There are twelve different notes in traditional music: C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, and B. After the B comes the C an octave higher than the first C, and this cycle continues. This sequence is called the chromatic scale. Each step in this scale is called a half step or semitone. The interval between two notes is defined by the number of half steps between them. Two notes a half step apart, like C and C#, define a minor second. Notes that are two half steps apart, like C and D, define a major second. This is also called a whole step. Expanding by half steps, the remaining intervals are the minor third, major third, perfect fourth, tritone, perfect fifth, minor sixth, major sixth, minor seventh, major seventh, and finally, the octave.
Most of these intervals have other names, as well. For example, a tritone is sometimes called an augmented fourth if the spelling of the notes in the interval appears to describe a fourth. For example, the tritone interval from C to F# is called an augmented fourth, because the interval from C to F is a perfect fourth. Conversely, if the spelling of the notes in the interval appears to describe a fifth, then the tritone is sometimes called a diminished fifth. For example, the tritone interval from C to Gb, which is actually the same as the interval from C to F#, is called a diminished fifth, because the interval from C to G is a perfect fifth. In general, if any major or perfect interval is expanded by a half step by changing an accidental (the flat or sharp indication on the note), the resultant interval is called augmented, and if any minor or perfect interval is reduced by a half step by changing an accidental, the resultant interval is called diminished.
All scales are simply subsets of the chromatic scale. Most scales have 7 different notes, although some have 5, 6, or 8. The simplest scale, which will be used as an example for the discussion of chords, is the C major scale, which is “C, D, E, F, G, A, B”. A major scale is defined by the intervals between these notes: “W W H W W W (H)”, where “W” indicates a whole step and “H” a half. Thus, a G major scale is “G, A, B, C, D, E, F#”, with a half step leading to the G that would start the next octave.
The scale consisting of the same notes as the C major scale, but starting on A (“A, B, C, D, E, F, G”) is the A minor scale. This is called the relative minor of C major, since it is a minor scale built from the same notes. The relative minor of any major scale is formed by playing the same notes starting on the sixth note of the major scale. Thus, the relative minor of G major is E minor.
A piece that is based on a particular scale is said to be in the key of that scale. For instance, a piece based on the notes C, D, E, F, G, A, and B is said to be in the key of either C major or A minor. The chord progression of the piece may distinguish between the two. Similarly, a piece based on the notes G, A, B, C, D, E, and F# is either in G major or E minor. If the word “major” or “minor” is omitted, “major” is assumed. The collection of flat and sharp notes in a scale defines the key signature of the associated key. Thus, the key signature of G major is F#.
You should try playing various major and minor scales. You may wish to write out the notes for each, or buy a book like Dan Haerle’s Scales For Jazz Improvisation, which contains many scales already written out for you. The more complex scales described below should be written out and practiced as well. Listeners should try enough of each scale to become familiar with the sound. In many cases, just one key will suffice. Performers should practice each scale in all twelve keys over the entire range of their instruments until they have complete mastery over all of them. However, do not become so bogged down in the various scales that you become frustrated and never advance to the next sections on applying the theory. You should start on the applications once you have some command of the dorian, mixolydian, lydian, and locrian modes discussed below.
A chord is a set of notes, usually played at the same time, that form a particular harmonic relationship with each other. The most basic chord is the triad. A triad, as the name implies, is composed of three notes, separated by intervals of a third. For instance, the notes C, E, and G played together comprise a C major triad. It is so called because the three notes come from the beginning of the C major scale. The interval from C to E is a major third, and from E to G a minor third. These intervals define a major triad. A G major triad is composed of G, B, and D; other major triads are constructed similarly.
The notes A, C, and E comprise an A minor triad, so called because the notes come from the beginning of the A minor scale. The interval from A to C is a minor third, and from C to E a major third. These intervals define a minor triad. An E minor triad is composed of E, G, and B; other minor triads are constructed similarly.
The two other types of triads are the diminished triad and the augmented triad. A diminished triad is like a minor triad, but the major third on top is reduced to a minor third. Thus, an A diminished triad would be formed by changing the E in an A minor triad to an Eb. An augmented triad is like a major triad, but the minor third on top is increased to a major third. Thus, a C augmented triad would be formed by changing the G in a C major triad to a G#. Note that a diminished triad can be formed from three notes of the major scale; for example, B, D, and F from C major. However, there are no naturally occurring augmented triads in the major or minor scales.
