Talk:159edo: Difference between revisions

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== Approximate errors ==

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::::::: 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 ~~now~~, 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)

::::::: 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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 ::::::: 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 now, 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)
+::::::: 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)