User talk:Godtone: Difference between revisions

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:: 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]]) 21:30, 22 January 2021 (UTC)

::: "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."<br/>Yes, I understood that part. I never said that the circles must accumulate less than half an EDOstep of error in their full/completed chains in an EDO or sub-EDO. I don't think a "circle" of an interval has to necessarily close on (a multiple of) the octave within half an EDOstep to be used as a "circle" because the interval could still be very or sufficiently accurate, although in the case of larger EDOs, having ''some'' strong circles that fulfill that condition is important for orientation. I now see my definition is technically not specific enough and would require that the error of generators don't accumulate so much as to cause inconsistency at any point in the chain up to the connection, but I was mainly intent on confirming understanding rather than restating the definition exactly.<br/>Also, I never claimed that EDOs 80, 29 or 87 succeed telicity in the 2.3 subgroup. That doesn't mean their circle of fifths or circles of other intervals can't be useful, interesting or equally valid as a method of organising them, for example the "circle of fifths" in meantone does not necessarily close within 50c to the octave, depending on tuning. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:21, 22 January 2021 (UTC)

Revision as of 21:30, 22 January 2021 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 6,012 edits resigning my comment again since I altered it significantly ← Older edit		Revision as of 22:21, 22 January 2021 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,583 edits m replied to specifics about telicity's definition Newer edit →
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	:: 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]]) 21:30, 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]]) 21:30, 22 January 2021 (UTC)

			::: "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."<br/>Yes, I understood that part. I never said that the circles must accumulate less than half an EDOstep of error in their full/completed chains in an EDO or sub-EDO. I don't think a "circle" of an interval has to necessarily close on (a multiple of) the octave within half an EDOstep to be used as a "circle" because the interval could still be very or sufficiently accurate, although in the case of larger EDOs, having ''some'' strong circles that fulfill that condition is important for orientation. I now see my definition is technically not specific enough and would require that the error of generators don't accumulate so much as to cause inconsistency at any point in the chain up to the connection, but I was mainly intent on confirming understanding rather than restating the definition exactly.<br/>Also, I never claimed that EDOs 80, 29 or 87 succeed telicity in the 2.3 subgroup. That doesn't mean their circle of fifths or circles of other intervals can't be useful, interesting or equally valid as a method of organising them, for example the "circle of fifths" in meantone does not necessarily close within 50c to the octave, depending on tuning. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 22:21, 22 January 2021 (UTC)