# Hexatonic and Octatonic Cycles



## Mr. Big Noodles (Oct 5, 2017)

I was watching this video and found something some of you might think is cool.



Summary of Neo-Riemannian Operations (NROs)

P = Parallel (Same root, different quality. ex. C to Cm, or Cm to C)
L = Leading tone exchange (If starting at a major chord, the root goes down a half step to become the fifth of a minor chord. If starting at minor, the fifth goes up a half step to become the root of a major chord. ex. C to Em, or Em to C)
R = Relative (Goes between relative minor/major. ex. C to Am, or Am to C)

The short of it: PL cycles create chord sequences contained within the hexatonic cycle (C C# E F G# A, which can be thought of as a recurring pattern of half step/minor third). In the video, the dude uses an example from Brahms' concerto for violin and cello that has the following cycle:

A♭-A♭m-E-Em-C-Cm-A♭

You can reverse the operations, and it takes you backwards through the cycle. Instead of PL, this is LP:

A♭-Cm-C-Em-E-A♭m-A♭

There is another cycle that creates an octatonic cycle: RP

If we start at C...

C-Am-A-F#m-F#-E♭m-E♭-Cm-C

You can also do PR, and it takes you backwards through the cycle:

C-Cm-E♭-E♭m-F#-F#m-A-Am-C

And yes, the octatonic cycle sticks within the octatonic scale (C D♭ E♭ E F# G A B♭, also known as the diminished scale; made from alternating half-steps and whole-steps).


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