Shallowtone - Revision history

Hill: Separate the comma groups with ";", as elsewhere in the field and on other regtemp pages

2026-09-08T15:19:19Z

Separate the comma groups with ";", as elsewhere in the field and on other regtemp pages

← Older revision		Revision as of 15:19, 8 September 2026
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	\| Title = Shallowtone		\| Title = Shallowtone
	\| Subgroups = 2.3.5, 2.3.5.7		\| Subgroups = 2.3.5, 2.3.5.7
	\| Comma basis = [[295245/262144]] (5-limit)<br>[[36/35]], [[295245/262144]] (7-limit)		\| Comma basis = [[295245/262144]] (5-limit);<br>[[36/35]], [[295245/262144]] (7-limit)
	\| Mapping = 1; 1 -10 12		\| Mapping = 1; 1 -10 12
	\| Edo join 1 = 7 \| Edo join 2 = 30b		\| Edo join 1 = 7 \| Edo join 2 = 30b

Overthink: This category feels fitting enough (no 9-odd-limit monotone and high error)

2026-07-06T02:37:33Z

This category feels fitting enough (no 9-odd-limit monotone and high error)

← Older revision		Revision as of 02:37, 6 July 2026
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	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]
			[[Category:Exotemperaments]]

FloraC: + infobox & rework on intro

2026-07-05T11:25:28Z

+ infobox & rework on intro

← Older revision		Revision as of 11:25, 5 July 2026
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	'''Shallowtone''' is a [[~~5-limit~~]] ~~and higher~~ [[~~regular temperament\|temperament~~]] ~~which~~ [[tempering out\|~~tempers~~ out~~]] the [[shallowtone comma~~]]. It is generated by a ~~flat~~ fifth, ~~which is~~ typically sharper than in [[mavila]] but flatter than in [[7edo~~]]. This gives it a high [[error~~]], ~~although not as much as mavila. The [[~]]~~[[5/4]] is reached by minus ten fifths octave-reduced, which is an augmented third (~~C–Ex~~) in melodic antidiatonic notation and a diminished third (~~C–Ebb~~) in harmonic antidiatonic notation. The only reasonable [[extension]] to the [[7-limit]] tempers out [[36/35]]. Additionally, there is a weak extension [[Greenwoodmic temperaments #Semishallowtone\|semishallowtone]] with a half-octave period, tempering out [[405/392]].		{{Infobox regtemp
			\| Title = Shallowtone
			\| Subgroups = 2.3.5, 2.3.5.7
			\| Comma basis = [[295245/262144]] (5-limit)<br>[[36/35]], [[295245/262144]] (7-limit)
			\| Mapping = 1; 1 -10 12
			\| Edo join 1 = 7 \| Edo join 2 = 30b
			\| Generators = 3/2
			\| Generators tuning = 681.2
			\| Optimization method = CWE
			\| MOS scales = [[2L 3s]], [[2L 5s]], [[7L 2s]]
			\| Odd limit 1 = 5 \| Mistuning 1 = 18.7 \| Complexity 1 = 16
			\| Odd limit 2 = 9 \| Mistuning 2 = 45.3 \| Complexity 2 = 23
			}}
			'''Shallowtone''' is a [[regular temperament\|temperament]] where the [[shallowtone comma]] is [[tempering out\|tempered out]]. It is generated by a flattened [[3/2\|perfect fifth]], typically sharper than in [[mavila]] but flatter than in [[7edo]], and [[5/4]] is reached by minus ten fifths [[octave reduction\|octave-reduced]], which is an augmented third (C–E𝄪) in melodic antidiatonic notation and a diminished third (C–E𝄫) in harmonic antidiatonic notation. This gives it a high [[error]], although not as much as mavila.

			The only reasonable [[extension]] to the [[7-limit]] tempers out [[36/35]]. Additionally, there is a weak extension [[Greenwoodmic temperaments #Semishallowtone\|semishallowtone]] with a half-octave period, tempering out [[405/392]].

	The name was coined by [[User:CompactStar\|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface".		The name was coined by [[User:CompactStar\|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface".

