Friday, May 20, 2016

What The Heck Is Neo-Riemannian Analysis?

Well that's... different. Let's do some exercises!

1) Let's start with transformation paths. For each of the following sets of chords, see if you can find the shortest set of transformations that will get you from one to the other:

  • G# minor to A major
  • Db major to G minor
  • F# major to F minor
  • C major to F major
  • B major to Bb minor
  • A minor to E major
2) Second... We broke down the compound transformations starting from a major triad, but what about minor? Try starting from A minor and build a tree like we did in the video. How does it compare to the major tree?

3) Discussion time! What do you think of this method? Does it make sense? Does it seem useful? If so, how would you use it? If not, does it at least seem interesting?

And that's Neo-Riemannian Analysis... For now. See you next week!

1 comment:

  1. For simplicity I will use / to mean Relative, \ to mean Leading-tone, and | to mean Parallel.
    G#m\E/C#m\A. If Ab is used instead:
    Abm|Ab/Fm|F\Am|A or Abm|Ab\Cm|C/Am|A.
    Db/Bbm|Bb/Gm. If C# is used instead the path is longer:
    F#|F#m\D|Dm/F|Fm. If Gb is used instead the path is shorter:
    C/Am\F. If B# is used instead the path is crazy long and B# isn't on my graph but here goes:
    B#|B#m\G#|G#m\E|Em\C/Am\F or B#|B#m/D#|D#m/F#|F#m\D|Dm/F or quite a few other ways since they are so far from each other.
    B|Bm\G|Gm/Bb. If A# is used the path is crazy long again. If Cb is used for B though it is even shorter than from B to Bb:
    Am/C\Em|E or Am|A\C#m/E. Since I am ignoring double sharps and double flats there are no 12TET enharmonics worth considering.

    2. It is hard to do a tree with just text and no images but here goes:
    0 m
    1 M bIII bVI
    2 iii vi v biii bvi iv
    3III V VI IV V bVII bV bI bI bIV IV bII
    4#v #i vii v #i #iv ii iv vii iii bvii ii bv bvii bi bvi bi biii biv bii ii vi bii bvii
    In 12TET the farthest scale degrees is the II. VII is equally far if you don't count the enharmonic bI. Minor is closer to flat scales and major to sharp scales.

    3. I think that Neo-Riemannian-analysis can be extended to include more chords to get more interesting connections and better represent the true relationships between keys. For example: V dominant is connected to I sus4 7. It also works to show how in tunings other than 12TET how distant those added notes and chords are voiceleading-wise from any given root. I think that it makes sense in the very pure way that forte numbers represent chords divorced from traditions and how the chords are actually used. I think that chord relation graphs are useful for interpolating between chords but maybe I am using it wrong.

    In 7 chords R and L are both about moving the 7th degree to the tonic or visa-versa. They look very symetrical to me on a graph so I am a little R, L dyslexic. Good thing R is right and L is left from Major on my graphs.

    I actually made three graphs of increasing complexity. First the standard Neo-Riemannian. Then I did 7 chords (Major, minor, dominant and minor Major). Then I added sus2 and sus4 with both 7 endings. With that last one you find new transition types where the leading tone moves to the new dominant as in the I sus2 to ii sus4 connection. Or where the dominant moves to become the tonic in the V dom to I sus2 connection. Or where the median moves to become the tonic as in the v minor to i sus4 connection. Any ideas for naming?
    Now I wonder what happens if diminished, augmented, flat 5, 9, 6 and 69 chords are added. These graphs are best left to machines I think. I will let you know when I am done. I also want to glue the ends of a slinky together to make a proper graph of chord relations.

    Anyways, I definitely find this interesting.