Chord progression graphs

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AndrewMeronek
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Chord progression graphs

Post by AndrewMeronek » Thu Mar 26, 2020 5:48 pm

This is an idea I've been poking at for a little while now. First, one of my weblog posts running the idea down:

Chord Graph for a 5-Limit Major Scale

https://andrewmeronek.com/music-resourc ... jor-scale/

Today, I finished writing some code that makes the last part of the post regarding alterations a practical reality, and to put it frankly, I'm pretty excited. The code outputs the same graph I drew, and I have stuff in there to make it pretty easy to alter some basic parameters. Probably the most work now is coming up with the adjacency matrices for other various scales. Maybe I can clean up the graphics a bit, but the platform I used (SageMath) doesn't seem to currently have an option to replace the numbered vertices in the graphics with other text. So, for now, I added the indexes. So - now, what to do with this? I'd definitely appreciate some ideas. The first thing that comes to mind is to make a "booklet" for each type of scale (starting with the 12EDO major scale) and just list all of the significant graphs that have some pattern beyond being a bunch of points with zero connections.

I'd also appreciate ideas on how to make this look cleaner, maybe another platform that has similar mathematical tools but with more graphical control. Now that I have the algorithm working, translating to various other programming languages isn't that much of a big deal, if there's a clear benefit.
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Last edited by AndrewMeronek on Sat Mar 28, 2020 8:49 am, edited 1 time in total.
“All musicians are subconsciously mathematicians.”

- Thelonious Monk
Digidog
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Joined: Thu Dec 13, 2018 3:31 pm

Re: Chord progression graphs

Post by Digidog » Sat Mar 28, 2020 4:12 am

Is frequency overlaid in the printing of the graphs, or is it just the relation between the notes? If not: the asymmetry you speak of would be because of the tempered scale and how the notes (the names) are unevenly distributed because of that.

Before I think further on this: what would be your purpose of extrapolating these relations as graphs?
Welcome to visit my web store: https://www.danieleng.com/
Digidog
Posts: 24
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Re: Chord progression graphs

Post by Digidog » Sat Mar 28, 2020 4:14 am

And I forgot to say: Neat work! Cool thinking! :good:
Welcome to visit my web store: https://www.danieleng.com/
AndrewMeronek
Posts: 435
Joined: Fri Mar 30, 2018 6:09 pm
Location: Detroit area
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Re: Chord progression graphs

Post by AndrewMeronek » Sat Mar 28, 2020 7:15 am

Digidog wrote:
Sat Mar 28, 2020 4:12 am
Is frequency overlaid in the printing of the graphs, or is it just the relation between the notes?
Just the relation between notes, and the relations are somewhat arbitrary based on whatever rules I want to consider as "consonance". In this case, the 5-limit scale results (in C major) D-F and D-A not being the simple intervals the other minor thirds and perfect fifths are, so I didn't consider them "consonant" in those graphs.
If not: the asymmetry you speak of would be because of the tempered scale and how the notes (the names) are unevenly distributed because of that.

Before I think further on this: what would be your purpose of extrapolating these relations as graphs?
A visual aid for composition. And, a way to "think outside the box" to suggest harmonic motion that may not be obvious in typical usage.
“All musicians are subconsciously mathematicians.”

- Thelonious Monk
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