Sqrt(25/24) - Revision history

Overthink: + rational intervals, misc. notes

2025-12-30T09:56:42Z

+ rational intervals, misc. notes

← Older revision		Revision as of 09:56, 30 December 2025
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	{{Infobox interval\|Ratio=\sqrt{25/24}\|Name=classical semichroma, ptolemaic semichroma\|Cents=35.336}}Sqrt(25/24), the '''classical semichroma''' or '''ptolemaic semichroma'''<ref group="note">It is not ''diptolemaic'' as it is only flattened by one [[81/80\|comma]] from the (hemi-)Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a ~~pure~~ neutral third [[~~Sqrt~~(3/2)]].		{{Infobox interval\|Ratio=\sqrt{25/24}\|Name=classical semichroma, ptolemaic semichroma\|Cents=35.336}}Sqrt(25/24), the '''classical semichroma''' or '''ptolemaic semichroma'''<ref group="note">It is not ''diptolemaic'' as it is only flattened by one [[81/80\|comma]] from the (hemi-)Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a neutral third [[sqrt(3/2)]] dividing the [[3/2\|perfect fifth]] in two.

	This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.		This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval. Any [[edo]] that maps [[25/24]] to an even number of steps, and thus any edo that contains a true neutral third, contains a representation of this interval.

	The interval, when stacked, yields a tuning system close to [[34edo]], which consistently represents it as one step.		Rational intervals that are close to this interval include [[49/48]] and [[50/49]], which stack to 25/24. The difference between 49/48 and 50/49 is [[2401/2400]], and tempering it out leads to the super-accurate [[Breed (temperament)\|breed]] temperament.

			This interval, when stacked, yields a tuning system close to [[34edo]], which consistently represents it as one step.

	== Listen ==		== Listen ==
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	EDOs that have both a good [[5-odd-limit]] and a sqrt(25/24) distinct from [[25/24]] include (among others) [[24edo#Counterpoint\|24]], [[27edo\|27]], [[31edo\|31]] and [[34edo\|34]].		EDOs that have both a good [[5-odd-limit]] and a sqrt(25/24) distinct from [[25/24]] include (among others) [[24edo#Counterpoint\|24]], [[27edo\|27]], [[31edo\|31]] and [[34edo\|34]].

	[[34edo~~\|34-edo~~]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo\|441]].		[[34edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo\|441]].
	<references group="note" />		<references group="note" />

VectorGraphics at 17:09, 3 June 2025

2025-06-03T17:09:11Z

← Older revision		Revision as of 17:09, 3 June 2025
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	{{Infobox interval\|Ratio=\sqrt{25/24}\|Name=classical semichroma, ptolemaic semichroma\|Cents=35.336}}Sqrt(25/24), the '''classical semichroma''' or '''ptolemaic semichroma'''<ref group="note">It is not ''diptolemaic'' as it is only flattened by one [[81/80\|comma]] from the Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]].		{{Infobox interval\|Ratio=\sqrt{25/24}\|Name=classical semichroma, ptolemaic semichroma\|Cents=35.336}}Sqrt(25/24), the '''classical semichroma''' or '''ptolemaic semichroma'''<ref group="note">It is not ''diptolemaic'' as it is only flattened by one [[81/80\|comma]] from the (hemi-)Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]].

	This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.		This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.

VectorGraphics at 17:07, 3 June 2025

2025-06-03T17:07:16Z

← Older revision		Revision as of 17:07, 3 June 2025
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	Sqrt(25/24), the '''classical semichroma''' or '''ptolemaic semichroma'''<ref group="note">It is not ''diptolemaic'' as it is only flattened by one [[81/80\|comma]] from the Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]].		{{Infobox interval\|Ratio=\sqrt{25/24}\|Name=classical semichroma, ptolemaic semichroma\|Cents=35.336}}Sqrt(25/24), the '''classical semichroma''' or '''ptolemaic semichroma'''<ref group="note">It is not ''diptolemaic'' as it is only flattened by one [[81/80\|comma]] from the Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]].

	~~{{Infobox interval\|Ratio=\sqrt{25/24}\|Name=classical semichroma, ptolemaic semichroma\|Cents=35.336}}~~

	This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.		This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.

VectorGraphics at 17:07, 3 June 2025

2025-06-03T17:07:08Z

← Older revision		Revision as of 17:07, 3 June 2025
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	~~{{Infobox ET}}~~		Sqrt(25/24), the '''classical semichroma''' or '''ptolemaic semichroma'''<ref group="note">It is not ''diptolemaic'' as it is only flattened by one [[81/80\|comma]] from the Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]].
	~~2ed25~~/24 is ~~a tuning system created~~ by ~~dividing~~ the ~~interval~~ of [[25/24]] ~~logarithmically into steps of about 35~~.~~336 cents each. Each step represents~~ a ~~frequency ratio of~~ the ~~square root of 25~~/24.

