Semicomma family - Revision history

Hkm: /* 13-limit */

2026-06-30T16:43:46Z

13-limit

← Older revision		Revision as of 16:43, 30 June 2026
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	Badness (Sintel): 0.815		Badness (Sintel): 0.815

			==== 2.3.5.7.11.13.19 ====
			Subgroup: 2.3.5.7.11.13.19

			Comma list: 99/98, 121/120, 176/175, 275/273, [[400/399]]

			Mapping: {{mapping\| 1 0 3 1 3 8 9\| 0 7 -3 8 2 -19 -21}}

			Optimal tunings:

			* WE: ~2 = 1200.320{{c}}, ~7/6 = 271.640{{c}}
			* CWE: ~2 = 1200.000{{c}}, ~7/6 = 271.566{{c}}

			Badness (Sintel): 0.881

	==== Blair ====		==== Blair ====

Lériendil: /* Newspeak */

2026-03-01T17:12:43Z

Newspeak

← Older revision		Revision as of 17:12, 1 March 2026
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	=== Newspeak ===		=== Newspeak ===
	In newspeak, the simplicity of obtaining ~[[11/8]] by stacking the generator ~[[7/6]] twice (as in basic 11-limit orwell) is sacrificed to gain accuracy for larger equal temperaments (such as [[84edo]] and [[115edo]]), at the cost of much higher complexity: it is reached only after stacking the generator 33 times and octave-reducing. Newspeak intersects with ~~basic 11-limit~~ orwell at [[31edo]].		In newspeak, the simplicity of obtaining ~[[11/8]] by stacking the generator ~[[7/6]] twice (as in basic 11-limit orwell) is sacrificed to gain accuracy for larger equal temperaments (such as [[84edo]] and [[115edo]]), at the cost of much higher complexity: it is reached only after stacking the generator 33 times and octave-reducing. Newspeak intersects with undecimal orwell at [[31edo]].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Overthink: /* Quadrawell */ alternate interpretation

2026-01-12T02:02:32Z

Quadrawell: alternate interpretation

← Older revision		Revision as of 02:02, 12 January 2026
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	== