Talk:56/45 - Revision history

FloraC: Update

2026-01-06T12:27:20Z

Update

← Older revision		Revision as of 12:27, 6 January 2026
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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)		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)

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

Aura at 15:28, 29 November 2020

2020-11-29T15:28:36Z

← Older revision		Revision as of 15:28, 29 November 2020
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	:: 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)		:: 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)

	:: 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)		:: 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)

FloraC: /* Criterion for a Marvelous intervals */ more

2020-11-29T15:15:44Z

Criterion for a Marvelous intervals: more

← Older revision		Revision as of 15:15, 29 November 2020
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	: 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)		: 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.		:: 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)		:: 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)

			:: 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)

FloraC: /* Criterion for a Marvelous intervals */ re

2020-11-29T15:01:21Z

Criterion for a Marvelous intervals: re

← Older revision		Revision as of 15:01, 29 November 2020
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	: 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)		: 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)

Aura at 14:31, 29 November 2020

2020-11-29T14:31:54Z

← Older revision		Revision as of 14:31, 29 November 2020
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	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)		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 ~~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)		: 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)

Aura at 14:29, 29 November 2020

2020-11-29T14:29:07Z

← Older revision		Revision as of 14:29, 29 November 2020
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	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)		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 indeed those that differ from 3-limit and 5-limit. Where the resulting 7-limit interval is something like 7/4 or 8/7, that is a different story~~, and 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)		: 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)

Aura at 14:22, 29 November 2020

2020-11-29T14:22:43Z

← Older revision		Revision as of 14:22, 29 November 2020
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	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)		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 indeed those that differ from 3-limit and 5-limit. Where the resulting 7-limit interval is something like 7/4 or 8/7, that is a different story, and 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)

Xenwolf: /* Criterion for a Marvelous intervals */ link to cat added

2020-11-29T13:51:30Z

Criterion for a Marvelous intervals: link to cat added

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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 ~~here~~? --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 13:49, 29 November 2020 (UTC)		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)

Xenwolf: /* Criterion for a Marvelous intervals */ new section

2020-11-29T13:49:02Z

Criterion for a Marvelous intervals: new section

New page

== 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 here? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:49, 29 November 2020 (UTC)

← Older revision		Revision as of 12:27, 6 January 2026
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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)		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)

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

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	:: 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)		:: 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)

	:: 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)		:: 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)