Diminished (temperament) - Revision history

Fitzgerald Lee: /* Tuning spectrum */Added vals accordingly for tuning spectrum

2026-03-15T03:56:03Z

Tuning spectrum: Added vals accordingly for tuning spectrum

← Older revision		Revision as of 03:56, 15 March 2026
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	\|		\|
	\| 690.000		\| 690.000
	\|		\| 40d val
	\|-		\|-
	\| [[52edo\|30\52]]		\| [[52edo\|30\52]]
	\|		\|
	\| 692.308		\| 692.308
	\|		\| 52dd val
	\|-		\|-
	\| [[64edo\|37\64]]		\| [[64edo\|37\64]]
	\|		\|
	\| 693.750		\| 693.750
	\|		\| 64dd val
	\|-		\|-
	\|		\|
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	\|		\|
	\| 712.500		\| 712.500
	\| ~~32c~~ val		\| 32cd val
	\|-		\|-
	\|		\|
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	\|		\|
	\| 720.000		\| 720.000
	\| ~~20c~~ val		\| 20cd val
	\|-		\|-
	\|		\|

Fitzgerald Lee: /* Tuning spectrum */Added links and more edos to tuning spectrum

2026-03-15T03:34:09Z

Tuning spectrum: Added links and more edos to tuning spectrum

← Older revision		Revision as of 03:34, 15 March 2026
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	! Comments		! Comments
	\|-		\|-
	\| 2\4		\| [[4edo\|2\4]]
	\|		\|
	\| 600.000		\| 600.000
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	\|-		\|-
	\|		\|
	\| 49/48		\| [[49/48]]
	\| 635.697		\| 635.697
	\|		\|
	\|-		\|-
	\|		\|
	\| 7/4		\| [[7/4]]
	\| 668.826		\| 668.826
	\|		\|
	\|-		\|-
	\|		\|
	\| 25/24		\| [[25/24]]
	\| 670.672		\| 670.672
	\| 1/2-comma		\| 1/2-comma
	\|-		\|-
	\| 9\16		\| [[16edo\|9\16]]
	\|		\|
	\| 675.000		\| 675.000
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	\|-		\|-
	\|		\|
	\| 21/20		\| [[21/20]]
	\| 684.467		\| 684.467
	\|		\|
	\|-		\|-
	\|		\|
	\| 21/16		\| [[21/16]]
	\| 685.390		\| 685.390
	\|		\|
	\|-		\|-
	\|16\28		\| [[28edo\|16\28]]
	\|		\|
	\| 685.714		\| 685.714
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	\|-		\|-
	\|		\|
	\| 5/4		\| [[5/4]]
	\| 686.314		\| 686.314
	\| 1/4-comma		\| 1/4-comma
			\|-
			\| [[40edo\|23\40]]
			\|
			\| 690.000
			\|
			\|-
			\| [[52edo\|30\52]]
			\|
			\| 692.308
			\|
			\|-
			\| [[64edo\|37\64]]
			\|
			\| 693.750
			\|
	\|-		\|-
	\|		\|
	\| 15/8		\| [[15/8]]
	\| 694.134		\| 694.134
	\| 1/8-comma		\| 1/8-comma
	\|-		\|-
	\| 7\12		\| [[12edo\|7\12]]
	\|		\|
	\| 700.000		\| 700.000
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	\|-		\|-
	\|		\|
	\| 3/2		\| [[3/2]]
	\| 701.955		\| 701.955
	\| Untempered		\| Untempered
			\|-
			\| [[32edo\|19\32]]
			\|
			\| 712.500
			\| 32c val
	\|-		\|-
	\|		\|
	\| 9/5		\| [[9/5]]
	\| 717.596		\| 717.596
	\| -1/4-comma		\| -1/4-comma
	\|-		\|-
	\|		\|
	\| 15/14		\| [[15/14]]
	\| 719.443		\| 719.443
	\|		\|
			\|-
			\| [[20edo\|12\20]]
			\|
			\| 720.000
			\| 20c val
	\|-		\|-
	\|		\|
	\| 9/7		\| [[9/7]]
	\| 735.084		\| 735.084
	\|		\|
	\|-		\|-
	\| 5\8		\| [[8edo\|5\8]]
	\|		\|
	\| 750.000		\| 750.000

