49/48 - Revision history

FloraC: Undo revision 230355 by VectorGraphics (talk)

2026-05-15T09:36:55Z

Undo revision 230355 by VectorGraphics (talk)

← Older revision		Revision as of 09:36, 15 May 2026
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	}}		}}
	{{Wikipedia\|Septimal diesis}}		{{Wikipedia\|Septimal diesis}}
	'''49/48''', the '''large septimal ~~diesis''' or '''interseptimal~~ diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo\|12tet]].		'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo\|12tet]].

	This interval has a function similar to [[25/24]] in that it separates the [[7/6]] and [[8/7]] intervals in a [[6:7:8]] triad, similarly to how [[25/24]] separates [[5/4]] and [[6/5]] in a [[4:5:6]] triad. The 6:7:8 triad consists of odd [[harmonic]]s [[1/1\|1]], [[3/1\|3]], and [[7/1\|7]] [[octave reduced]] to span the [[4/3\|perfect fourth]], while the 4:5:6 triad consists of odd harmonics 1, 3, and 5 octave reduced to span the [[3/2\|perfect fifth]]. In that regard, tempering out 49/48 can be considered a form of [[exotemperament\|exotempering]] that neutralizes the 6:7:8 chord and equates it with its inverse [[21:24:28\|1/(8:7:6)]], just like how [[dicot]], which tempers out 25/24, neutralizes the 4:5:6 chord and equates it with its inverse [[10:12:15\|1/(6:5:4)]].		This interval has a function similar to [[25/24]] in that it separates the [[7/6]] and [[8/7]] intervals in a [[6:7:8]] triad, similarly to how [[25/24]] separates [[5/4]] and [[6/5]] in a [[4:5:6]] triad. The 6:7:8 triad consists of odd [[harmonic]]s [[1/1\|1]], [[3/1\|3]], and [[7/1\|7]] [[octave reduced]] to span the [[4/3\|perfect fourth]], while the 4:5:6 triad consists of odd harmonics 1, 3, and 5 octave reduced to span the [[3/2\|perfect fifth]]. In that regard, tempering out 49/48 can be considered a form of [[exotemperament\|exotempering]] that neutralizes the 6:7:8 chord and equates it with its inverse [[21:24:28\|1/(8:7:6)]], just like how [[dicot]], which tempers out 25/24, neutralizes the 4:5:6 chord and equates it with its inverse [[10:12:15\|1/(6:5:4)]].

VectorGraphics at 23:25, 14 May 2026

2026-05-14T23:25:13Z

← Older revision		Revision as of 23:25, 14 May 2026
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	}}		}}
	{{Wikipedia\|Septimal diesis}}		{{Wikipedia\|Septimal diesis}}
	'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo\|12tet]].		'''49/48''', the '''large septimal diesis''' or '''interseptimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo\|12tet]].

	This interval has a function similar to [[25/24]] in that it separates the [[7/6]] and [[8/7]] intervals in a [[6:7:8]] triad, similarly to how [[25/24]] separates [[5/4]] and [[6/5]] in a [[4:5:6]] triad. The 6:7:8 triad consists of odd [[harmonic]]s [[1/1\|1]], [[3/1\|3]], and [[7/1\|7]] [[octave reduced]] to span the [[4/3\|perfect fourth]], while the 4:5:6 triad consists of odd harmonics 1, 3, and 5 octave reduced to span the [[3/2\|perfect fifth]]. In that regard, tempering out 49/48 can be considered a form of [[exotemperament\|exotempering]] that neutralizes the 6:7:8 chord and equates it with its inverse [[21:24:28\|1/(8:7:6)]], just like how [[dicot]], which tempers out 25/24, neutralizes the 4:5:6 chord and equates it with its inverse [[10:12:15\|1/(6:5:4)]].		This interval has a function similar to [[25/24]] in that it separates the [[7/6]] and [[8/7]] intervals in a [[6:7:8]] triad, similarly to how [[25/24]] separates [[5/4]] and [[6/5]] in a [[4:5:6]] triad. The 6:7:8 triad consists of odd [[harmonic]]s [[1/1\|1]], [[3/1\|3]], and [[7/1\|7]] [[octave reduced]] to span the [[4/3\|perfect fourth]], while the 4:5:6 triad consists of odd harmonics 1, 3, and 5 octave reduced to span the [[3/2\|perfect fifth]]. In that regard, tempering out 49/48 can be considered a form of [[exotemperament\|exotempering]] that neutralizes the 6:7:8 chord and equates it with its inverse [[21:24:28\|1/(8:7:6)]], just like how [[dicot]], which tempers out 25/24, neutralizes the 4:5:6 chord and equates it with its inverse [[10:12:15\|1/(6:5:4)]].

