Cycles giant steps.pdf

The ‘Giant Steps’ Progression and Cycle Diagrams

Dan Adler

One of the challenges faced by any intermediate Jazz student is to master the Coltrane

changes in every key. The term Coltrane changes refers to the harmonic progression

associated with the tune ‘Giant Steps’ by John Coltrane. Besides using this progression as

the basis of ‘Giant Steps’, Coltrane also applied these changes as a substitute pattern over

the chord changes of a number of standard tunes to which he composed new melodies,

such as Countdown (based on Tune Up), Sattelite (based on How High The Moon), 26-2

(based on Confirmation). In some cases (Body and Soul, But Not For Me) Coltrane

applied the same changes as substitute patterns for turnarounds using slight modifications

of the original melodies. Clearly, Coltrane viewed this chord progression as a formula

that can be applied in many contexts and in many keys.

Most approaches to learning the Coltrane harmonic progressions are based on

memorization, and when faced with memorizing a long chord sequence in 12 keys – most

people find the task daunting. However, you will see in this article that the ‘Giant Steps’

harmonic progression is a musical cycle , and like all musical cycles is based on easy to

memorize formulas.

I started to investigate musical cycles systematically following a master class by the great

alto saxophonist Gary Bartz at Michiko Rehearsal Studios in NYC, where he made the

statement that all the secrets of Jazz harmonic progressions and substitutions can be

deduced from studying cycles. I was fascinated by this idea that everything from II-V-I

patterns to Tritone substitutions to Coltrane changes can all be deduced from a simple set

of rules, and so I started down the path of understanding the principles behind cycles .

Basic Cycle Math

A musical cycle is an ordered set of notes obtained by successively applying the same

interval. In other words: take any interval from a starting note, find the next note, take the

same interval from that note, and so on. When do you stop? When you reach the same

note you started out with. Hence the name cycle .

Lets look at some simple math relating to cycles. First of all, there are 12 semi-tones

(notes) in an octave. On the other hand, interval numbers are based on the location of the

note in the 7-note major scale. We think of an 8 th interval as an octave, and we use major

and minor (or augmented and diminished ) to modify the intervals. Thus, a half step is

called a minor 2 nd (m2), and a whole step is called a major 2 nd (M2).

Now, you probably already know the cycle of fifths, so you know that you can read that

cycle as 5 th s in one direction and as 4 th s in the other direction. What’s the general

“‘Giant Steps’ and Cycle Diagrams” by Dan Adler

principle here? Any cycle will have the property that if you read it one-way or the other –

the intervals will add up to 9 (e.g. for the cycle of fifths: 4+5 = 9). There are 12 semi-

tones, and a major scale octave, why do the intervals then add up to 9 instead of 7 (7

being the number of intervals between 8 scale notes)? Before you read on, you might

want to stop for a moment and try to figure this out yourself.

The answer is that we count intervals in ordinal numbers starting from 1 (unison). If we

were counting the spaces between the notes, we would count a unison as 0 rather than 1,

and a 2 nd as 1 – but since we count in this way in both directions – we add one from both

directions and end up with 9 instead of 7. Following is one octave with the scale intervals

written above (counting up) and below (counting down) and you can see that the upper

number and the lower always add up to 9.

1 2 3 4 5 6 7 8

C D E F G A B C

8 7 6 5 4 3 2 1

If you expand this to include all 12 notes, you will notice that the numbers still add up to

9, and that one is always M (major) and the other is m (minor), or both are the same (the

tritone) or both are perfect (4 th and 5 th unison and octave).

1 m2 M2 m3 M3 4 TT 5 m6 M6 m7 M7 8 (up)

C C# D Eb E F Gb G Ab A Bb B C

8 M7 m7 M6 m6 5 TT 4 M3 m3 M2 m2 1 (down)

Now that we’ve got that mystery solved, lets get back to cycles. In order to systematically

cover all possible cycles, lets walk through all of the interval combinations above and

below each note and see what cycles each one yields. So, here’s the second puzzle for you

to think about before reading on: How many possible musical cycles are there?

The answer is that there are only 7 musical cycles. If you look at the sequence above

again, you will notice that we only have to walk half way left-to-right up to the tritone,

because from that point onwards the interval pairs simply get repeated (inverted) and

since a cycle goes in both directions – we will have already included them. So, there are

only 7 possible cycles in all of music. That’s pretty amazing if you think about it.

The next interesting point to think about is how many notes are there in each cycle before

we get back to the same note? Well, that varies from cycle to cycle. The maximum is,

obviously 12, and the minimum is clearly 1. What do you do when there are less notes in

the cycle than 12? You have multiple instances of the same cycle.

