Talk:Just intonation point: Difference between revisions
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Math rant: The p-limit is a submodule of Q (the rational numbers) under multiplication. The only reason to take a logarithm is because addition is easier for us (and allows us to use the tools developed in linear algebra). So really, the logarithm is an isomorphism between p-limit JI and the free Z-modules under addition we use in RTT. The generators of JI are just the primes, so the JIP is nothing more than the generators under this isomorphism. I know this sounds pretty abstract but maybe this helps: you can think of the p-limit JI as a temperament with the identity matrix as its map, and the JIP is its generator (list). As such there should probably be a mention of generators, and I propose renaming JIP to something like "just generators". | Math rant: The p-limit is a submodule of Q (the rational numbers) under multiplication. The only reason to take a logarithm is because addition is easier for us (and allows us to use the tools developed in linear algebra). So really, the logarithm is an isomorphism between p-limit JI and the free Z-modules under addition we use in RTT. The generators of JI are just the primes, so the JIP is nothing more than the generators under this isomorphism. I know this sounds pretty abstract but maybe this helps: you can think of the p-limit JI as a temperament with the identity matrix as its map, and the JIP is its generator (list). As such there should probably be a mention of generators, and I propose renaming JIP to something like "just generators". | ||
: EDIT: I have written up an explanation [[ | : EDIT: I have written up an explanation [[User:Sintel/The_mathematics_of_temperaments|here]]. | ||
- [[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 22:20, 18 December 2021 (UTC) | - [[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 22:20, 18 December 2021 (UTC) | ||