TallKite: updated the comma color name

2026-04-29T04:05:49Z

updated the comma color name

← Older revision		Revision as of 04:05, 29 April 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma		\| Name = large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma
	\| Color name = zz2, zozo 2nd,<br>~~Zozo comma~~		\| Color name = zz2, zozo 2nd,<br>zzM, zozoma
	\| Sound = Ji-49-48-csound-foscil-220hz.mp3		\| Sound = Ji-49-48-csound-foscil-220hz.mp3
	\| Comma = yes		\| Comma = yes

Overthink: /* Temperaments */ other interpretation

2026-03-21T18:29:18Z

Temperaments: other interpretation

← Older revision		Revision as of 18:29, 21 March 2026
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	== Temperaments ==		== Temperaments ==
	49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where 7/6 and 8/7 are equated, and the fourth is split in a perfect half. 3/1 is also split into two [[7/4]]'s. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''.		49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where 7/6 and 8/7 are equated, and the fourth is split in a perfect half. 3/1 is also split into two [[7/4]]~[[12/7]]'s. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''.

	''It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct'', but it ''can'' be equated with other commas; for example:		''It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct'', but it ''can'' be equated with other commas; for example:

Squib: /* Temperaments */

2026-03-21T16:37:05Z

Temperaments

← Older revision		Revision as of 16:37, 21 March 2026
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	== Temperaments ==		== Temperaments ==
	49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where ~~the two intervals~~ are equated, and the fourth is split in a perfect half. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''.		49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where 7/6 and 8/7 are equated, and the fourth is split in a perfect half. 3/1 is also split into two [[7/4]]'s. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''.

	''It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct'', but it ''can'' be equated with other commas; for example:		''It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct'', but it ''can'' be equated with other commas; for example:

Overthink: + chroma function

2025-12-30T09:45:42Z

+ chroma function

← Older revision		Revision as of 09:45, 30 December 2025
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	{{Wikipedia\|Septimal diesis}}		{{Wikipedia\|Septimal diesis}}
	'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo\|12tet]].		'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo\|12tet]].

			This interval has a function similar to [[25/24]] in that it separates the [[7/6]] and [[8/7]] intervals in a [[6:7:8]] triad, similarly to how [[25/24]] separates [[5/4]] and [[6/5]] in a [[4:5:6]] triad. The 6:7:8 triad consists of odd [[harmonic]]s [[1/1\|1]], [[3/1\|3]], and [[7/1\|7]] [[octave reduced]] to span the [[4/3\|perfect fourth]], while the 4:5:6 triad consists of odd harmonics 1, 3, and 5 octave reduced to span the [[3/2\|perfect fifth]]. In that regard, tempering out 49/48 can be considered a form of [[exotemperament\|exotempering]] that neutralizes the 6:7:8 chord and equates it with its inverse [[21:24:28\|1/(8:7:6)]], just like how [[dicot]], which tempers out 25/24, neutralizes the 4:5:6 chord and equates it with its inverse [[10:12:15\|1/(6:5:4)]].

	== Temperaments ==		== Temperaments ==

Overthink: /* Approximations */ remove unison approximations

2025-12-24T09:18:50Z

Approximations: remove unison approximations

← Older revision		Revision as of 09:18, 24 December 2025
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	== Approximations ==		== Approximations ==
	{{interval edo approximation}}		{{interval edo approximation\|min_edo=5}}

	== See also ==		== See also ==

Pailiaq at 00:47, 27 November 2025

2025-11-27T00:47:36Z

← Older revision		Revision as of 00:47, 27 November 2025
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	See [[Semaphoresmic family]] for the rank-3 family where it is tempered out. See [[Semaphoresmic clan]] for the rank-2 clan where it is tempered out.		See [[Semaphoresmic family]] for the rank-3 family where it is tempered out. See [[Semaphoresmic clan]] for the rank-2 clan where it is tempered out.

			== Approximations ==
			{{interval edo approximation}}

	== See also ==		== See also ==

Hkm at 15:01, 22 July 2025

2025-07-22T15:01:30Z

← Older revision		Revision as of 15:01, 22 July 2025
Line 12:		Line 12:
	}}		}}
	{{Wikipedia\|Septimal diesis}}		{{Wikipedia\|Septimal diesis}}
	'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].		'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo\|12tet]].

	== Temperaments ==		== Temperaments ==

FloraC: + "large septimal sixth-tone"

2025-07-22T13:21:30Z

+ "large septimal sixth-tone"

← Older revision		Revision as of 13:21, 22 July 2025
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	}}		}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = large septimal diesis, slendro diesis, semaphore comma, semaphoresma		\| Name = large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma
	\| Color name = zz2, zozo 2nd,<br>Zozo comma		\| Color name = zz2, zozo 2nd,<br>Zozo comma
	\| Sound = Ji-49-48-csound-foscil-220hz.mp3		\| Sound = Ji-49-48-csound-foscil-220hz.mp3
Line 12:		Line 12:
	}}		}}
	{{Wikipedia\|Septimal diesis}}		{{Wikipedia\|Septimal diesis}}
	'''49/48''', the '''large septimal diesis''' (or '''slendro diesis'''), is a [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].		'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].

	== Temperaments ==		== Temperaments ==