Very low accuracy temperaments - Revision history

FloraC: Mujannab -> sept and move it here

2026-05-29T10:55:06Z

Mujannab -> sept and move it here

← Older revision		Revision as of 10:55, 29 May 2026
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	[[Badness]] (Sintel): 1.22		[[Badness]] (Sintel): 1.22

			== Sept ==
			Sept preserves the 2.3.7-subgroup of mapping of 7edo, and harmonic 5 is mapped to an independent generator. As harmonic 5 is way more accurately approximated than 7 by 7edo, this temperament provides little improvement to 7edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 5-limit structure of 7edo and give prime 7 an independent generator instead, which is exactly what [[jamesbond]] does.

			This temperament used to be known as ''mujannab''.

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 54/49, 64/63

			{{Mapping\|legend=1\| 7 11 0 20 \| 0 0 1 0 }}

			[[Optimal tuning]]s:
			* [[WE]]: ~9/8 = 170.823{{c}}, ~5/4 = 393.792{{c}} (~15/14 = 52.145{{c}})
			: [[error map]]: {{val\| -4.236 -22.898 -0.994 +47.642 }}
			* [[CWE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.719{{c}} (~15/14 = 49.862{{c}})
			: error map: {{val\| 0.000 -16.241 +6.406 +59.746 }}

			{{Optimal ET sequence\|legend=1\| 7, 14d }}

			[[Badness]] (Sintel): 2.68

			=== 11-limit ===
			Subgroup: 2.3.5.7.11

			Comma list: 45/44, 54/49, 64/63

			Mapping: {{mapping\| 7 11 0 20 8 \| 0 0 1 0 1 }}

			Optimal tunings:
			* WE: ~11/10 = 170.817{{c}}, ~5/4 = 393.252{{c}} (~33/32 = 51.619{{c}})
			* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 391.840{{c}} (~33/32 = 48.983{{c}})

			{{Optimal ET sequence\|legend=0\| 7, 14de }}

			Badness (Sintel): 2.02

			=== 13-limit ===
			Subgroup: 2.3.5.7.11.13

			Comma list: 27/26, 45/44, 52/49, 64/63

			Mapping: {{mapping\| 7 11 0 20 8 26 \| 0 0 1 0 1 0 }}

			Optimal tunings:
			* WE: ~11/10 = 170.795{{c}}, ~5/4 = 393.611{{c}} (~33/32 = 52.021{{c}})
			* CWE: ~11/10 = 171.429{{c}}, ~5/4 = 392.725{{c}} (~33/32 = 49.868{{c}})

			{{Optimal ET sequence\|legend=0\| 7, 14de }}

			Badness (Sintel): 1.77

	== Geryon ==		== Geryon ==

FloraC: /* Plutus */ + distinguish

2026-04-02T11:17:42Z

Plutus: + distinguish

← Older revision		Revision as of 11:17, 2 April 2026
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	== Plutus ==		== Plutus ==
			{{Distinguish\| Pluto }}
	{{See also\| Meantone family }}		{{See also\| Meantone family }}

Overthink: integrate this better

2026-03-02T22:58:14Z

integrate this better

← Older revision		Revision as of 22:58, 2 March 2026
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	{{Technical data page}}		{{Technical data page}}
	Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to [[tempering out\|temper out]] very large intervals such as [[9/8]], [[10/9]], [[32/27]], or [[15/14]], equating wildly different interval sizes with [[semitone (interval size measure)\|semitone]]-level or even greater [[error]]s~~. A lot~~ of ~~temperaments listed here don't have [[diamond monotone]] tunings because of their sheer inaccuracy~~. As a result, all of them are right on or even beyond the edge of what can be sensibly called a temperament at all; that is to say, they are [[exotemperament]]s.		Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to [[tempering out\|temper out]] very large intervals such as [[9/8]], [[10/9]], [[32/27]], or [[15/14]], equating wildly different interval sizes with [[semitone (interval size measure)\|semitone]]-level or even greater [[error]]s, and often swapping the sizes of simple ratios compared to just intonation. As a result, all of them are right on or even beyond the edge of what can be sensibly called a temperament at all; that is to say, they are [[exotemperament]]s.

	== Antitonic ==		== Antitonic ==

Xenllium at 10:05, 2 March 2026

2026-03-02T10:05:44Z

← Older revision		Revision as of 10:05, 2 March 2026
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	* CWE: ~2 = 1200.000{{c}}, ~3/2 = 800.996{{c}}		* CWE: ~2 = 1200.000{{c}}, ~3/2 = 800.996{{c}}

	{{Optimal ET sequence\|legend=0\| 2c, 3d }}		{{Optimal ET sequence\|legend=0\| 1c, 3d }}

