Hexatonic and Octatonic Cycles

Discussion in 'Music Theory, Lessons & Techniques' started by Mr. Big Noodles, Oct 5, 2017.

  1. Mr. Big Noodles

    Mr. Big Noodles Theory God

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    May 29, 2008
    Los Angeles, CA
    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:


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


    There is another cycle that creates an octatonic cycle: RP

    If we start at C...


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


    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).
    Aion and chopeth like this.

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