#Tag
#music #math #algebra #earworms
'Behind many great melodies, researchers found something surprisingly powerful: symmetry. Their work shows that advanced algebra can reveal deep musical patterns that are not always obvious by ear or even on a written score.'
https://uwaterloo.ca/news/media/secret-math-behind-catchy-melodies
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?
