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 of these systems 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, which allows for representation any rational number given enough digits. | ::::: 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 of these systems 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, which allows for representation any rational number given enough digits. | ||
::::: 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. Prime limits are replaced with "factorial limits". | ||
::::: [[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) | ||