Music Fundamentals

The western musical system is made up of a series of 12 pitches. Each set of neighboring pitches is separated by a half step. The names of the pitches are as follows:

Any pitch can be raised ½ step by adding a sharp(#) or removing an existing flat (b). Any pitch can be lowered a half step by adding a flat or removing an existing sharp. This sequence of pitches in order makes a chromatic scale. Once the last pitch is reached, the scale cycles from the beginning again.

An interval is the distance between two pitches. Different interval sizes have different names:

The most basic of all scales is the major scale. Starting on C, a major scale is constructed as follows:

As with the chromatic scale, the pattern recycles itself after the 7^th scale degree. The scale can be transposed to any key by starting on a different pitch and keeping the intervals between the notes in the scale the same. Another fundamental scale is the harmonic minor scale. Starting on C a harmonic minor scale would be constructed as follows:

As with the major scale, the harmonic minor scale can be transposed to begin on any pitch.

Measures

The building block for rhythm is most often the quarter note. Every note’s rhythmic value is usually compared to a quarter note. A note longer than a quarter note is notated as the number of quarter notes it occupies, while a note shorter than a quarter note is referred to as the portion of a quarter notes length that it occupies. A quarter note receives its name because it is usually a quarter the length of another important rhythmic unit: the measure (or bar). Most frequently, a measure occupies the time space of four quarter notes. While the quarter note is the fundamental frame of reference for rhythm, the measure is the fundamental cell in which these rhythms are grouped.

Building Jazz Chords

A chord is a collection of notes called chord tones that are played simultaneously. Using the major scale as a basis, jazz chords can be built. Jazz chords are noted in the form

{root}{quality}^{{extensions}{altered tones}}

Chord tones are referred to by the scale degree of the chord tone relative to the root of the chord. The most common chord tones are the root (1), the third, the fifth and the seventh.

Conventions for Chord Quality Notation

In addition to these chord tones, a chord can have any number of extensions. Each extension is referred to numerically. The number of the extension is equal to seven plus the number of the chord tone. This is because chord extensions are usually played an octave above chord tones. For example, the 13^th of a chord is actually the 6^th scale degree relative to the root of the chord.

The quality of a chord is determined by the interval between the root of the chord and each of its chord tones. There are three main chord qualities: major, dominant, and minor. The following conventions are adhered to when constructing jazz chords:

Conventions for Chord Extension Notation

Introduction to Jazz Harmony

This section will attempt to provide a basic understand of jazz harmony from the ground up. Harmony is the way in which chords relate to each other. Every song has a set of chord changes that form its harmonic basis. A set of chord changes is any number of chords, each having a specific duration. These chords provide a harmonic structure for the melody of a song and are again used during the improvised section of a song, repeating them once they end. The way in which a chord relates to the chords around it determines it’s harmonic function (or function for short). There are three basic chord functions: a tonic function, a dominant function, or an embellishing function. It is very important that the reader note the difference between chord functions and chord qualities. A chord’s quality is solely a result of the chord tones and extensions of a chord. A chord’s function refers to the way in which a chord relates harmonically to the chords around it. For instance, a dominant functioning chord is different from a dominant quality chord.

The tonic chord is the harmonic “home.” All chords pull toward it, and there is little harmonic tension (how strongly a chord pulls to other chords) when the harmony remains on the tonic chord. The dominant chord represents the point of greatest harmonic tension. The dominant chord pulls most strongly toward the tonic. The remaining chords are somewhere in between the tonic and dominant in terms of harmonic tension. These are called embellishing chords because in some way they serve to get from the dominant to the tonic or vice-versa.

Chord functions are notated using roman numerals. Each roman numeral refers to the scale degree of the root of the chord relative to the tonic. Capital numerals are used for major chords, and lower case numerals for minor chords. For instance, if the tonic is C (or we are in the key of C) we could have the following chord functions:

Note that all these functions are diatonic, that is, they only use chord tones in the tonic key (C in this case). When the chords are diatonic, often the chord qualities are implied and need not be stated. For instance, a IV is implied to be a major 7 chord and a V is implied to be a dominant 7 chord.

Tonic functioning chords are always the I, I7 or i chord because they serve as the basis for determining chord function. In jazz harmony they are several chords which could have a dominant function. The most common chords of dominant function are:

1. V7

2. bII of any chord quality (major, dominant or minor)

3. bVII7

One other chord that has a dominant function is the ii-V7-I. The ii-V7-I is the most common chord progression in jazz. It can resolve to a minor chord (ii-V7-i), a major chord (ii-V7-I) or a dominant chord (ii-V7-I7). Although it is referred to as a ii-V7-I, the V7 chord could actually be any dominant from the above list (i.e. a bII or a bVII). In addition to this, sometimes a II7 is substituted for the ii. The ii and V chords in a ii-V7-I function together as a chord of dominant function.

Passing chords

Passing chords are chords which add interest to a long tonic chord without altering the harmony significantly. A group of chords can be defined as passing chords when they meet the following criteria:

1. They begin with a tonic.

2. The root movement is by half and whole steps diatonically.

3. The chord qualities are diatonic with respect to the tonic.

4. None of the chords has any other possible function

All passing chords have an embellishing function.

For instance, if we are in the key of F and had the following: (it should be noted that a vertical bar indicates a new measure)

The chord progression could be embellished in the following manner:

An experienced improviser realizes that the last three chords in the chord progression are passing chords which embellish the first chord.

Specific Rules For Determining Chord Functions

Chord function can be categorized in a very general way by determining whether a chord is a tonic function chord, an embellishing function chord or a dominant function chord.

Major chord quality:

Dominant chord quality:

Minor chord quality:

Given the specific function of a chord, the choices for extensions can be derived:

Major Quality Chords:

Minor Quality chords:

Dominant Quality chords:

Chord Substitutions

All dominant function chords can be substituted for each other.

Any single dominant function chord can be substituted for an entire ii-V7.

A ii-V7 can be substituted for any dominant function chord.

Passing chords can be substituted for a tonic chord.

A tonic chord can be substituted for several passing chords.

Any chord can be preceded by a chord of dominant function.