[HN Gopher] Music and Geometry: Intervals and Scales
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Music and Geometry: Intervals and Scales
Author : coloneltcb
Score : 80 points
Date : 2024-12-19 18:52 UTC (4 hours ago)
(HTM) web link (roelsworld.eu)
(TXT) w3m dump (roelsworld.eu)
| rekado wrote:
| If you like this you may also be interested in Emmett Chapman's
| Offset Modal System:
|
| https://www.stick.com/method/articles/offsetmodal/
| https://www.stick.com/method/articles/parallel/
| mlochbaum wrote:
| My own take on relating scales geometrically:
| https://mlochbaum.github.io/BQN-Musician/theory/modulation.h...
|
| It does seem that I include all Chapman's scales (while saying
| nothing about chords), although oddly enough he's chosen to use
| the modes of harmonic major but not those of its inversion,
| harmonic minor?
|
| Edit: In fact I found the second link (first one's pretty vague
| and wasn't enough for me to follow the diagram) relevant enough
| that I added a paragraph to point out the connection!
| pohl wrote:
| I love this. Here's another interesting thing I encountered. It's
| a way of organizing chromatic subsets by brightness
|
| https://www.reddit.com/r/musictheory/comments/1etydas/i_made...
| hammock wrote:
| That is cool and different. Glancing at the bottom several rows
| I tend to agree with the classification, as a trained musician.
| I wonder though, what is (the mathematical principle) behind it
| that is causing the brightness/ darkness in the sound of these
| chords?
|
| Don't say "dissonance" (or explain what dissonance is)- that
| much is obvious, looking for something a bit more detailed,
| e.g. why 1-2-5 sounds brighter than 1-4-5
| dbcurtis wrote:
| It is going to be the relative amplitudes of the overtones.
| Pure tone (like flute) is bright, many overtones present with
| the appropriate mix can sound dark (french horn). Next, you
| are going to ask me for the coefficients, but I don't know
| that. Break into the nearest church with a proper pipe organ
| and start pulling and pushing stops to see what happens. (Or
| ask your friend the organist to take you so that you don't
| get arrested)
| recursive wrote:
| I don't really understand this chart at all, but I think it's
| based on the idea that an upward movement of a fifth is
| bright, and a downward movement is dark. 1-2-5 can be built
| on two upward movements of a fifth, whereas 1-4-5 can be
| built be one upwards movement, and one downward (from the
| tonic)
| tugu77 wrote:
| The diagrams look nice, but in the end of the day, they are
| merely nice visualizations of what's fundamentally algebra. There
| is not much geometry going on besides a quite simple group
| structure of order 12.
| openrisk wrote:
| Besides geometry there is not a lot of music either, in the
| sense that even this simple symmetry is kinda fake, effectively
| a forced resolution of an essentially unsolvable "problem":
| hammering the intervals into place to inject some "logic" into
| the task of dividing the octave in heptatonic scales. Despite
| the unrepentant Pythogereans across all ages, our musical brain
| is not mathematical except in a very loose way.
|
| Besides aesthetics, though, there might be educational value
| given that the equal temperament tuning is a cornerstone of
| western music education.
| PaulDavisThe1st wrote:
| > the task of dividing the octave in heptatonic scales.
|
| that's not task. The octave has already been divided into
| twelve tones here.
|
| The task is to pick sets of those twelve tones to serve some
| aesthetic purpose. The sets may be of various sizes, though 7
| is common in a lot of european music.
|
| If the task was to generate heptatonic scales from within the
| octave, there are a huge number of possibilities not
| described here, and most of them are rarely used (though many
| more than the ones based on a 12TET system are).
| Rochus wrote:
| > _There is not much geometry going on_
|
| You can use the geometric representation ("necklace") to
| explain modulation of e.g. diatonic scales as axial mirroring.
| This can be regarded as a geometric operation. When you look at
| harmony in this way, some interesting insights open up. I've
| even built a tool to explore it: https://github.com/rochus-
| keller/MusicTools/tree/master.
| PittleyDunkin wrote:
| Whenever someone says "there's not much geometry going on"
| you've identified a person with little capacity for imagination
| ChocMontePy wrote:
| I never realized until now that in the the two different circles
| pictured (the Chromatic Circle and the Circle of Fifths) the
| pairs of notes opposite each other are the same in each circle.
| For example in both circles B is opposite from F.
|
| And if you move around the Chromatic Circle, swapping every
| second pair of notes with its opposite on the other side of the
| circle, you have the Circle of Fifths.
| smitelli wrote:
| That interval (B-F) would be the tritone, arguably the most
| dissonant one in the toolbox.
| Duanemclemore wrote:
| Amazing. A deeper dive of the methods John Coltrane used.
|
| https://www.openculture.com/2024/12/john-coltrane-draws-a-pi...
|
| And
|
| https://www.openculture.com/2017/10/john-coltrane-draws-a-my...
|
| With plenty of great links to dive deeper in both!
| ziofill wrote:
| I've been playing piano for 30+ years, and I only learned to use
| the circle of fifths this year. It's been short of a revelation
| and I can't recommend enough to practice scales and drills based
| on it.
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