	~~It is almost equal to [[34edo]].~~		{{Infobox interval\|Ratio=\sqrt{25/24}\|Name=classical semichroma, ptolemaic semichroma\|Cents=35.336}}
	~~==Theory~~==
	~~One step of this tuning, the '''~~classical semichroma~~'''~~, ~~is the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]]~~.

	This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.		This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.

			The interval, when stacked, yields a tuning system close to [[34edo]], which consistently represents it as one step.

	== Listen ==		== Listen ==
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	[[34edo\|34-edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo\|441]].		[[34edo\|34-edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo\|441]].
			<references group="note" />

VectorGraphics: VectorGraphics moved page 2ed25/24 to Sqrt(25/24) over redirect: There's precedent for radical intervals having their own pages, and additionally, most of what this page discusses is the radical interval, not the tuning system.

2025-06-03T17:01:50Z

VectorGraphics moved page 2ed25/24 to Sqrt(25/24) over redirect: There's precedent for radical intervals having their own pages, and additionally, most of what this page discusses is the radical interval, not the tuning system.

← Older revision	Revision as of 17:01, 3 June 2025
(No difference)

VectorGraphics: relation to sqrtP5 probably more important than voice leading, also plan to reformat this as a radical interval page rather than an ET page at some point

2025-06-03T11:56:52Z

relation to sqrtP5 probably more important than voice leading, also plan to reformat this as a radical interval page rather than an ET page at some point

← Older revision		Revision as of 11:56, 3 June 2025
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	It is almost equal to [[34edo]].		It is almost equal to [[34edo]].
	==Theory==		==Theory==
	One step of this tuning is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.		One step of this tuning, the '''classical semichroma''', is the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]].

			This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.

	== Listen ==		== Listen ==

Eliora at 16:24, 26 November 2022

2022-11-26T16:24:09Z

← Older revision		Revision as of 16:24, 26 November 2022
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	{{Infobox ~~Interval~~		{{Infobox ET}}
	~~\| Ratio = \sqrt{25/24~~}		2ed25/24 is a tuning system created by dividing the interval of [[25/24]] logarithmically into steps of about 35.336 cents each. Each step represents a frequency ratio of the square root of 25/24.
	~~\| Monzo = -3/2 -1/2 1~~
	~~\| Cents = 35.33621343214121~~
	~~\| Name = square root of 25/24~~
	~~\| Calc = sqrt(25~~/24)
	}}
	~~The '''square root~~ of [[25/24]]~~''' ('''sqrt(25/24)''') is an interval measuring approximately~~ 35.336~~{{cent}} that allows to pass from~~ a ~~just major third (5~~/~~4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa~~.

	Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.		It is almost equal to [[34edo]].
			==Theory==
			One step of this tuning is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.

	== Listen ==		== Listen ==

Eliora: Eliora moved page Sqrt(25/24) to 2ed25/24: There is no need for pages about individual ET steps when they can be perfectly doubled by the same edonoi.

2022-11-26T16:20:49Z

Eliora moved page Sqrt(25/24) to 2ed25/24: There is no need for pages about individual ET steps when they can be perfectly doubled by the same edonoi.

← Older revision	Revision as of 16:20, 26 November 2022
(No difference)

Plumtree: Infobox Interval added

2022-10-27T18:03:45Z

Infobox Interval added

← Older revision		Revision as of 18:03, 27 October 2022
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			{{Infobox Interval
			\| Ratio = \sqrt{25/24}
			\| Monzo = -3/2 -1/2 1
			\| Cents = 35.33621343214121
			\| Name = square root of 25/24
			\| Calc = sqrt(25/24)
			}}
	The '''square root of [[25/24]]''' ('''sqrt(25/24)''') is an interval measuring approximately 35.336{{cent}} that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa.		The '''square root of [[25/24]]''' ('''sqrt(25/24)''') is an interval measuring approximately 35.336{{cent}} that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa.

	Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.		Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.

	~~[https://www.yacavone.net/xen-calc/?q=sqrt(25/24) xen-calc]~~

	== Listen ==		== Listen ==
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	[[34edo\|34-edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo\|441]].		[[34edo\|34-edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo\|441]].

	~~[[Category:Irrational intervals]]~~

Xenwolf: It would be good to have a small article (or section) about the voice leading concept of equal contrary motion

2022-10-03T20:49:42Z

It would be good to have a small article (or section) about the voice leading concept of equal contrary motion

← Older revision		Revision as of 20:49, 3 October 2022
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	The '''square root of [[25/24]]''' ('''sqrt(25/24)''') is an interval measuring approximately 35.336{{cent}} that allows to pass from a just major third (5/4) to a just minor third (6/5) by equal contrary motion, and vice versa.		The '''square root of [[25/24]]''' ('''sqrt(25/24)''') is an interval measuring approximately 35.336{{cent}} that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa.

	Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.		Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.