Discussion
Is there a #microtonal#MusicTheory community on fedi? I'm looking for resources for ear training and building musical intuitions around temperaments generally, but also math like what number theory sounds like.
Boosts appreciated, especially into the kinds of math/music/autism communities where the phrase "what number theory sounds like" doesn't seem all that strange.
Like, concretely: Lately I've been fascinated with JI beyond the restrictions of periodic scales. If I'm synthesizing without a keyboard then do I care how well 31EDO approximates 5/4. What does good voice leading look like in JI. Do prime harmonics play a part in neo-Riemannian transformations. What does the singer's formant do with choral overtone clusters. How much trouble is an 81/80 comma really in the face of a funky detuned chorus supersaw.
Can I train my ear to just know this stuff.
In theory most instruments look like a pile of integer harmonics through a filter, right? And chords are consonant when parts play in small integer ratios—harmonics of some shared lower chord root. In some sense chord harmonics form a subset of the rationals.
12edo tempers out intervals to 2^{1/12} semitones. So do we get anything musically if we analyze ed harmonies as subsets of field extensions, like Q(2^{1/12}) for 12edo?
How do different field extensions sound?
And, like, is there a text I should be reading for this? Surely someone in the history of tuning theory or temperaments has thought through some of this already. I'm enjoying stumbling randomly through xenwiki until I get it, but I can't be the first person to ask these sorts of questions.
Okay, maybe it's not something that everyone asks. I might only be the third or fourth. But surely not the first, right?
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