User talk:Godtone: Difference between revisions

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:: I'm afraid your understanding of the concept of telicity is an oversimplification. While the concept of telicity does in fact include the idea of a "circle of n'ths" where "n" is some interval of interest, incomplete circles are still counted, hence the term "chains", and while the concept of telicity not only involves connectivity between multiple chains- specifically of primes- and the the patent val for an EDO agreeing with the connection, the fact remains that the [[direct mapping]] for every interval in both chains up to the point of connection must also agree with the connection.

:: Stated more mathematically, where "N" is the number of steps in a given EDO, "r" is the ratio of an interval in one of the two circles, and "M" is the monzo of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) ''must'' hold true along ''both'' prime chains up ~~until~~ the point of connection.

:: Stated more mathematically, where "N" is the number of steps in a given EDO, "r" is the ratio of an interval in one of the two circles, and "M" is the monzo of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) ''must'' hold true along ''both'' prime chains up to and including the point of connection.

:: Just looking at 3-to-2 telicity, which, by definition, involves a circle of fifths as the 2-prime is the only available telos for the 3 prime chain, the first seven EDOs that pass the test for this telicity are 2, 5, 12, 24, 53, 106, and 159. 80edo, despite being almost half of 159edo, fails the test, which is why I'm not interested in it, the same is true of both 29edo and 87edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:27, 22 January 2021 (UTC)

:: Just looking at 3-to-2 telicity, which, by definition, involves a circle of fifths as the 2-prime is the only available telos for the 3 prime chain, the first seven EDOs that pass the test for this telicity are 2, 5, 12, 24, 53, 106, and 159. 80edo, despite being almost half of 159edo, fails the test, which is why I'm not interested in it, the same is true of both 29edo and 87edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:34, 22 January 2021 (UTC)

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 :: I'm afraid your understanding of the concept of telicity is an oversimplification.  While the concept of telicity does in fact include the idea of a "circle of n'ths" where "n" is some interval of interest, incomplete circles are still counted, hence the term "chains", and while the concept of telicity not only involves connectivity between multiple chains- specifically of primes- and the the patent val for an EDO agreeing with the connection, the fact remains that the [[direct mapping]] for every interval in both chains up to the point of connection must also agree with the connection.
-:: Stated more mathematically, where "N" is the number of steps in a given EDO, "r" is the ratio of an interval in one of the two circles, and "M" is the monzo of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) ''must'' hold true along ''both'' prime chains up until the point of connection.
+:: Stated more mathematically, where "N" is the number of steps in a given EDO, "r" is the ratio of an interval in one of the two circles, and "M" is the monzo of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) ''must'' hold true along ''both'' prime chains up to and including the point of connection.
-:: Just looking at 3-to-2 telicity, which, by definition, involves a circle of fifths as the 2-prime is the only available telos for the 3 prime chain, the first seven EDOs that pass the test for this telicity are 2, 5, 12, 24, 53, 106, and 159.  80edo, despite being almost half of 159edo, fails the test, which is why I'm not interested in it, the same is true of both 29edo and 87edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:27, 22 January 2021 (UTC)
+:: Just looking at 3-to-2 telicity, which, by definition, involves a circle of fifths as the 2-prime is the only available telos for the 3 prime chain, the first seven EDOs that pass the test for this telicity are 2, 5, 12, 24, 53, 106, and 159.  80edo, despite being almost half of 159edo, fails the test, which is why I'm not interested in it, the same is true of both 29edo and 87edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:34, 22 January 2021 (UTC)