FloraC: Cleanup on infobox

2026-02-09T10:02:42Z

Cleanup on infobox

← Older revision		Revision as of 10:02, 9 February 2026
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	\| de = Verminderte Temperaturen		\| de = Verminderte Temperaturen
	}}		}}
	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Diminished		\| Title = Diminished
	\| Subgroups = 2.3.5, 2.3.5.7		\| Subgroups = 2.3.5, 2.3.5.7
	\| Comma basis = [[648/625]] (2.3.5),<br>[[36/35]], [[50/49]] (2.3.5.7)		\| Comma basis = [[648/625]] (2.3.5); <br>[[36/35]], [[50/49]] (2.3.5.7)
	\| Edo join 1 = 4 \| Edo join 2 = 12		\| Edo join 1 = 4 \| Edo join 2 = 12
	\| Mapping = 4; 1 1 1		\| Mapping = 4; 1 1 1
	\| ~~Generator~~ = 3/2		\| Generators = 3/2
	\| ~~Generator~~ tuning = 696.0		\| Generators tuning = 696.0
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[4L 4s]], [[4L 8s]], [[12L 4s]]		\| MOS scales = [[4L 4s]], [[4L 8s]], [[12L 4s]]
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	\| Color name = Quadguti		\| Color name = Quadguti
	\| Odd limit 1 = 5 \| Mistuning 1 = 15.6 \| Complexity 1 = 8		\| Odd limit 1 = 5 \| Mistuning 1 = 15.6 \| Complexity 1 = 8
	\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 33.1 \| Complexity 2 = 12		\| Odd limit 2 = 7-limit 21 \| Mistuning 2 = 33.1 \| Complexity 2 = 12
	}}		}}
	'''Diminished''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] that [[tempering out\|tempers out]] the diminished comma, [[648/625]], in the [[5-limit]], and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator\|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned.		'''Diminished''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] that [[tempering out\|tempers out]] the diminished comma, [[648/625]], in the [[5-limit]], and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator\|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned.

Overthink: + Infobox Regtemp; fix error (strongly consistent circle means tempered comma is less than 25% of a step, which is not the case)

2025-12-15T02:23:51Z

+ Infobox Regtemp; fix error (strongly consistent circle means tempered comma is less than 25% of a step, which is not the case)

← Older revision		Revision as of 02:23, 15 December 2025
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	\| en = Diminished (temperament)		\| en = Diminished (temperament)
	\| de = Verminderte Temperaturen		\| de = Verminderte Temperaturen
			}}
			{{Infobox Regtemp
			\| Title = Diminished
			\| Subgroups = 2.3.5, 2.3.5.7
			\| Comma basis = [[648/625]] (2.3.5),<br>[[36/35]], [[50/49]] (2.3.5.7)
			\| Edo join 1 = 4 \| Edo join 2 = 12
			\| Mapping = 4; 1 1 1
			\| Generator = 3/2
			\| Generator tuning = 696.0
			\| Optimization method = CWE
			\| MOS scales = [[4L 4s]], [[4L 8s]], [[12L 4s]]
			\| Pergen = (P8/4, P5)
			\| Color name = Quadguti
			\| Odd limit 1 = 5 \| Mistuning 1 = 15.6 \| Complexity 1 = 8
			\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 33.1 \| Complexity 2 = 12
	}}		}}
	'''Diminished''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] that [[tempering out\|tempers out]] the diminished comma, [[648/625]], in the [[5-limit]], and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator\|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned.		'''Diminished''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] that [[tempering out\|tempers out]] the diminished comma, [[648/625]], in the [[5-limit]], and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator\|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned.
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	It can be extended to the 2.3.5.7.19-[[subgroup]] where the 1/4-octave period stands in for both ~6/5 and ~19/16 since this ~19/16 is more accurate, though its mos structure of 4L 4s is very flexible, so one could use 3\4 minus ~8/7 as a ~670{{cent}} fifth for a 2.7.19 subgroup version of diminished, for example.		It can be extended to the 2.3.5.7.19-[[subgroup]] where the 1/4-octave period stands in for both ~6/5 and ~19/16 since this ~19/16 is more accurate, though its mos structure of 4L 4s is very flexible, so one could use 3\4 minus ~8/7 as a ~670{{cent}} fifth for a 2.7.19 subgroup version of diminished, for example.

