User talk:Lhearne: Difference between revisions

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:::::::::::::::::: Now that I'm looking at the diaschisma, it seems that that interval acts more as a diminished second rather than an augmented unison, and, now that I really think about it, the commas we need to use for this system are functionally types of prime, much like the meantone comma. I'm thinking that while the diaschisma is important, it's generally more of a dieses that a comma- only worth tempering out for the sake of easy enharmonics. The same thing is true of the Schisma, the Pythagorean comma, the Alpharabian comma the Betarabian comma, and even the Nexus comma. Now that I really think about it, the septimal kleisma is a rather poor choice too in light of this. Sorry for leading you down that rabbit trail with the septimal kleisma. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:04, 8 February 2021 (UTC)

:::::::::::::::::: Anyhow, now that we've hopefully narrowed down the comma selection in terms of what to use to define a well-ordered system, let's take a look at the available 5-limit commas, seeing as that seems to be where you're most focused at the moment. I will say that a number of the common 5-limit commas are likely to be pulled down by combinations of the [[schisma]] and the [[monzisma]] as the commas that are generated by these combinations seem likely to be to be among the optimal 5-limit temperament generators within our EDO range- if this is actually the case in terms of things like accuracy with respect to JI, I'm pretty sure it would be a bad idea to use them as commas for well-ordered interval lists. I think you may need to run an algorithm to find most of the commas that need to be eliminated as candidates based on the resulting list, though I can already tell you that the [[counterschisma]], the [[tricot comma]], [[Mercator's comma]], the [[vulture comma]], the [[amity comma]], the [[kleisma]] and the [[semicomma]] are on that avoid list based on my own personal calculations. ~~We seriously~~ need to find better candidates than these. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:39, 8 February 2021 (UTC)

:::::::::::::::::: Anyhow, now that we've hopefully narrowed down the comma selection in terms of what to use to define a well-ordered system, let's take a look at the available 5-limit commas, seeing as that seems to be where you're most focused at the moment. I will say that a number of the common 5-limit commas are likely to be pulled down by combinations of the [[schisma]] and the [[monzisma]], and I'm pretty sure it would be a bad idea to use them as commas for well-ordered interval lists because 159edo is still among the EDOs we need to make a well-ordered interval naming system for, and I can tell you that both the schisma and the monzisma are tempered out in that EDO, thus eliminating virtually all of the commas in that chain. I think you may need to run an algorithm to find most of the commas that need to be eliminated as candidates based on the resulting list, though I can already tell you that the [[counterschisma]], the [[tricot comma]], [[Mercator's comma]], the [[vulture comma]], the [[amity comma]], the [[kleisma]] and the [[semicomma]] are on that avoid list based on my own personal calculations. Therefore, I think we need to find better candidates than these. Even if the five-limit comma we end up choosing is virtually unknown to the community at large, I still think something like this is likely to be the better option in the end- after all I just found {{monzo| -99 61 1 }} by digging through combinations of the schisma that the monzisma, and that comma is definitely not well known to the community. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:07, 9 February 2021 (UTC)

Revision as of 23:46, 8 February 2021 view source Aura (talk \| contribs) autopatrolled 5,920 edits No edit summary ← Older edit		Revision as of 00:07, 9 February 2021 view source Aura (talk \| contribs) autopatrolled 5,920 edits No edit summary Newer edit →
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	:::::::::::::::::: Now that I'm looking at the diaschisma, it seems that that interval acts more as a diminished second rather than an augmented unison, and, now that I really think about it, the commas we need to use for this system are functionally types of prime, much like the meantone comma. I'm thinking that while the diaschisma is important, it's generally more of a dieses that a comma- only worth tempering out for the sake of easy enharmonics. The same thing is true of the Schisma, the Pythagorean comma, the Alpharabian comma the Betarabian comma, and even the Nexus comma. Now that I really think about it, the septimal kleisma is a rather poor choice too in light of this. Sorry for leading you down that rabbit trail with the septimal kleisma. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 16:04, 8 February 2021 (UTC)		:::::::::::::::::: Now that I'm looking at the diaschisma, it seems that that interval acts more as a diminished second rather than an augmented unison, and, now that I really think about it, the commas we need to use for this system are functionally types of prime, much like the meantone comma. I'm thinking that while the diaschisma is important, it's generally more of a dieses that a comma- only worth tempering out for the sake of easy enharmonics. The same thing is true of the Schisma, the Pythagorean comma, the Alpharabian comma the Betarabian comma, and even the Nexus comma. Now that I really think about it, the septimal kleisma is a rather poor choice too in light of this. Sorry for leading you down that rabbit trail with the septimal kleisma. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 16:04, 8 February 2021 (UTC)

	:::::::::::::::::: Anyhow, now that we've hopefully narrowed down the comma selection in terms of what to use to define a well-ordered system, let's take a look at the available 5-limit commas, seeing as that seems to be where you're most focused at the moment. I will say that a number of the common 5-limit commas are likely to be pulled down by combinations of the [[schisma]] and the [[monzisma]] as the commas that are generated by these combinations seem likely to be to be among the optimal 5-limit temperament generators within our EDO range- if this is actually the case in terms of things like accuracy with respect to JI, I'm pretty sure it would be a bad idea to use them as commas for well-ordered interval lists. I think you may need to run an algorithm to find most of the commas that need to be eliminated as candidates based on the resulting list, though I can already tell you that the [[counterschisma]], the [[tricot comma]], [[Mercator's comma]], the [[vulture comma]], the [[amity comma]], the [[kleisma]] and the [[semicomma]] are on that avoid list based on my own personal calculations. ~~We seriously~~ need to find better candidates than these. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 23:39, 8 February 2021 (UTC)		:::::::::::::::::: Anyhow, now that we've hopefully narrowed down the comma selection in terms of what to use to define a well-ordered system, let's take a look at the available 5-limit commas, seeing as that seems to be where you're most focused at the moment. I will say that a number of the common 5-limit commas are likely to be pulled down by combinations of the [[schisma]] and the [[monzisma]], and I'm pretty sure it would be a bad idea to use them as commas for well-ordered interval lists because 159edo is still among the EDOs we need to make a well-ordered interval naming system for, and I can tell you that both the schisma and the monzisma are tempered out in that EDO, thus eliminating virtually all of the commas in that chain. I think you may need to run an algorithm to find most of the commas that need to be eliminated as candidates based on the resulting list, though I can already tell you that the [[counterschisma]], the [[tricot comma]], [[Mercator's comma]], the [[vulture comma]], the [[amity comma]], the [[kleisma]] and the [[semicomma]] are on that avoid list based on my own personal calculations. Therefore, I think we need to find better candidates than these. Even if the five-limit comma we end up choosing is virtually unknown to the community at large, I still think something like this is likely to be the better option in the end- after all I just found {{monzo\| -99 61 1 }} by digging through combinations of the schisma that the monzisma, and that comma is definitely not well known to the community. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 00:07, 9 February 2021 (UTC)