Talk:159edo: Difference between revisions

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== Approximate errors ==

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:::::: I can't say anything about that. Considering the precision of 3.7 cents with which any interval is hit in 159edo and the generally accepted detuning degree of 13.7 cents of the major third in 12edo, considerations regarding consistency seem rather remote to me. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:47, 17 January 2021 (UTC)

::::::: Actually, if you think about it, the generally accepted detuning of the major third in [[12edo]] still follows the same rules that I'm laying down, as the Syntonic comma ([[81/80]]), which is responsible for that detuning, is smaller than half a step in 12edo, and it's still smaller than half a step in [[24edo]]. In fact, the [[Pythagorean comma]] is also less than half of a step in 24edo, and thus, the 3-prime and the 5-prime can both be regarded as having "complete consistency" in 24edo as well as in 12edo. However, when you start looking at [[36edo]], [[48edo]] and [[72edo]], suddenly, things don't turn out as good on this front, as the relative error percentage in these EDOs- especially for the Pythagorean comma- exceeds 50%. This is why I moved on from the larger 12-based EDOs and was finally open to detwelvulating. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:41, 17 January 2021 (UTC)

::::::: If you apply this same type of thinking to smaller EDOs, you see that 2edo is the first to have complete consistency in the 3-limit, but 3edo and 4edo both fail this test as the commas produced by their respective circles of fifths are larger than half of their respective step size. After that, the next EDO to have complete consistency in the 3-limit is 5edo, which accomplishes a completely consistent representation of the 3-prime as 256/243, the interval produced from a single circle of fifths in 5edo, is smaller than half of a step in 5edo. After that, the next EDO to have complete consistency in the 3-prime is 12edo itself, as 6edo, 7edo, 8edo, 9edo, 10edo, and 11edo all fail the test- of course, as I said, 24edo, which is related to 12edo, also passes this test. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:50, 17 January 2021 (UTC)

::::::: So, what about the EDOs between 12edo and 24edo? Well, according to my calculations, literally none of the EDOs from 13edo to 23edo demonstrate complete consistency in the 3-limit. Even the well known [[22edo]] fails this test- looks like I've found one of that EDO's significant weaknesses, and a good enough reason for me not to use it. Anyhow, I'll continue my calculations to see what other EDOs demonstrate the kind of complete 3-prime consistency, and I'll let y'all know about the first dozen or so members of the sequence that emerges from this. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:12, 17 January 2021 (UTC)

::::::: I just got to thinking, and, the term "complete consistency" seems like a misleading term for the type of consistency I'm after- perhaps "telic consistency" or even "telicity" are a better terms for this, since this type of consistency means that stacking intervals of one prime will eventually reach an interval of a lower prime without reaching or exceeding 50% relative error, and "telic" is related to "telos" meaning "end" or "goal". Since "telicity" is the noun used to refer to the property of being "telic", I think I'll use the term "telicity" for this type of n-consistency from now on. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:30, 18 January 2021 (UTC)

== Linking 159edo Songs to This Page ==

Hey, Xenwolf, since I've written like three songs in 159edo now, I'm wondering how to link these songs of mine to this page. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:37, 26 February 2021 (UTC)

: I started the [[159edo #Music|''Music'']] section, please feel free to add what you like there. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:04, 26 February 2021 (UTC)

== Gentle comma (364/363) and region, also tempering out 352/351 ==

Please note that while this article correctly notes that 159-ed2 tempers out364/363, the gentle region and grntle temperament also involves tempering out 352/351. In other words, -3 fifths represents 13/11 or 33/28; and +4 fifths represents 14/11 or 33/28. Thus there sre two genle commas: 159-ed2 tempers out 364/363, but not 352/351; compare 38\159 for 13/11 or 33/28 with 39\159 (-3 fifths) for 32/27. In gentle temperament as I described it in 2002, 32;27 and 13/11 or 33/28 map to -3 fifths.

[[User:Mschulter1325|Mschulter1325]] 01:18, 11 November 2022 (UTC)

: Would you say the gentle comma should refer to either 352/351 or 364/363? And that gentle temperament is the 13-limit temperament tempering out both 352/351 and 364/363? In that case we'll need to come up with another name for 364/363 cuz right now it's known specifically as ''the'' gentle comma. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 05:14, 11 November 2022 (UTC)

I eould say it's important that any change or updating of terms be graceful and as backward-compatible as possible. Maybe the larger minthma/gentle comma for 352/351 (old minthma) and smaller minthma/gentle comma for 364/363 (old gentle comma). I know that people have relied on the old names, and developed temperaments that, unlike my gentle but just as validly, temper out one but not the other. So this kind of collegiality and consultation is very helpful in seeking out, if you'll forgive the pun, the kindest and most gentle solution. [[User:Mschulter1325|Mschulter1325]] 02:46, 13 November 2022 (UTC)

