Well-formed scales

[Barrymagrew]

Description

We’ll-formed (musical) scales lie on the intersection of a number of interesting topics, including group theory, continued fractions, and Christoffel words. Such scales have been shown to form a basis of the Western diatonic and chromatic scales, the pervasive anhemitonic pentatonic scale, and numerous other scales in world music. They can be (and have been) used to generate new microtonal scales. Well-formed scales are also know as MOS (moment of symmetry) scales

About the author

I am Norman Carey, who, along with David Clampitt, described these scales in a number of articles, the first being “Aspects of Well-formed scales” in an article in Music Theory Spectrum (1989: 11/2, 187-206). Considerable work has followed this initial paper on the topic. I am the executive officer of the music department of the CUNY Graduate Center.

Quick Summary

The project would be aimed at a fairly general audience, although it could become a bit lengthy if expositions of group theory and continued fractions are necessary. These might get a suitably foreshortened exposition for the sake of the project. The main point would be to see well-formed scales generated and brought to life through sounds and diagrams.

Target medium

The project would be best served in video format. A collaborator would be someone with considerable experience making math videos and someone with some familiarity with music, but that familiarity doesn’t need to start at a particularly high level. A secondary project might be a stand-alone app for generating these scales.

More details

As mentioned above, there are quite a number of articles on this topic now, but the one I cited earlier would be sufficient to get a sense of it.

The first motivating screen might be the picture of a piano keyboard with a query about that odd pattern of black keys in alternating groups of threes and twos. I would need help storyboarding further, but sounds and circle diagrams could be animated to generate well-formed scales from scratch.

Contact details

Norman Carey ncarey@gc.cuny.edu

Additional context

not at this time

[ghost]

I contacted you via Twitter DM!

[Barrymagrew]

Hasn’t appeared so far.

Sent from my iPhone

On Jun 9, 2022, at 2:55 PM, Markus Heimerl @.***> wrote:



I contacted you via Twitter DM!

— Reply to this email directly, view it on GitHubhttps://urldefense.com/v3/__https://github.com/leios/SoME_Topics/issues/40*issuecomment-1151486496__;Iw!!GekbXoL5ynDpFgM!Q9jSOyCcay7cQK52QIaRbJq4qDN73zrH0gtyN-moMazxPweV709PeWWhRTQgODkHV3F_BadV-xD7HgMWEy19xqhkVA$, or unsubscribehttps://urldefense.com/v3/__https://github.com/notifications/unsubscribe-auth/AZR2MO4OUXQMTKOWZUW2LLTVOI43LANCNFSM5YKCYX3A__;!!GekbXoL5ynDpFgM!Q9jSOyCcay7cQK52QIaRbJq4qDN73zrH0gtyN-moMazxPweV709PeWWhRTQgODkHV3F_BadV-xD7HgMWEy1J5GQL1Q$. You are receiving this because you authored the thread.Message ID: @.***>

[ghost]

Sorry, I commented under the wrong post!

[MarcTheSpark]

Hey --- not sure if the musical tools I built would be of any help here (we'd still need an animator regardless), but you might check out my post: https://github.com/leios/SoME_Topics/issues/62

[Barrymagrew]

Thanks so much for your response.

Yes, these tools are exactly in line with what would be needed. Here’s a little Desmos demo of how well-formed scales behave — the demo is actually more general, in that it allows you to construct any generated scale with any size generator:

https://www.desmos.com/calculator/ptgmmhyokv

By the way, there’s a good many connections between such scales and the Fourier stuff you’re doing. In its most recent guise, this started with the work of Ian Quinn, his Perspectives of New Music article, "“General Equal-Tempered Harmony.” Such work has also been done by Jason Yust, Andrew Milne, Emanuel Amiot, and Thomas Noll.

But yes, if you’d like to figure out how this might move forward, I’d love to figure it out. I have heard from someone how does the animation, but the musical sophistication is not as great as yours, but perhaps the animations stuff would work.

Let me know what your thoughts are.

All best,

Norman Carey Executive Officer Ph.D/D.M.A. Programs in Music CUNY Graduate Center Tel: (212) 817-8594 Office: 3102.05

On Jun 10, 2022, at 12:55 PM, MarcTheSpark @.**@.>> wrote:

Hey --- not sure if the musical tools I built would be of any help here (we'd still need an animator regardless), but you might check out my post: #62https://urldefense.com/v3/__https://github.com/leios/SoME_Topics/issues/62__;!!GekbXoL5ynDpFgM!WcsERjklaaR1wxaAXF_Uf0RzT7AeVk86P5ivR4lvHei35jdqKKzQosN1uKyh5UFqFka8ZPEC-wKIRUFbWFGvv2nKIQ$

— Reply to this email directly, view it on GitHubhttps://urldefense.com/v3/__https://github.com/leios/SoME_Topics/issues/40*issuecomment-1152556359__;Iw!!GekbXoL5ynDpFgM!WcsERjklaaR1wxaAXF_Uf0RzT7AeVk86P5ivR4lvHei35jdqKKzQosN1uKyh5UFqFka8ZPEC-wKIRUFbWFHokG325w$, or unsubscribehttps://urldefense.com/v3/__https://github.com/notifications/unsubscribe-auth/AZR2MO6YEQMTZWXKPM37HJTVONXPPANCNFSM5YKCYX3A__;!!GekbXoL5ynDpFgM!WcsERjklaaR1wxaAXF_Uf0RzT7AeVk86P5ivR4lvHei35jdqKKzQosN1uKyh5UFqFka8ZPEC-wKIRUFbWFFkhennXQ$. You are receiving this because you authored the thread.Message ID: @.***>

[MarcTheSpark]

Sorry for the slow response! Looks interesting :-) I've looked briefly at Ian Quinn's article, but not in depth, but I did see that it used Fourier analysis.

If you have an animator, and see a useful role for some of my python music tools, I'd be open to chatting more! Feel free to reach out by e-mail: marc [at] marcevanstein [dot] com