## 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.

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 Circle Of Fifths

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.

## Chord/Scale Relationships

Most improvisation in mainstream jazz is based on chord progressions. The chord progression is the sequence of chords that harmonizes the melody. Usually each chord lasts a measure; sometimes two, sometimes only half. A fakebook will give the symbol representing a particular chord above the corresponding point in the melody.

Even more important than the actual chords, however, are the scales implied by those chords. An improviser, when playing over a D minor chord, whose symbol is Dm, will normally play lines built from notes in the D dorian scale. This section documents the various chords and associated scales used in jazz. Familiarity with note names and locations is assumed.

If your aim is to become a jazz performer, you should practice improvising lines based on all the scales presented here, and in all twelve keys. Otherwise, you may stick to just one key per scale, but you should still practice improvising over each chord/scale relationship in order to better recognize their sounds.

## Jazz Fundamentals

Now that you are listening to jazz, you need to be more conscious of what you are hearing. The most important aspects to which you should pay attention are structure, swing, and creativity.

## Structure

Most jazz since the bebop era is based on a form that is actually quite similar to the sonata allegro form from classical theory: an optional introduction, the exposition or theme (possibly repeated), the development section, and the recapitulation, possibly followed by a coda. The introduction, if present, sets the tone for the piece; the exposition is the main melody; the development section is where the composer extends the ideas of the exposition; the recapitulation is a restatement of the theme; and the coda is an ending. In jazz terms, these sections of a piece would be called the the intro, the head (possibly repeated), the solo section, the head out, and possibly a coda or tag ending. The intro establishes the mood; the head is the main melody; the solo section is where the soloists improvise on the melody and/or chord progression of the tune; the head out is a restatement of the theme; and the coda or tag is an ending.

While not every piece follows this form, the vast majority of traditional jazz stays very close to it. During the solo section, the rhythm section generally keeps following the chord progression of the head while the soloists take turns improvising. Each time through the progression is called a chorus, and each soloist may take several choruses. In this respect, the theme-and-variations form of classical music is also a valid analogy. Each soloist plays an improvised variation on the theme.

The improvisation is the most important aspect of jazz, just as the development is often considered the most important part of the classical sonata. While listening to a piece, try to sing the theme to yourself behind the solos. You may notice that some soloists, particularly Thelonious Monk and Wayne Shorter, often base their solos on the melodic theme as much as on the chord progression. You will also notice that liberties are often taken with the theme itself; players such as Miles Davis, Coleman Hawkins, Sonny Rollins, and John Coltrane were especially adept at making personal statements even while just playing the head.

There are two very common forms for a head or theme in jazz. The first is the blues form, which is normally a twelve bar form. There are many variants on blues chord progressions, but most are based on the idea of three four bar phrases. In its original form, the second phrase would be a repeat of the first, and the third would be an answer to that phrase, although this convention is rarely adhered to in jazz. You may wish to check out the blues progressions listed later to get an idea of what they sound like, so you can recognize blues forms when you hear them. Liner notes and song titles will also often help identify which tunes are based on the blues. Some well known jazz tunes based on blues progressions include “Now’s The Time” and “Billie’s Bounce” by Charlie Parker, “Straight, No Chaser” and “Blue Monk” by Thelonious Monk, and “Freddie Freeloader” and “All Blues” by Miles Davis.

The other common form in jazz is the AABA song form, used extensively in popular music from the turn of the century until the dawn of rock and roll. This form consists two sections, called the verse or A-section and the bridge. The form is verse 1, verse 2, bridge, verse 3. The verses are similar or identical except for the lyrics and perhaps the last two bars. The song “I Got Rhythm” by George Gershwin, is one example of an AABA form. There are literally hundreds of tunes based on the chord progression to that tune, including “Anthropology” by Charlie Parker and “Oleo” by Sonny Rollins. Other songs with the AABA form include “Darn That Dream” by Jimmy Van Heusen, and “There Is No Greater Love” by Isham Jones. Songs such as these, popular songs from the first half of the century that have been interpreted by many jazz musicians, are often called standards.

These structures are only guidelines. Musicians such as Cecil Taylor showed us long ago that it is possible to express oneself without such well defined structures, and indeed this type of expression is often more personal that any more organized form. I have described these common structures to help you understand the context in which many musicians work, not to suggest that they are the only way. You should learn to discern for yourself when listening to other musicians what type of structures they are using, if any. You should also decide for yourself which structures to use in your own playing.

## Swing

Understanding the structure of the music is the first step toward an increased appreciation of it. The rest of this primer will deal mainly with hands-on musical examples. Before you delve into the theory, however, you need to develop a feel for swing. This is part of the rationale behind doing so much listening, since it is virtually impossible to teach swing analytically. Nonetheless, I will try to explain what you should be hearing and trying to achieve in your own playing.

