Talk:159edo: Difference between revisions

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:::: This kind of consistency ("complete circle of fifths") seems problematic to me: How will you generalize these rings to other prime intervals? Also, aren't you interested in combinations of multiple prime dimensions (besides 2, of course)? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:22, 7 January 2021 (UTC)

::::: As I said, this kind of n-consistency means being able to go from the unison through a set of nodes in one p-limit to connect with an interval of a lower p-limit without the relative error reaching or exceeding the 50% marker. Since the 3-prime can only connect with the 2-prime in this fashion, and since the 2-prime simply results in manifestations of the unison at different registers, that means that the 3-prime requires a complete circle of fifths without accumulating 50% relative error or more to achieve a form of "complete consistency", however, higher primes have more options for a form of "complete consistency". For instance, the 11-prime in 159edo connects with the 3-prime easily without breaching the 50% relative error marker by means of tempering out the nexus comma, and similarly, the 5-prime connects with the 3-prime by means of tempering out the schisma. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:31, 7 January 2021 (UTC)

::::: As I said, this kind of n-consistency means being able to go from the unison through a set of nodes in one p-limit to connect with an interval of a lower p-limit without the relative error reaching or exceeding the 50% marker. Since the 3-prime can only connect with the 2-prime in this fashion, and since the 2-prime simply results in manifestations of the unison at different registers- meaning that the unison is the only available target- that means that the 3-prime requires a complete circle of fifths without accumulating 50% relative error or more to achieve a form of "complete consistency", however, higher primes have more options for a form of "complete consistency". For instance, the 11-prime in 159edo connects with the 3-prime easily without breaching the 50% relative error marker by means of tempering out the nexus comma, and similarly, the 5-prime connects with the 3-prime by means of tempering out the schisma. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:31, 7 January 2021 (UTC)

::::: As to combinations of multiple prime dimensions, I find these to be largely of secondary importance, but to be fair, they are subject to the same constraints- they must be able to connect to a p-limit lower than the lowest p-limit that is directly involved in the combination in question. For example, stacks of 14/13 trienthirds connect with the 5-prime by means of tempering out the cantonisma- the factor of 2 in 14 is trivial for this since the 2-prime simply results in manifestations of the unison at different registers. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:36, 7 January 2021 (UTC)

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 :::: This kind of consistency ("complete circle of fifths") seems problematic to me: How will you generalize these rings to other prime intervals? Also, aren't you interested in combinations of multiple prime dimensions (besides 2, of course)? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:22, 7 January 2021 (UTC)
-::::: As I said, this kind of n-consistency means being able to go from the unison through a set of nodes in one p-limit to connect with an interval of a lower p-limit without the relative error reaching or exceeding the 50% marker.  Since the 3-prime can only connect with the 2-prime in this fashion, and since the 2-prime simply results in manifestations of the unison at different registers, that means that the 3-prime requires a complete circle of fifths without accumulating 50% relative error or more to achieve a form of "complete consistency", however, higher primes have more options for a form of "complete consistency".  For instance, the 11-prime in 159edo connects with the 3-prime easily without breaching the 50% relative error marker by means of tempering out the nexus comma, and similarly, the 5-prime connects with the 3-prime by means of tempering out the schisma. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:31, 7 January 2021 (UTC)
+::::: As I said, this kind of n-consistency means being able to go from the unison through a set of nodes in one p-limit to connect with an interval of a lower p-limit without the relative error reaching or exceeding the 50% marker.  Since the 3-prime can only connect with the 2-prime in this fashion, and since the 2-prime simply results in manifestations of the unison at different registers- meaning that the unison is the only available target- that means that the 3-prime requires a complete circle of fifths without accumulating 50% relative error or more to achieve a form of "complete consistency", however, higher primes have more options for a form of "complete consistency".  For instance, the 11-prime in 159edo connects with the 3-prime easily without breaching the 50% relative error marker by means of tempering out the nexus comma, and similarly, the 5-prime connects with the 3-prime by means of tempering out the schisma. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:31, 7 January 2021 (UTC)
 ::::: As to combinations of multiple prime dimensions, I find these to be largely of secondary importance, but to be fair, they are subject to the same constraints- they must be able to connect to a p-limit lower than the lowest p-limit that is directly involved in the combination in question.  For example, stacks of 14/13 trienthirds connect with the 5-prime by means of tempering out the cantonisma- the factor of 2 in 14 is trivial for this since the 2-prime simply results in manifestations of the unison at different registers. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:36, 7 January 2021 (UTC)