Talk:Frequency temperament: Difference between revisions
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::::: If we want to preserve uniqueness, the frequency equivalent of a monzo (the sum of the multiples of some basis elements) is not possible unless we restrict the multiplying factor to a certain range, resulting in what is essentially place value systems (like binary and decimal). I think the most useful such system as.a frequency monzo would be the [https://en.wikipedia.org/wiki/Factorial_number_system factorial number system], where the place values (basis elements) are the factorials and reciprocals of them: | ::::: If we want to preserve uniqueness, the frequency equivalent of a monzo (the sum of the multiples of some basis elements) is not possible unless we restrict the multiplying factor to a certain range, resulting in what is essentially place value systems (like binary and decimal). I think the most useful such system as.a frequency monzo would be the [https://en.wikipedia.org/wiki/Factorial_number_system factorial number system], where the place values (basis elements) are the factorials and reciprocals of them: | ||
1/2 = 1/2! (a "frequency monzo" of {{monzo|1}}) | ::::: 1/2 = 1/2! (a "frequency monzo" of {{monzo|1}}) | ||
1/3 = 2/3! (a "frequency monzo" of {{monzo|0 2}}) | ::::: 1/3 = 2/3! (a "frequency monzo" of {{monzo|0 2}}) | ||
1/4 = 1/3! + 2/4! (a "frequency monzo" of {{monzo|0 1 2}}) | ::::: 1/4 = 1/3! + 2/4! (a "frequency monzo" of {{monzo|0 1 2}}) | ||
1/5 = 1/3! + 4/5! (a "frequency monzo" of {{monzo|0 1 0 4}}) | ::::: 1/5 = 1/3! + 4/5! (a "frequency monzo" of {{monzo|0 1 0 4}}) | ||
Mappings and patent vals would work essentially the same except using reciprocals of factorials instead of primes as the basis elements, and using AFSes instead of ETs. "Tempering out" a comma also now means to reduce it to 0 instead of 1. | ::::: Mappings and patent vals would work essentially the same except using reciprocals of factorials instead of primes as the basis elements, and using AFSes instead of ETs. "Tempering out" a comma also now means to reduce it to 0 instead of 1. | ||
[[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 09:42, 17 May 2023 (UTC) | [[User:CompactStar|CompactStar]] ([[User talk:CompactStar|talk]]) 09:42, 17 May 2023 (UTC) | ||