User talk:Godtone: Difference between revisions

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::: "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)

:::: I must admit that I wanted to make sure your understanding was completely correct before I confirmed it, as you can never completely tell online. Yes, it's true that there are other EDOs with other circles of fifths, but if they don't succeed at having telicity, I find them to be less than ideal, since the 3-prime is the most commonly used prime outside the octave. That said, you did more or less hit the nail on the head when you mentioned that large EDOs need some strong circles that fulfill the telicity condition for the sake of orientation- in fact, even something like the 11-to-3 telicity of 159edo and 24edo are very useful for navigation, though making the best use of this kind of telicity involves building on good 3-to-2 telicity. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:38, 23 January 2021 (UTC)

Revision as of 22:21, 22 January 2021 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,420 edits m replied to specifics about telicity's definition ← Older edit		Revision as of 00:38, 23 January 2021 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 6,010 edits No edit summary Newer edit →
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	::: "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)		::: "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)

			:::: I must admit that I wanted to make sure your understanding was completely correct before I confirmed it, as you can never completely tell online. Yes, it's true that there are other EDOs with other circles of fifths, but if they don't succeed at having telicity, I find them to be less than ideal, since the 3-prime is the most commonly used prime outside the octave. That said, you did more or less hit the nail on the head when you mentioned that large EDOs need some strong circles that fulfill the telicity condition for the sake of orientation- in fact, even something like the 11-to-3 telicity of 159edo and 24edo are very useful for navigation, though making the best use of this kind of telicity involves building on good 3-to-2 telicity. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 00:38, 23 January 2021 (UTC)