Talk:56/45: Difference between revisions
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== Criterion for a Marvelous intervals == | == 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. | |||
:: 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) | |||
::: Right. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:28, 29 November 2020 (UTC) | |||
Latest revision as of 12:27, 6 January 2026
Criterion for a Marvelous intervals
Maybe the addition to the marvel category was wrong. How can we decide which intervals belong into Category:Marvel? --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. --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.
- 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.) FloraC (talk) 15:01, 29 November 2020 (UTC)