were established during the Renaissance. Although the descriptions may not apply to the way modern ears hear these intervals, the principles still form the basis for Western harmonic practice, including jazz harmony.

Chapter 1 Exercises

1. Identify the following intervals.

2. Provide the following intervals above the given pitch.

3. Write the following intervals (from any pitch).

4. Write the following intervals above the given note.

5. Identify each interval as either consonant or dissonant by writing con or diss below.

CHAPTER 2 JAZZ HARMONY BASICS

Two or more notes played simultaneously form a chord. Chords are traditionally constructed by stacking 3rds on top of each other. This method of building chords is called tertian harmony. The note at the bottom of the stack of 3rds is called the root of the chord. The next note, a 3rd higher, is called the 3rd, and the next higher, a 5th above the root, is called the 5th, and so on. A complete list of chords would include 7th, 9th, 11 th, and 13th chords. They are so named because of the interval between the root and the highest note in the stack of 3rds.

Triads

As the name implies, a triad consists of three notes, or two superimposed 3rds:

The triad type depends on the quality of the 3rds that are included in the chord. The most convenient way to build or analyze triads is to start with a major triad, by taking the 1st, 3rd, and 5th notes of the major scale. The other forms can be seen as alterations of the major triad, as shown below.

Here are triads built from the root C, and their commonly-used names.

Major Triad (1-3-5): C, CM, Cmaj

3–5): C-, Cm, Cmin

5): C+, Caug

5): C°, Cdim

In the suspended triad, the 4th replaces the 3rd. Despite the implications of the word suspension (and the rules of consonance and dissonance), the 4th does not need to resolve to the 3rd (although it may). In jazz, unlike classical music, the suspended triad (usually called a sus chord) is a fixed and stable harmonic structure unto itself.

Suspended Triad (1-4-5): C4, Csus or Csus4

In order to hear the sonority of each triad quality, play the root in the bass with your left hand and the triad with your right hand. The resultant sound is stronger and easier to recognize when the root is reinforced in this way.

All the previous triads are said to be in root position: the root of the chord lies at the bottom of the triad.

Triad Inversion

Inverting a triad rearranges the notes so that the 3rd or the 5th is placed at the bottom of the triad structure. The lowest note is called the bass, which is not to be confused with the root. The bass is the lowest note in any chord inversion. The root is the note on which the chord is built and cannot change.

Play the triad qualities discussed so far in all twelve keys, in all possible inversions. Include them in your practice routine until you can play them without using the book or writing them down. Wind players should practice triad arpeggios (chords played one note at a time) in all keys and inversions.

7th Chords

7th chords provide the building blocks of jazz harmony. Unlike classical music, which relies upon the triad as the fundamental structure, jazz uses triads infrequently. Instead, most jazz styles employ 7th chords as the basic harmonic unit. A 7th chord is built by stacking three 3rds on top of one another so that the total distance from the root to the uppermost note forms the interval of a 7th. There are seven commonly-used types of 7th chords. While the content of these chords is specific and unchanging, the symbols used to designate these chords can vary substantially, as can be seen below.

The Major 7th Chord, written: M7, maj7, or 4

The Minor 7th Chord, written: -7, min7, or m7

5), or ∅

The Diminished 7th Chord, written: °7 or dim7

The Dominant 7th Chord, written: 7

The Suspended Dominant 7th Chord, written: 7sus or 7sus4

Here are the correct intervallic spellings of these chords with examples built on C.

As with triads, 7th chords should be practiced in all keys, in all inversions, without reading them. Wind (and indeed all) players should practice them as arpeggiated lines in all keys and inversions.

Chord Extensions

A chord is generally extended by adding notes that increase its richness and dissonance without altering its function. These notes are called extensions, tensions, or upper structures; the results are called extended chords, and in some cases polychords or polytonal/polymodal chords.

Extensions beyond the 7th follow the same pattern of construction as 7th chords with a general rule being that if a chord tone of the triad is altered (raised or lowered), the quality is also altered, while alteration of extensions does not change the quality of the chord. Here are some examples of 7th chords with natural and altered extensions.

Not all possible extensions and alterations are used in jazz harmony. The ones that work with a specific chord type are said to be available. The ear is one’s best guide. The following suggestions for available extensions are intended to apply to bebop or straight-ahead (as opposed to free, avant garde, or modern) jazz harmony, and are sanctioned by more than fifty years of nearly total consensus among jazz musicians.

Major triad:

add 6th and 9th,

add M7 and 13,

11 to either of the above for extra dissonance.

Minor 7th (functioning as ii):

(See Chapter 3 for more on chord function.)

add 9,

add 11 and/or 13 above the 9th for extra dissonance.

Minor triad (functioning as i):

add 6 and 9,

add M7,

add 9 and/or 13 above for extra dissonance.

7sus4:

add 9 and/or 13.

Dominant 7th (functioning as V7):

add 9 and possibly 13,

13,

11 to either of the above for extra dissonance. In short, V7 can take all extensions except 11 and M7.

Diminished 7th:

may add the note a whole step above any chord tone.

diminished chord extensions do not usually receive numbers.

Half-Diminished