FloraC: Cleanup

2026-03-10T07:10:55Z

Cleanup

← Older revision		Revision as of 07:10, 10 March 2026
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	'''Shallowtone''' is a [[5-limit]] and higher [[temperament]] which tempers out the [[shallowtone comma]]. It is generated by a flat fifth, which is typically sharper than in [[mavila]] but flatter than in [[7edo]]. This gives it a high [[error]], although not as much as mavila. The ~[[5/4]] is reached by minus ten fifths octave-reduced, which is an augmented third (~~C-Ex~~) in melodic antidiatonic notation and a diminished third (~~C-Ebb~~) in harmonic antidiatonic notation. The only reasonable extension to the 7-limit tempers out [[36/35]]. Additionally, there is a weak extension [[Greenwoodmic temperaments#Semishallowtone\|semishallowtone]] with a half-octave period, tempering out [[405/392]].		'''Shallowtone''' is a [[5-limit]] and higher [[regular temperament\|temperament]] which [[tempering out\|tempers out]] the [[shallowtone comma]]. It is generated by a flat fifth, which is typically sharper than in [[mavila]] but flatter than in [[7edo]]. This gives it a high [[error]], although not as much as mavila. The [[~]][[5/4]] is reached by minus ten fifths octave-reduced, which is an augmented third (C–Ex) in melodic antidiatonic notation and a diminished third (C–Ebb) in harmonic antidiatonic notation. The only reasonable [[extension]] to the [[7-limit]] tempers out [[36/35]]. Additionally, there is a weak extension [[Greenwoodmic temperaments #Semishallowtone\|semishallowtone]] with a half-octave period, tempering out [[405/392]].

	The name was coined by [[User:CompactStar\|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface".		The name was coined by [[User:CompactStar\|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface".

	See [[~~Syntonic–chromatic equivalence continuum~~#Shallowtone]] for technical data.		See [[Mint temperaments #Shallowtone]] for technical data.

	== Interval chain ==		== Interval chain ==
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! rowspan="2" \| &#~~35;~~		! rowspan="2" \| #
	! rowspan="2" \| Cents*		! rowspan="2" \| Cents*
	! colspan="2" \| Approximate ratios		! colspan="2" \| Approximate ratios
Line 97:		Line 97:
	\| [[117/80]], [[189/128]]		\| [[117/80]], [[189/128]]
	\|}		\|}
	<nowiki />* In 5-limit CTE tuning		<nowiki/>* In 5-limit CTE tuning, octave reduced

	[[Category:Shallowtone\| ]] <!-- main article -->		[[Category:Shallowtone\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]

FloraC: - parent category

2025-04-28T14:40:40Z

- parent category

← Older revision		Revision as of 14:40, 28 April 2025
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	<nowiki />* In 5-limit CTE tuning		<nowiki />* In 5-limit CTE tuning

	~~[[Category:Temperaments]]~~
	[[Category:Shallowtone\| ]] <!-- main article -->		[[Category:Shallowtone\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]

Lériendil at 23:46, 19 April 2025

2025-04-19T23:46:58Z

← Older revision		Revision as of 23:46, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Shallowtone\| ]] <!-- main article -->		[[Category:Shallowtone\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]

