Introduction
I had a computer printout from my old MacIntosh dated 1984, showing some cryptic chord forms I read once in a Tal Farlow interview. These were mostly altered chords which could be moved around in minor thirds and (more or less) belong to the same family of altered chords.
At one time I thought I understood this and filed it away. Due to recent discussion in the forum (eg. Cycles in General and Coltrane Changes), I was explaning something about tritone substitutions and moving tritones through cycle four, to a ex-student of mine and decided to get this out for reference.
It just so happened that I was thinking it was time to write a new article for Ibm.
Tritone Subs
So I got this (nearly) 20 year old sheet out and started trying to really understand it.
I got Excel up and started twiddling. I made a spreadsheet that allowed me to type in the intervals of a four note chord and show me the tensions of it and each copy of it moved up in minor thirds. This was a cool way to see what chords were usable as movable chord forms.(The Excel document is available for download in this forum thread)
I soon realized that it was going to take some time and effort.
To preface this I want to discuss the topic of Tritone movement through Cycle four and Tritone substitution.
All Dom7 chords contain a tritone between the third and the seventh (or vice versa since an inverted tritone is a tritone).
The jazz gurus tell us the third and seventh are the 'active' tones of the chord.
So these are the 'important' notes in a Dom7.
If you move from a Dom7 to it's tritone substitution you are basically pivoting on the tritone to a chord up a tritone.
Example: from A7 to Eb7 pivoting on C# and G which is the third and seventh of the A7 but becomes the seventh and third of the Eb7(actually Db is the seventh but it is enharmonic with C#).
So by pivoting I mean you keep the tritone note in place and move the root (and or fifth) to the new one. In this case I am talking about 3 note voicings.
Since a tritone is 6 half steps and a perfect fourth is 5 half steps, you can play the IV7 chord by moving the tritone down a half step (and the root up a perfect fourth).
So you can move tritones down chromatically to move through cycle four, just place the root accordingly.
Movable chord forms: Special cases of Altered chords
Lets talk about our old friend the Dim7 chord, This guy is two tritones a minor third apart or a stack of minor third's if you prefer. This guy is a truly special case as it is completely symmetrical every inversion is a replica of the previous one, because it is built on all minor thirds.
First of all lets look at the Dim7 as though it was the 3 5 b7 and b9 of a Dom 7b9 chord.
So the tritone moving down in half steps will once again give us Cycle four in this case using Dom 7b9.
Dim7 chords replicate themselves through inversion, in other words moving them up in steps of a minor third creates the same chord just inverted, (the chord up a minor third is just an inversion of the same chord you started with).
So you can move up a minor third (same chord) then down a half step to create cycle four movement. This results in up a major second. So I Dom7b9 up major second creates IV Dom7b9.
You can also move down an minor third (same chord) and then down another half step which results in down a major third and this will result in Cycle four movement.
Cycle Four Summary
- Move down a half step.
- Move up a whole step.
- Move down two whole steps.
Tritone Symmetrical Voicings
Now let us discuss another class of chords who are symmetrical about the tritone.
Lets take our friend the Dom7b5. This chord contains 1 3 b5 and b7 if you move each of these up (or down) a tritone you get b5 b7 1 3 from the same root! This also means that since this new chord is up a tritone it could be called bV Dom7b5.
Once again you can move this down a half step and create the IV Dom7b5.
Now let us discuss Dom9#5 in a four note voicing with no root 3 #5 b7 9.
Moving this by a tritone yields b7 9 3 #5 so by the previous argument this becomes IV Dom7#5 by lowering a half step.
More special cases of Tritone Symmetrical Chords
The Dom7#5#9 with no root voiced 3 #5 b7 #9 displaced by a tritone becomes b7 9 3 13 from the same root. So lowering this chord a half step results in IV 13.
The Dom7b5#9 with no seventh, 1 3 b5 #9 displaced by a tritone yields b5 b7 1 13.
So down a half step yields IV 13b5.
Another special case
The Dom7#9 with no seventh 1 3 5 #9 up a minor third becomes #9 5 b7 b5, up a tritone becomes b5 b7 b9 13, down a minor third becomes 13 -9 3 1, all from the same root. Since this has similar symmetry to a Dim7 you can move down a major third or up a major second or down a half step to create Cycle four movement.
Down a half step > IV 13b5b9
Cycle:7+9>13b5b9>7+9>13b5b9
Up a major second > IV 13b9
Cycle:7+9>13b9>13b9b5>7+11+9
Down a major third > IV Dom7b5#9
Cycle:13b9>7+9>7+11+9>13b9b5
Ok so what does it all mean?
You can use this information to select chord voicings for altered Dominant chords that can be moved in minor thirds and not change their function.
You can use these ideas in your solos to create tension during cycles of altered dominant chords. You can even use these ideas to create tension when playing over un-altered Dominant cycles.
Since the arpeggios from these movable forms will have the same interval structure when displaced by some number of minor thirds you can create interest in your solo by repeating patterns based on thes arpeggios.
In general this should help your understanding of the reasons why tritone substitution works and why movement in descending half steps, ascending whole steps and descending major thirds creates cycle four movement.
There are numerous voicings for Altered Dominant chords that can be displaced through any number of minor third interval sand still retain their function. I have only shown one example. If you truly appreciate this and want to know more you can reveal the other possibilities for voicings that work this way.
If you read the "'Giant Steps' and Cycle Diagrams" by Dan Adler (the link can be found in this thread: Cycles in General and Coltrane Changes)
He talks about the cycle based on major thirds.
Coltrane used these 4 cycles as the basis for the root motion of 'Giant Steps' – which brings us back to why we started looking at these cycles in the first place. In fact, the top right triangle is the entire formula of the tonal centers of ‘Giant Steps’ in the original key.
We can expand this slightly by merging in one piece of extra information from the cycle of the fifths: precede each root by its V7. This leads to two possibilities of traversing the triangle: walk to the left or walk to the right.
Right: B - Bb7 | Eb - D7 | G - F#7 | B ||
Left : B - D7 | G - Bb7 | Eb - F#7 | B || (Giant Steps)
My guess is that Coltrane chose the 2nd option because adding the V7 before the roots in the first instance created a 1/2 step downward bass motion, which makes the progression sound more predictable, since root motion from I to VII7 is a common vehicle for going to the diatonic III and this progression would then sound like a standard major/minor deceptive cadence (going to IIImaj7 instead of IIIm7).
I believe tht real reason Coltrane chose the counter-clockwise version of this is the observation I stated earlier about how moving down a major 3rd is equivalent to moving up a perfect fourth (for chords with m3 symmetry).