	[[12edo]] is an obvious tuning. Another possible tuning is [[16edo]] which has the interesting feature of being relatively good in the 2.7.19 subgroup so that the fifth is approximately [[28/19]], or [[28edo]], which uses something like {{nowrap\| ~[[95/64]] {{=}} ~([[19/16]])⋅([[5/4]]) }} as its fifth, of which the latter is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[~~strongly~~ consistent circle]] of them.		[[12edo]] is an obvious tuning. Another possible tuning is [[16edo]] which has the interesting feature of being relatively good in the 2.7.19 subgroup so that the fifth is approximately [[28/19]], or [[28edo]], which uses something like {{nowrap\| ~[[95/64]] {{=}} ~([[19/16]])⋅([[5/4]]) }} as its fifth, of which the latter is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[consistent circle]] of them.

	See [[Diminished family #Diminished]] for technical data.		See [[Diminished family #Diminished]] for technical data.
			__TOC__
			{{Clear}}
	== Interval chain ==		== Interval chain ==
	In the following table, odd harmonics 1–9 are in '''bold'''.		In the following table, odd harmonics 1–9 are in '''bold'''.

Fitzgerald Lee: /* Tuning spectrum */

2025-11-22T03:28:49Z

Tuning spectrum

← Older revision		Revision as of 03:28, 22 November 2025
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	\| 685.390		\| 685.390
	\|		\|
			\|-
			\|16\28
			\|
			\| 685.714
			\|
	\|-		\|-
	\|		\|

FloraC: Text replacement - "Prime-optimized" to "Norm-based"

2025-09-12T14:08:22Z

Text replacement - "Prime-optimized" to "Norm-based"

← Older revision		Revision as of 14:08, 12 September 2025
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	== Tunings ==		== Tunings ==
	=== ~~Prime~~-~~optimized~~ tunings ===		=== Norm-based tunings ===
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 5-limit norm-based tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 5-limit norm-based tunings

FloraC: Text replacement - "prime-optimized" to "norm-based"

2025-09-12T14:05:35Z

Text replacement - "prime-optimized" to "norm-based"

← Older revision		Revision as of 14:05, 12 September 2025
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	=== Prime-optimized tunings ===		=== Prime-optimized tunings ===
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 5-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 5-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
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	\|}		\|}
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|

Jerdle: /* Interval chain */ Given the other 96s, this is clearly 96, not 92.

2025-09-12T11:26:05Z

Interval chain: Given the other 96s, this is clearly 96, not 92.

← Older revision		Revision as of 11:26, 12 September 2025
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	\|-		\|-
	\| 1		\| 1
	\| 92.0		\| 96.0
	\| 15/14, 21/20, 25/24, 49/48		\| 15/14, 21/20, 25/24, 49/48
	\| 396.0		\| 396.0

FloraC at 12:15, 21 August 2025

2025-08-21T12:15:57Z

← Older revision		Revision as of 12:15, 21 August 2025
Line 3:		Line 3:
	\| de = Verminderte Temperaturen		\| de = Verminderte Temperaturen
	}}		}}
	'''Diminished''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] that [[tempering out\|tempers out]] the diminished comma, [[648/625]], in the 5-limit, and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator\|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned.		'''Diminished''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] that [[tempering out\|tempers out]] the diminished comma, [[648/625]], in the [[5-limit]], and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator\|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned.

