Talk:56/45: Difference between revisions

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== Criterion for a Marvelous intervals ==

Maybe the [https://en.xen.wiki/index.php?title=56/45&diff=prev&oldid=53728 addition to the marvel category] was wrong. How can we decide which intervals belong into [[:Category:Marvel]]? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:51, 29 November 2020 (UTC)

: I'm personally thinking that "marvelous intervals" are the more complex 7-limit intervals that differ from 3-limit and 5-limit by [[225/224]]. Where the resulting 7-limit interval is something like [[7/4]] or [[8/7]], that is a different story as these two intervals are simple, and [[7/6]] and [[9/7]] similarly don't count for much the same reason. Furthermore, we should remember that marvelous intervals always have a second function, and that function should be acknowledged. After all, there's a reason I call 7/4 a "Varicant"- it simultaneously acts as both a subminor seventh and a type of sixth, with the former behavior being consistent with the nature of its relation to both [[4/3]] and [[3/2]], and the latter behavior being consistent with the nature of its relation to both [[5/4]] and [[11/8]]. I don't know how good this idea is, but I suspect that it's a start. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:22, 29 November 2020 (UTC)

:: By pure logic, since 56/45 is not ''a marvel comma to a Pythagorean interval'', it's not really a marvelous interval. It's [[:Category:Hemifamity]] instead cuz it's [[5120/5103]] to the Pythagorean d4. However, I suppose musicians rarely approach it this way. The point is – it's by equating the interval with 5/4 (not Pythagorean d4) that "consonance" is obtained when it arises, so marvel (not hemifamity) is usually the targeted comma.

~~Maybe the~~ [~~https:~~//en.~~xen~~.~~wiki/index~~.~~php?title=56/45&diff=prev&oldid=53728 addition to~~ the marvel ~~category] was wrong~~. ~~How can we decide which intervals belong into~~ [[:~~Category~~:~~Marvel~~]]~~? --~~[[User:~~Xenwolf~~|~~Xenwolf~~]] ([[User talk:~~Xenwolf~~|talk]]) 13:51, 29 November 2020 (UTC)

:: If that makes sense to you, you'll also see [[25/21]] and [[63/50]] should belong to marvel (not starling), but again people are comparing them with [[6/5]] and [[5/4]], respectively. So there's not a true criterion but pragmaticism. (For clarity, I'm just stating what I found and not suggesting any changes.) [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:01, 29 November 2020 (UTC)

::: Good points... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:28, 29 November 2020 (UTC)

::: Okay, I'm changing it by at least clarifying that the marvel comma is attached to a ptolemaic interval. I'm also adding an alternative name based on d4. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:27, 6 January 2026 (UTC)

:: And no, 7/4, 7/6, and 14/9 are simply ''archytas''. It's weird for these 2.3.7 intervals to involve any comma of 5. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:15, 29 November 2020 (UTC)

: I'm personally thinking that "marvelous intervals" are indeed those that differ from 3-limit and 5-limit by [[225/224]]. Where the resulting 7-limit interval is something like [[7/4]] or [[8/7]], that is a different story as these two intervals belong directly in the chain of 7 prime intervals. Furthermore, we should remember that marvelous intervals always have a second function, and that function should be acknowledged. After all, there's a reason I call 7/4 a "Varicant"- it simultaneously acts as both a subminor seventh and a type of sixth, with the former behavior being consistent with the nature of its relation to both [[4/3]] and [[3/2]], and the latter behavior being consistent with the nature of its relation to both [[5/4]] and [[11/8]]. I don't know how good this idea is, but I suspect that it's a start. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:22, 29 November 2020 (UTC)

::: Right. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:28, 29 November 2020 (UTC)

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 == Criterion for a Marvelous intervals ==
+Maybe the [https://en.xen.wiki/index.php?title=56/45&diff=prev&oldid=53728 addition to the marvel category] was wrong. How can we decide which intervals belong into [[:Category:Marvel]]? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:51, 29 November 2020 (UTC)
+: I'm personally thinking that "marvelous intervals" are the more complex 7-limit intervals that differ from 3-limit and 5-limit by [[225/224]].  Where the resulting 7-limit interval is something like [[7/4]] or [[8/7]], that is a different story as these two intervals are simple, and [[7/6]] and [[9/7]] similarly don't count for much the same reason.  Furthermore, we should remember that marvelous intervals always have a second function, and that function should be acknowledged.  After all, there's a reason I call 7/4 a "Varicant"- it simultaneously acts as both a subminor seventh and a type of sixth, with the former behavior being consistent with the nature of its relation to both [[4/3]] and [[3/2]], and the latter behavior being consistent with the nature of its relation to both [[5/4]] and [[11/8]].  I don't know how good this idea is, but I suspect that it's a start. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:22, 29 November 2020 (UTC)
+:: By pure logic, since 56/45 is not ''a marvel comma to a Pythagorean interval'', it's not really a marvelous interval. It's [[:Category:Hemifamity]] instead cuz it's [[5120/5103]] to the Pythagorean d4. However, I suppose musicians rarely approach it this way. The point is – it's by equating the interval with 5/4 (not Pythagorean d4) that "consonance" is obtained when it arises, so marvel (not hemifamity) is usually the targeted comma.
-Maybe the [https://en.xen.wiki/index.php?title=56/45&diff=prev&oldid=53728 addition to the marvel category] was wrong. How can we decide which intervals belong into [[:Category:Marvel]]? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:51, 29 November 2020 (UTC)
+:: If that makes sense to you, you'll also see [[25/21]] and [[63/50]] should belong to marvel (not starling), but again people are comparing them with [[6/5]] and [[5/4]], respectively. So there's not a true criterion but pragmaticism. (For clarity, I'm just stating what I found and not suggesting any changes.) [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:01, 29 November 2020 (UTC)
+::: Good points... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:28, 29 November 2020 (UTC)
+::: Okay, I'm changing it by at least clarifying that the marvel comma is attached to a ptolemaic interval. I'm also adding an alternative name based on d4. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:27, 6 January 2026 (UTC)
+:: And no, 7/4, 7/6, and 14/9 are simply ''archytas''. It's weird for these 2.3.7 intervals to involve any comma of 5. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:15, 29 November 2020 (UTC)
-: I'm personally thinking that "marvelous intervals" are indeed those that differ from 3-limit and 5-limit by [[225/224]].  Where the resulting 7-limit interval is something like [[7/4]] or [[8/7]], that is a different story as these two intervals belong directly in the chain of 7 prime intervals.  Furthermore, we should remember that marvelous intervals always have a second function, and that function should be acknowledged.  After all, there's a reason I call 7/4 a "Varicant"- it simultaneously acts as both a subminor seventh and a type of sixth, with the former behavior being consistent with the nature of its relation to both [[4/3]] and [[3/2]], and the latter behavior being consistent with the nature of its relation to both [[5/4]] and [[11/8]].  I don't know how good this idea is, but I suspect that it's a start. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:22, 29 November 2020 (UTC)
+::: Right. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:28, 29 November 2020 (UTC)