Talk:56/45

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)

Good points... --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. —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. FloraC (talk) 15:15, 29 November 2020 (UTC)

Right. --Aura (talk) 15:28, 29 November 2020 (UTC)