## Basic Theory

This section reviews the concepts of intervals, scales, keys, and chords from classical theory. Those readers with basic classical theory training should be able to skip this section if they wish.

### Intervals

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.

### Major And Minor Scales

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.

### Chords

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.

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.