### Definition

The most basic element of swing is the swing eighth note. In classical music, a set of eighth notes in 4/4 time are meant to take exactly one half of a beat each. This style is called straight eighth notes. Play a C major scale “C, D, E, F, G, A, B, C” in straight eighth notes. If you have a metronome, set it to 96 beats per minute. Those are quarter notes, “one, two, three, four”. Subdivide this in your mind, “one and two and three and four and”.

A common approximation to swing eighth notes uses triplets. The basic beats are be subdivided in your mind as “one-and-uh two-and-uh three-and-uh four-and-uh”, and you play only on the beat and on the “uh”. The first note of every beat will be twice as long as the second. This will sound like Morse Code dash-dot-dash-dot-dash-dot-dash-dot and is far too exaggerated for most jazz purposes. Somewhere in between straight eighth notes (1:1 ratio between first and second note) and triplets (2:1 ratio) lie true swing eighth notes. I cannot give an exact ratio, however, because it varies depending on the tempo and the style of the piece. In general, the faster the tempo, the straighter the eighth notes. Also, pre-bebop era players often use a more exaggerated swing than later performers, even at the same tempo. No matter what the ratio, the second “half” of each beat is usually accented, and beats two and four are usually accented as well. Again, the amount of accent depends on the player and the situation.

There is also the issue of playing behind or ahead of the beat. When Dexter Gordon plays, even the notes that should fall on the beat are usually played a little bit late. This is often called laying back. It can lend a more relaxed feel to the music, whereas playing notes that should fall on the beat a little bit early can have the opposite effect. Bassists often play slightly ahead of the beat, particularly at faster tempos, to keep the music driving forward.

Not all styles of jazz use swing in the same way. Most Latin jazz styles and many fusion and modern styles use straight eighths, or eighth notes that are only slightly swung. Shuffles and some other rock styles use very exaggerated swing. Listen closely to recordings in different styles, paying attention to the differences. Do not be fooled into thinking that swing is a universal constant.

### Practicing Swing

Learning to play natural sounding swing eighth notes is often the hardest part of learning to play jazz, since it can sound so bad until you can do it well. There are some techniques that can help you overcome this initial awkward stage.

If you have been listening carefully to other musicians, you may be better at recognizing swing than at playing it. Therefore, I highly recommend recording yourself playing swing eighth notes at various tempos, and then listening to yourself on tape. You can judge for yourself whether your swing sounds natural or forced. It has been said that if you cannot swing unaccompanied, you cannot swing. It is important to work on your own concept of swing in this way so that your perception of how you sound is not influenced by the sound of your accompanists.

You should work on your swing no matter what you are playing. When you practice scales, work on swing as well as simply playing the right notes. Try varying the rhythm you use to play the scale. In addition to scales, you should try practicing swing when playing other exercises or songs. Any practice method book or fakebook will probably contain several appropriate pieces. Try playing songs with many consecutive eighth notes, but also try songs with longer notes and rests. Having to play many consecutive eighth notes can make you too self-conscious of your swing.

While being able to swing unaccompanied is important, it is not easy to do at first, and when developing your swing concept, it can also help to hear it occasionally in the context of a group performance. One thing that would help at times is to have a rhythm section accompaniment. If you have Band-In-A-Box, you can program it to play endless choruses of C major, and then you can practice playing or improvising on your C major scale while working on your swing. Aebersold records can provide accompaniment as well, but be aware that most of the tunes have many chord changes and are too complex to use for this purpose. There are a few suitable tracks, however, such as some of those on Volumes 1, 16, 21, 24, and 54, which are geared toward beginners. The books included with these, especially the first four, also contain some useful instructional material.

If you have a partner, or a tape recorder, or a sequencer (computer hardware and/or software to record and play back on a synthesizer) you can create do-it-yourself accompaniment. The basic components of a swing drum beat are the ride pattern and the hi-hat pattern. The ride cymbal pattern, at its most basic, is “1, 2 and, 3, 4 and”; or, phonetically, “ding ding-a ding ding-a”. The eighth notes on 2 and 4 should be swung, of course. The hi-hat is closed (with the foot pedal) on 2 and 4. Walking bass lines can be constructed by following a few simple rules. First, play quarter notes. Second, keep them in the two octaves below middle C. Third, play only notes from the scale on which you are working. Fourth, most notes should be only a step away from the previous note, although occasional leaps are acceptable. For instance, a C major bass line might consist of “C, D, E, F, G, E, F, G, A, B, A, G, F, E, D, B, C”. You will need a lot of patience to create your own accompaniment with a tape recorder, since you will want to record many measures so you do not have to keep rewinding the tape when improvising later. A sequencer will allow you to set up loops, so you can record only a few measures and have them repeat endlessly.

## Creativity

### The Creative Process

Trumpet player Clark Terry summarizes the creative process as “imitate, assimilate, innovate”. Listening to other musicians can give you ideas you may wish to develop further, and being able to successfully duplicate what they are doing is one step toward being able to express yourself. Next, you must understand why the things you are playing sound the way they do, so that when you want to create a particular sound, you will know how to achieve it. The theory presented in the following sections can help you structure your thoughts, and can also help you identify the sounds you hear. However, analytic processes are an aid to the creative process, not a replacement for it. Two analogies, one with language and one with mathematics, should help make this clear.

