Talk:159edo: Difference between revisions

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::::: 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)

::::: Now this is fascinating... According to my calculations, subtracting the [[symbiosma]] from [[7/4]] results in an interval with the prime factorization of (3^9)/(2^10*11), so it looks like the symbiosma bridges the 7-prime and a combination of 3 and 11. Perhaps I should fix my definition of "complete consistency" by adding the following condition- if one is able to go from the unison through a set of nodes in one p-limit to connect with an interval made purely from a combination of two other primes, complete consistency is only achieved when the highest prime directly involved in the combination in question connects to the lowest prime in that same combination without breaching the 50% relative error marker once octave equivalence is accounted for. This would ~~means~~ that in 159edo, the connection between the 7-prime on one hand and a combination of 11 and 3 on the other can only be regarded as "complete consistency" because the 11-prime connects to the 3-prime without breaching the 50% relative error marker on account of the nexus comma being tempered out. I still need to work out the details regarding more complicated combinations, but other than that, do you have any thoughts on this idea Xenwolf? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:20, 17 January 2021 (UTC)

::::: Now this is fascinating... According to my calculations, subtracting the [[symbiosma]] from [[7/4]] results in an interval with the prime factorization of (3^9)/(2^10*11), so it looks like the symbiosma bridges the 7-prime and a combination of 3 and 11. Perhaps I should fix my definition of "complete consistency" by adding the following condition- if one is able to go from the unison through a set of nodes in one p-limit to connect with an interval made purely from a combination of two other primes, complete consistency is only achieved when the highest prime directly involved in the combination in question connects to the lowest prime in that same combination without breaching the 50% relative error marker once octave equivalence is accounted for. This would mean that in 159edo, the connection between the 7-prime on one hand and a combination of 11 and 3 on the other can only be regarded as "complete consistency" because the 11-prime connects to the 3-prime without breaching the 50% relative error marker on account of the nexus comma being tempered out. I still need to work out the details regarding more complicated combinations, but other than that, do you have any thoughts on this idea Xenwolf? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:20, 17 January 2021 (UTC)

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	::::: 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)		::::: 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)

	::::: Now this is fascinating... According to my calculations, subtracting the [[symbiosma]] from [[7/4]] results in an interval with the prime factorization of (3^9)/(2^10*11), so it looks like the symbiosma bridges the 7-prime and a combination of 3 and 11. Perhaps I should fix my definition of "complete consistency" by adding the following condition- if one is able to go from the unison through a set of nodes in one p-limit to connect with an interval made purely from a combination of two other primes, complete consistency is only achieved when the highest prime directly involved in the combination in question connects to the lowest prime in that same combination without breaching the 50% relative error marker once octave equivalence is accounted for. This would ~~means~~ that in 159edo, the connection between the 7-prime on one hand and a combination of 11 and 3 on the other can only be regarded as "complete consistency" because the 11-prime connects to the 3-prime without breaching the 50% relative error marker on account of the nexus comma being tempered out. I still need to work out the details regarding more complicated combinations, but other than that, do you have any thoughts on this idea Xenwolf? --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:20, 17 January 2021 (UTC)		::::: Now this is fascinating... According to my calculations, subtracting the [[symbiosma]] from [[7/4]] results in an interval with the prime factorization of (3^9)/(2^10*11), so it looks like the symbiosma bridges the 7-prime and a combination of 3 and 11. Perhaps I should fix my definition of "complete consistency" by adding the following condition- if one is able to go from the unison through a set of nodes in one p-limit to connect with an interval made purely from a combination of two other primes, complete consistency is only achieved when the highest prime directly involved in the combination in question connects to the lowest prime in that same combination without breaching the 50% relative error marker once octave equivalence is accounted for. This would mean that in 159edo, the connection between the 7-prime on one hand and a combination of 11 and 3 on the other can only be regarded as "complete consistency" because the 11-prime connects to the 3-prime without breaching the 50% relative error marker on account of the nexus comma being tempered out. I still need to work out the details regarding more complicated combinations, but other than that, do you have any thoughts on this idea Xenwolf? --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 20:20, 17 January 2021 (UTC)