“‘Giant Steps’ and Cycle Diagrams” by Dan Adler

Enumerating the cycles

Lets enumerate all 7 possible cycles and see what we can learn from them. For simplicity,

I will start with the 2 cycles that encompass all 12 notes: the m2/M7 cycle (known as the

chromatic cycle ) and the 4/5 cycle (known as the cycle of fifths ).

The first cycle is the chromatic cycle. Walking clockwise, you get m2 intervals, and

counter clockwise you get M7 intervals. I am only showing flats since those are more

common as root movements in Jazz – but you should also think of the equivalent sharp

notes. Hopefully, you already know this cycle by heart, so there is nothing here to learn.

Figure 1: Chromatic Cycle (m2/M7)

The diagram below shows the cycle of fifths. In this cycle, if you walk clockwise, you

will be moving perfect 4 th each step, and if you walk counter-clockwise, you will be

moving a 5 th each step.

“‘Giant Steps’ and Cycle Diagrams” by Dan Adler

Figure 2: Cycle of Fifths (P4/P5)

It’s impossible to overstate the importance of the cycle of fifths in Jazz. In fact, if you

start from any note and walk clockwise 2 notes, you are basically covering a II-V-I

sequence. If you walk 4 notes – you are covering a III-VI-II-V chord sequence. If you

walk clockwise 6 notes, you get a sequence that is typically harmonized as bVm7b5 –

VII7 and then proceeds down to III-VI-II-V. You can use this cycle as the basis for many

reharmonizations by picking a target chord and “back-cycling” to it from any point that is

up to a tritone away (diagonal) on the cycle of fifths.

Did you notice some amazing symmetries between the chromatic cycle and the cycle of

fifths? The first thing to notice about both of these cycles is that the tritone (Gb or F#) is

in the middle of both cycles at the 6 o’clock position. The tritone divides the octave in

half. And you can get to it from the root by taking 6 succesive minor 2 nd s, 6 successive

Major 7 th s, 6 successive perfect 4 th s, or 6 successive perfect 5 th s.

In fact, if you trace the diagnoal between any two notes that are across from each other –

they form a tritone interval. This is true of both cycles ! No wonder people called the

tritone the devil’s interval !

As if that’s not surprising enough, did you notice that in both cycles, C, Eb, Gb and A are

in the same exact spot at the 12, 3, 6 and 9 o’clock positions? That works out because

going up three 4 th s is a minor 10 th which is equivalent to a minor 3 rd .

You can take the symmetry even further: take every other note in the cycle of 5 th s and flip

it with its tritone (which is diagonally across) – you get the chromatic cycle, and vice

versa. But then, you already knew that, didn’t you? It’s the tritone substitution! If you

take a II-V-I and flip the V with its tritone you get II-bII7-I which is a chromatic

progression. Similarly, III-VI-II-V becomes III-bIII7-II-bII. So, the chromatic cycle and

the cycle of fifths are related through the tritone substitution.

“‘Giant Steps’ and Cycle Diagrams” by Dan Adler

Five more cycles to go. Lets get the trivial one out of the way: the unison/octave cycle.

This is really a degenrated cycle of one. Each note is its own unison and its own octave,

so we end up with 12 possible cycles of 1 note each. Pretty useless. So, lets ignore it.

The next one we will look at is the tritone cycle. In this cycle, the intervals going both

ways are the same, so this results in only two notes per cycle. No point in depicting that

as a circle, so lets depict it as a line connecting the two notes. We can see that there are 6

instances of this cycle needed to cover all 12 notes:

Figure 3: Cycle of Tritones (6 instances of b5 pairs)

So, there are only 6 different tritone pairs to memorize. The tritone interval is very

important in Jazz as it represents one of the most common substitutions. Typically, this is

notated as substituting a V7 chord with a bII7 – however, this way of thinking about it

would lead you to believe that you need to memorize 12 such pairs, when in fact there are

only 6 pairs when you think of them as cycles.

The fifth cycle to consider is the M2/m7 cycle (also known as the whole tone cycle ).

There are only two whole tone cycles each containing 6 notes, so we can arrange them as

two hexagons . Notice that the tritone appears in this cycle as well: each two notes across

from each other are a tritone apart (hence the name: tritone = 3 whole tones). We already

saw that this was also true of the chromatic cycle and the cycle of fifths.

Another important thing about this cycle is that if you walk it counter-clockwise the

intervals are minor 7ths. Also, think about how you could super impose the two whole

tone cycles to get the chromatic cycle.

“‘Giant Steps’ and Cycle Diagrams” by Dan Adler

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