	It can be extended to the 2.3.5.7.19-[[subgroup]] where the 1/4-octave period stands in for both ~6/5 and ~19/16 since this ~19/16 is more accurate, though its mos structure of 4L 4s is very flexible, so one could use 3\4 minus ~8/7 as a ~670{{cent}} fifth for a 2.7.19 subgroup version of diminished, for example.		It can be extended to the 2.3.5.7.19-[[subgroup]] where the 1/4-octave period stands in for both ~6/5 and ~19/16 since this ~19/16 is more accurate, though its mos structure of 4L 4s is very flexible, so one could use 3\4 minus ~8/7 as a ~670{{cent}} fifth for a 2.7.19 subgroup version of diminished, for example.
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	[[12edo]] is an obvious tuning. Another possible tuning is [[16edo]] which has the interesting feature of being relatively good in the 2.7.19 subgroup so that the fifth is approximately [[28/19]], or [[28edo]], which uses something like {{nowrap\| ~[[95/64]] {{=}} ~([[19/16]])⋅([[5/4]]) }} as its fifth, of which the latter is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[strongly consistent circle]] of them.		[[12edo]] is an obvious tuning. Another possible tuning is [[16edo]] which has the interesting feature of being relatively good in the 2.7.19 subgroup so that the fifth is approximately [[28/19]], or [[28edo]], which uses something like {{nowrap\| ~[[95/64]] {{=}} ~([[19/16]])⋅([[5/4]]) }} as its fifth, of which the latter is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[strongly consistent circle]] of them.

	See [[~~Dimipent~~ family #Diminished]] for technical data.		See [[Diminished family #Diminished]] for technical data.

	== Interval chain ==		== Interval chain ==
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	[[Category:Diminished\| ]] <!-- Main article -->		[[Category:Diminished\| ]] <!-- Main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Dimipent~~ family]]		[[Category:Diminished family]]
	[[Category:Jubilismic clan]]		[[Category:Jubilismic clan]]
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]
	[[Category:Starling temperaments]]		[[Category:Starling temperaments]]

FloraC: /* Tunings */ tabulate

2025-08-18T13:03:00Z

Tunings: tabulate

← Older revision		Revision as of 13:03, 18 August 2025
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	== Tunings ==		== Tunings ==
	=== Prime-optimized tunings ===		=== Prime-optimized tunings ===
	* 5-limit		{\| class="wikitable mw-collapsible mw-collapsed"
	** [[CTE]]: ~~~6/5 = 1\4,~~ ~3/2 = 696.9833		\|+ style="font-size: 105%; white-space: nowrap;" \| 5-limit prime-optimized tunings
	** [[CWE]]: ~6/5 = ~~1\4,~~ ~3/2 = ~~698~~.~~2661~~		\|-
	* 7-limit		! rowspan="2" \|
	** [[CTE]]: ~~~6/5 = 1\4,~~ ~3/2 = 691.9545		! colspan="3" \| Euclidean
	** [[CWE]]: ~6/5 = ~~1\4,~~ ~3/2 = ~~695~~.~~9618~~		\|-
			! Constrained
			! Constrained & skewed
			! Destretched
			\|-
			! Tenney
			\| CTE: ~3/2 = 696.9833{{c}}
			\| CWE: ~3/2 = 698.2661{{c}}
			\| POTE: ~3/2 = 699.5072{{c}}
			\|}
			{\| class="wikitable mw-collapsible mw-collapsed"
			\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit prime-optimized tunings
			\|-
			! rowspan="2" \|
			! colspan="3" \| Euclidean
			\|-
			! Constrained
			! Constrained & skewed
			! Destretched
			\|-
			! Tenney
			\| CTE: ~3/2 = 691.9545{{c}}
			\| CWE: ~3/2 = 695.9618{{c}}
			\| POTE: ~3/2 = 699.5235{{c}}
			\|}

	=== Others ===		=== Others ===
	* 5-limit [[DKW theory\|DKW]]: ~6/5 = ~~1\4~~, ~3/2 = 690.289		* 5-limit [[DKW theory\|DKW]]: ~6/5 = 300.000{{c}}, ~3/2 = 690.289{{c}}

	=== Tuning spectrum ===		=== Tuning spectrum ===