	Badness (Sintel): 0.720		Badness (Sintel): 0.720
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	== Quad ==		== Quad ==
	Quad is identical to 4et in the 5-limit, but has an independent generator for prime 7.		Quad is identical to [[4edo\|4et]] in the 5-limit, but has an independent generator for prime 7.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.~~037~~) <!-- Please review, last digit may be wrong -->		* [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.038) <!-- Please review, last digit may be wrong -->
	: [[error map]]: {{val\| -17.921 -10.628 +50.676 -1.966 }}		: [[error map]]: {{val\| -17.921 -10.628 +50.676 -1.966 }}
	* [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)		* [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)

Overthink: /* Quint */ add error maps

2026-02-27T05:35:22Z

Quint: add error maps

← Older revision		Revision as of 05:35, 27 February 2026
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.037) <!-- Please review, last digit may be wrong -->		* [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.037) <!-- Please review, last digit may be wrong -->
			: [[error map]]: {{val\| -17.921 -10.628 +50.676 -1.966 }}
	* [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)		* [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)
			: error map: {{val\| 0.000 +18.045 +93.686 +36.309 }}

	{{Optimal ET sequence\|legend=1\| 5, 15ccd }}		{{Optimal ET sequence\|legend=1\| 5, 15ccd }}

Overthink: /* Quint */ Standardize

2026-02-27T05:32:58Z

Quint: Standardize

← Older revision		Revision as of 05:32, 27 February 2026
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	{{Mapping\|legend=1\| 5 8 12 0 \| 0 0 0 1 }}		{{Mapping\|legend=1\| 5 8 12 0 \| 0 0 0 1 }}

	: Mapping generators: ~9/8, ~7		: Mapping generators: ~6/5, ~7

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~POTE~~]]: ~9/8 = ~~1\5~~, ~7/4 = ~~1017~~.~~903~~ (~21/20 = 57.~~903~~)		* [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.037) <!-- Please review, last digit may be wrong -->
	* [[~~CTE~~]]: ~9/8 = ~~1\5~~, ~7/4 = ~~968~~.~~8259~~ (~63/64 = 8.~~8259~~)		* [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)

	{{Optimal ET sequence\|legend=1\| 5, 15ccd }}		{{Optimal ET sequence\|legend=1\| 5, 15ccd }}

	[[Badness]]: 0.~~048312~~		[[Badness]] (Sintel): 1.22

	== Geryon ==		== Geryon ==

Overthink: move quint here

2026-02-27T05:26:42Z

move quint here

← Older revision		Revision as of 05:26, 27 February 2026
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	[[Badness]] (Sintel): 1.16		[[Badness]] (Sintel): 1.16

			== Quint ==
			Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is way more accurately approximated than 5 by 5edo, this temperament provides little improvement to 5edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 16/15, 27/25

			{{Mapping\|legend=1\| 5 8 12 0 \| 0 0 0 1 }}

			: Mapping generators: ~9/8, ~7

			[[Optimal tuning]]s:
			* [[POTE]]: ~9/8 = 1\5, ~7/4 = 1017.903 (~21/20 = 57.903)
			* [[CTE]]: ~9/8 = 1\5, ~7/4 = 968.8259 (~63/64 = 8.8259)

			{{Optimal ET sequence\|legend=1\| 5, 15ccd }}

			[[Badness]]: 0.048312

	== Geryon ==		== Geryon ==

Xenllium: /* Antonian */

2026-02-14T10:51:12Z

Antonian

@@ Line 158: / Line 158: @@
 Badness (Sintel): 0.606
 === Brutus ===
@@ Line 175: / Line 205: @@
 === Phlegyas ===
 Subgroup: 2.3.5.7
@@ Line 190: / Line 222: @@
 === Charon ===
 Subgroup: 2.3.5.7

Xenllium at 04:58, 14 February 2026

2026-02-14T04:58:38Z

← Older revision		Revision as of 04:58, 14 February 2026
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	== Antonian ==		== Antonian ==
			{{Main\| Antonian }}
	This temperament family is characterized by the [[color notation\|yo 2nd]] ([[10/9]]) being tempered out. It identifies [[3/2]] with [[5/3]], [[4/3]] with [[6/5]], and [[5/4]] with [[9/8]].		This temperament family is characterized by the [[color notation\|yo 2nd]] ([[10/9]]) being tempered out. It identifies [[3/2]] with [[5/3]], [[4/3]] with [[6/5]], and [[5/4]] with [[9/8]].

Overthink: /* Oxygen */ separately give OPV

2026-02-14T04:52:06Z

Oxygen: separately give OPV

← Older revision		Revision as of 04:52, 14 February 2026
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	: error map: {{val\| 0.000 -0.083 -16.526 -100.911 }}		: error map: {{val\| 0.000 -0.083 -16.526 -100.911 }}

	{{Optimal ET sequence\|legend=1\| 1c, …, 6bcd, 7d }}		{{Optimal ET sequence\|legend=1\| 1c, …, 6bcd, 7d }}*

			<nowiki/>*[[Optimal patent val]]: [[8edo\|8]]

	[[Badness]] (Sintel): 1.52		[[Badness]] (Sintel): 1.52