When you began to speak, you learned at first by listening to others and imitating them. Gradually, you became aware of grammar, and eventually the grammar was codified for you in English classes. Your vocabulary has probably been growing ever since you spoke your first word. In both writing and conversation, your tools are your knowledge of grammar, vocabulary, and appropriate subject matter. To write or say anything interesting, however, you must have a certain amount of inspiration. It is not sufficient to merely string together grammatically correct phrases of words. What you have to say is generally more important than how you say it, although proper use of the language can help to get your point across. Similarly, in music, knowledge of theory and fundamentals are the tools of composition and improvisation, but inspiration plays the most important role in determining your success. It is not enough to merely play the “right” notes; you must also play interesting music. Jazz improvisation is often likened to “telling a story”, and, like a good story, should be well structured and also convey something interesting to the listener.

In mathematics, creativity can often be crucial as well. Learning the various axioms, formulas, and equations normally does not tell you how to solve a particular word problem, integrate a certain function, or prove a new theorem. Some ingenuity is required to be able to apply your knowledge to the problem at hand. Often, knowing how similar problems have been solved in the past can give you an idea of where to start, and experience working with a particular type of problem can help direct you. In all but the simplest of math problems, however, some original thinking is required. Similarly, in jazz, your familiarity with the works of other musicians can help you get started, and your knowledge of theory can help direct you, but in order to be a successful improviser, you will need to be creative. Just as long columns of numbers are not particularly interesting, even if they add up correctly, neither is an improvisation that consists of nothing but scales and patterns based on those scales.

Your listening experience, your knowledge of music theory, and experimentation on your instrument will define the musical context in which you are able to express yourself. You should continually strive to expand that context by listening to many different musicians, analyzing what you hear, and practicing as much as possible. Still, the final ingredient, the inspiration, you will have to find on your own.

### Playing

You should by now, if you have not already, be starting to improvise. You should start the same way you began to practice swing: alone and unaccompanied at first, with a tape recorder if possible, and then with some sort of rhythm section accompaniment. Again, Band-In-A-Box, Aebersold records, or do-it-yourself accompaniment will be invaluable.

For your first attempts at improvisation, pick a key with which you are comfortable and then start to play whatever comes into your head. Invent little melodies that use mainly notes from the selected scale. Do not try to fill all available space with notes. Instead, concentrate on hearing a short phrase in your head, and then try to play that phrase. Do not worry if this means there are breaks of several seconds or more between phrases. Miles Davis used this style of phrasing all the time.

At some point while improvising in a given key, try playing notes that are not in that key. Playing notes that are not in the current key is sometimes called playing outside. You will find that in many cases, it sounds very natural, while in other cases, it sounds dissonant, or harsh. The later sections on theory may help you understand why this is so, but your ear is the ultimate judge. When you finally run out of ideas in one key, you may wish to switch to another. You may also wish to try improvising without any key center at all. I believe this should be just as natural as improvising within a key.

Transcribing solos played by other musicians is one way to get some ideas of what to play. You can examine the structure of the solo, see how they use the various chord/scale relationships discussed later in this primer, and try to apply what you learn to your own playing. One of the best solos for a beginner to study is Miles Davis’ solo on “So What” from the album Kind Of Blue. The chord structure is simple: sixteen bars of D minor, followed by 8 bars of Eb minor, and then 8 bars of D minor again. Miles’ lines are easy enough to transcribe note for note. The theory sections below will help you understand the framework in which Miles was working, but transcribing his solo will help you see what he was doing within that framework.

Another way to get ideas for soloing is by using patterns, or short phrases that you have practiced beforehand and know will fit the chord changes at a particular point. In general, improvising is much more than simply stringing together patterns, but pattern practicing can be a good way to develop your technique as well as your ear, particularly if you practice your patterns in all twelve keys. There are several books, including Jerry Coker’s Patterns For Jazz, that give some useful patterns.

A technique used often in the bebop era and since is quoting, or using a recognizable phrase from another composition or well-known recorded improvisation as part of one’s own improvisation. This is also sometimes called interpolation. You may have noticed this taking place in solos you have heard. There is usually some humor value in quoting, particularly if the interpolated work is something silly like “Pop Goes The Weasel”.

The most important obstacles for a beginning improviser to overcome are his or her own inhibitions. At first, when practicing improvisation by yourself, you may feel you have no idea what to play. Once you have reached the point where you feel comfortable in the practice room and decide it is time to play with other musicians, you may feel self-conscious about playing in front of your peers. Finally, when you can play with other musicians in private, you may feel nervous when you first perform in public. I have no miracle cures for these problems. I can only suggest you play as much as possible at each stage, and continually push yourself to take chances.