ArrowHead294 at 18:32, 7 January 2025

2025-01-07T18:32:53Z

← Older revision		Revision as of 18:32, 7 January 2025
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	== Interval chain ==		== Interval chain ==
	In the following table, prime harmonics are labeled in '''bold'''.		In the following table, prime harmonics are labeled in '''bold'''.
	{\|class="wikitable"
			{\| class="wikitable"
	\|-		\|-
	!rowspan="2"\|#		! rowspan="2" \| #
	!rowspan="2"\|Cents*		! rowspan="2" \| Cents*
	!colspan="2"\|Approximate ratios		! colspan="2" \| Approximate ratios
	\|-		\|-
	!5-limit		! 5-limit
	!13-limit extension		! 13-limit extension
	\|-		\|-
	\|0		\| 0
	\|0.000		\| 0.000
	\|[[1/1]]		\| [[1/1]]
	\|		\|
	\|-		\|-
	\|1		\| 1
	\|681.801		\| 681.801
	\|'''[[3/2]]'''		\| '''[[3/2]]'''
	\|[[13/9]]		\| [[13/9]]
	\|-		\|-
	\|2		\| 2
	\|163.602		\| 163.602
	\|[[9/8]]		\| [[9/8]]
	\|[[11/10]], [[13/12]], [[35/32]], [[81/70]], [[8192/8019]]		\| [[11/10]], [[13/12]], [[35/32]], [[81/70]], [[8192/8019]]
	\|-		\|-
	\|3		\| 3
	\|845.403		\| 845.403
	\|[[27/16]]		\| [[27/16]]
	\|'''[[13/8]]''', [[117/70]], [[4096/2673]]		\| '''[[13/8]]''', [[117/70]], [[4096/2673]]
	\|-		\|-
	\|4		\| 4
	\|327.204		\| 327.204
	\|[[81/64]]		\| [[81/64]]
	\|[[39/32]], [[99/80]], [[1024/891]]		\| [[39/32]], [[99/80]], [[1024/891]]
	\|-		\|-
	\|5		\| 5
	\|1009.0511		\| 1009.0511
	\|[[243/128]]		\| [[243/128]]
	\|[[117/64]], [[512/297]]		\| [[117/64]], [[512/297]]
	\|-		\|-
	\|6		\| 6
	\|490.806		\| 490.806
	\|[[512/405]], [[729/512]]		\| [[512/405]], [[729/512]]
	\|[[128/99]]		\| [[128/99]]
	\|-		\|-
	\|7		\| 7
	\|1172.607		\| 1172.607
	\|[[256/135]]		\| [[256/135]]
	\|[[64/33]]		\| [[64/33]]
	\|-		\|-
	\|8		\| 8
	\|654.408		\| 654.408
	\|[[64/45]]		\| [[64/45]]
	\|'''[[16/11]]''', [[112/81]]		\| '''[[16/11]]''', [[112/81]]
	\|-		\|-
	\|9		\| 9
	\|136.209		\| 136.209
	\|[[16/15]]		\| [[16/15]]
	\|[[12/11]], [[28/27]]		\| [[12/11]], [[28/27]]
	\|-		\|-
	\|10		\| 10
	\|818.010		\| 818.010
	\|'''[[8/5]]'''		\| '''[[8/5]]'''
	\|[[14/9]], [[18/11]], [[64/39]]		\| [[14/9]], [[18/11]], [[64/39]]
	\|-		\|-
	\|11		\| 11
	\|299.811		\| 299.811
	\|[[6/5]]		\| [[6/5]]
	\|[[7/6]], [[27/22]], [[63/52]]		\| [[7/6]], [[27/22]], [[63/52]]
	\|-		\|-
	\|12		\| 12
	\|981.612		\| 981.612
	\|[[9/5]]		\| [[9/5]]
	\|'''[[7/4]]''', [[26/15]], [[81/44]]		\| '''[[7/4]]''', [[26/15]], [[81/44]]
	\|-		\|-
	\|13		\| 13
	\|463.413		\| 463.413
	\|[[27/20]]		\| [[27/20]]
	\|[[13/10]], [[21/16]], [[243/176]]		\| [[13/10]], [[21/16]], [[243/176]]
	\|-		\|-
	\|14		\| 14
	\|1145.214		\| 1145.214
	\|[[81/40]]		\| [[81/40]]
	\|[[39/20]], [[63/32]], [[729/352]]		\| [[39/20]], [[63/32]], [[729/352]]
	\|-		\|-
	\|15		\| 15
	\|627.015		\| 627.015
	\|[[243/160]]		\| [[243/160]]
	\|[[117/80]], [[189/128]]		\| [[117/80]], [[189/128]]
	\|}		\|}
			<nowiki />* In 5-limit CTE tuning
	<nowiki>*~~</nowiki> in~~ 5-limit CTE tuning

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Shallowtone\| ]] <!-- main article -->		[[Category:Shallowtone\| ]] <!-- main article -->
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]

ArrowHead294 at 01:59, 4 December 2024

2024-12-04T01:59:40Z

← Older revision		Revision as of 01:59, 4 December 2024
Line 3:		Line 3:
	The name was coined by [[User:CompactStar\|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface".		The name was coined by [[User:CompactStar\|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface".

	See [[Syntonic-chromatic equivalence continuum#Shallowtone]] for technical data.		See [[Syntonic–chromatic equivalence continuum#Shallowtone]] for technical data.

	== Interval chain ==		== Interval chain ==

CompactStar at 07:47, 4 August 2024

2024-08-04T07:47:34Z

← Older revision		Revision as of 07:47, 4 August 2024
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	\|818.010		\|818.010
	\|'''[[8/5]]'''		\|'''[[8/5]]'''
	\|[[14/9]], [[18/11]]		\|[[14/9]], [[18/11]], [[64/39]]
	\|-		\|-
	\|11		\|11

CompactStar: /* Interval chain */

2024-08-04T01:16:55Z

Interval chain

← Older revision		Revision as of 01:16, 4 August 2024
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	\|}		\|}

	* in 5-limit CTE tuning		<nowiki>*</nowiki> in 5-limit CTE tuning

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Shallowtone\| ]] <!-- main article -->		[[Category:Shallowtone\| ]] <!-- main article -->
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]