A triad can be extended by adding more thirds on top. For instance, if you take the C major triad (“C E G”), and add B, you have a major seventh chord (Cmaj7 or CM7), so called because the notes come from the C major scale. Similarly, if you take an A minor triad (“A C E”), and add G, you have a minor seventh chord (Am7 or A-7), so called because the notes come from the A minor scale. The most common type of seventh chord in classical harmony, however, is the dominant seventh, which is obtained by adding a minor seventh to the major triad built on the fifth note of the major scale, also called the dominant. For instance, in the key of C major, the fifth note is G, so a G major triad (G B D) with a seventh added (F) is a dominant seventh chord (G7).
These three types of seventh chords have a very important relationship to each other. In any major key, for example, C, the chord built on the second step of the scale is a minor seventh chord; the chord built on the fifth step of the scale is a dominant seventh chord; and the seventh chord built on the root of the scale, also called the tonic, is a major seventh chord. Roman numerals are often used to indicate scale degrees, with capital letters indicating major triads and their sevenths, and lower case letters indicating minor triads and their sevenths. The sequence Dm7 – G7 – Cmaj7 in the key of C can thus be represented as ii-V-I. This is a very common chord progression in jazz, and is discussed in much detail later. The motion of roots in this progression is upwards by perfect fourth, or, equivalently, downward by perfect fifth. This is one of the strongest resolutions in classical harmony as well.
Sevenths can also be added to diminished triads or augmented triads. In the case of a diminished triad, the third added can either be a minor third, which creates a fully diminished seventh (for example, A C Eb Gb, or Adim) or a major third, which creates a half diminished seventh (for example, B D F A, or Bm7b5). A minor third can be added to an augmented triad, although this is a very rarely used chord that does not have a standard name in classical theory. Adding a major third to an augmented triad would create a seventh chord in name only, since added note is a duplicate an octave higher of the root (lowest note) of the chord. For example, C E G# C. Technically, the seventh is a B# instead of a C, but in modern tuning systems these are the same note. Two notes that have different names but the same pitch, like B# and C or F# and Gb, are called enharmonic. Classical theory is usually very picky about the correct enharmonic spelling of a chord, but in jazz, the most convenient spelling is often used.
More extensions to all types of seventh chords can be created by adding more thirds. For instance, the C major seventh chord (C E G B) can be extended into a C major ninth by adding D. These further extensions, and alterations formed by raising or lowering them by a half step, are the trademarks of jazz harmony, and are discussed in sections below. While there is an almost infinite variety of possible chords, most chords commonly used in jazz can be classified as either major chords, minor chords, dominant chords, or half diminished chords. Fully diminished chords and augmented chords are used as well, but as will be seen, they are often used as substitutes for one of these four basic types of chords.
The interval of a perfect fifth is significant in many ways in music theory. Many people use a device called the circle of fifths to illustrate this significance. Picture a circle in which the circumference has been divided into twelve equal parts, much like the face of a clock. Put the letter C at the top of the circle, and then label the other points clockwise G, D, A, E, B, F#/Gb, C#/Db, G#/Ab, D#/Eb, A#/Bb, and F. The interval between any two adjacent notes is a perfect fifth. Note that each note of the chromatic scale is included exactly once in the circle.
One application of the circle of fifths is in determining key signatures. The key of C major has no sharps or flats. As you move clockwise around the circle, each new key signature adds one sharp. For example, G major has one sharp (F#); D major has two (F# and C#); A major has three (F#, C#, and G#); E major has four (F#, C#, G#, and D#); and so forth. Also note that the sharps added at each step themselves trace the circle of fifths, starting with F# (added in G major), then C# (in D), then G# (in A), then D# (in E), and so forth. Conversely, if you trace the circle counterclockwise, the key signatures add flats. For example, F major has one flat (Bb); Bb major has two (Bb and Eb); Eb major has three (Bb, Eb, and Ab); and so forth. The flats added at each step also trace the circle of fifths, starting with Bb (added in F major), then Eb (in Bb), then Ab (in Eb), and so forth.
The circle of fifths can also define scales. Any set of seven consecutive notes can be arranged to form a major scale. Any set of five consecutive notes can be arranged to form a pentatonic scale, which is discussed later.
If the labels on the circle of fifths are considered as chord names, they show root movement downward by perfect fifth when read counter-clockwise. This root movement has already been observed to be one of the strongest resolutions there is, especially in the context of a ii-V-I chord progression. For example, a ii-V-I progression in F is Gm7 – C7 – F, and the names of these three chords can be read off the circle of fifths. One can also find the note a tritone away from a given note by simply looking diametrically across the circle. For example, a tritone away from G is Db, and these are directly across from each other. This can be useful in performing tritone substitutions, discussed later.