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 == Approximate errors ==
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 :::::: I can't say anything about that. Considering the precision of 3.7 cents with which any interval is hit in 159edo and the generally accepted detuning degree of 13.7 cents of the major third in 12edo, considerations regarding consistency seem rather remote to me. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:47, 17 January 2021 (UTC)
+::::::: Actually, if you think about it, the generally accepted detuning of the major third in [[12edo]] still follows the same rules that I'm laying down, as the Syntonic comma ([[81/80]]), which is responsible for that detuning, is smaller than half a step in 12edo, and it's still smaller than half a step in [[24edo]].  In fact, the [[Pythagorean comma]] is also less than half of a step in 24edo, and thus, the 3-prime and the 5-prime can both be regarded as having "complete consistency" in 24edo as well as in 12edo.  However, when you start looking at [[36edo]], [[48edo]] and [[72edo]], suddenly, things don't turn out as good on this front, as the relative error percentage in these EDOs- especially for the Pythagorean comma- exceeds 50%.  This is why I moved on from the larger 12-based EDOs and was finally open to detwelvulating. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:41, 17 January 2021 (UTC)
+::::::: If you apply this same type of thinking to smaller EDOs, you see that 2edo is the first to have complete consistency in the 3-limit, but 3edo and 4edo both fail this test as the commas produced by their respective circles of fifths are larger than half of their respective step size.  After that, the next EDO to have complete consistency in the 3-limit is 5edo, which accomplishes a completely consistent representation of the 3-prime as 256/243, the interval produced from a single circle of fifths in 5edo, is smaller than half of a step in 5edo.  After that, the next EDO to have complete consistency in the 3-prime is 12edo itself, as 6edo, 7edo, 8edo, 9edo, 10edo, and 11edo all fail the test- of course, as I said, 24edo, which is related to 12edo, also passes this test. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:50, 17 January 2021 (UTC)
+::::::: So, what about the EDOs between 12edo and 24edo?  Well, according to my calculations, literally none of the EDOs from 13edo to 23edo demonstrate complete consistency in the 3-limit.  Even the well known [[22edo]] fails this test- looks like I've found one of that EDO's significant weaknesses, and a good enough reason for me not to use it.  Anyhow, I'll continue my calculations to see what other EDOs demonstrate the kind of complete 3-prime consistency, and I'll let y'all know about the first dozen or so members of the sequence that emerges from this. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:12, 17 January 2021 (UTC)
+::::::: I just got to thinking, and, the term "complete consistency" seems like a misleading term for the type of consistency I'm after- perhaps "telic consistency" or even "telicity" are a better terms for this, since this type of consistency means that stacking intervals of one prime will eventually reach an interval of a lower prime without reaching or exceeding 50% relative error, and "telic" is related to "telos" meaning "end" or "goal".  Since "telicity" is the noun used to refer to the property of being "telic", I think I'll use the term "telicity" for this type of n-consistency from now on. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:30, 18 January 2021 (UTC)
+== Linking 159edo Songs to This Page ==
+Hey, Xenwolf, since I've written like three songs in 159edo now, I'm wondering how to link these songs of mine to this page. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:37, 26 February 2021 (UTC)
+: I started the [[159edo #Music|''Music'']] section, please feel free to add what you like there. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:04, 26 February 2021 (UTC)
+== Gentle comma (364/363) and region, also tempering out 352/351 ==
+Please note that while this article correctly notes that 159-ed2 tempers out364/363, the gentle region and grntle temperament also involves tempering out 352/351. In other words, -3 fifths represents 13/11 or 33/28; and +4 fifths represents 14/11 or 33/28. Thus there sre two genle commas: 159-ed2 tempers out 364/363, but not 352/351; compare 38\159 for 13/11 or 33/28 with 39\159 (-3 fifths) for 32/27. In gentle temperament as I described it in 2002, 32;27 and 13/11 or 33/28 map to -3 fifths.
+[[User:Mschulter1325|Mschulter1325]] 01:18, 11 November 2022 (UTC)
+: Would you say the gentle comma should refer to either 352/351 or 364/363? And that gentle temperament is the 13-limit temperament tempering out both 352/351 and 364/363? In that case we'll need to come up with another name for 364/363 cuz right now it's known specifically as ''the'' gentle comma. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 05:14, 11 November 2022 (UTC)
+I eould say it's important that any change or updating of terms be graceful and as backward-compatible as possible. Maybe the larger minthma/gentle comma for 352/351 (old minthma) and smaller minthma/gentle comma for 364/363 (old gentle comma). I know that people have relied on the old names, and developed temperaments that, unlike my gentle but just as validly, temper out one but not the other. So this kind of collegiality and consultation is very helpful in seeking out, if you'll forgive the pun, the kindest and most gentle solution. [[User:Mschulter1325|Mschulter1325]] 02:46, 13 November 2022 (UTC)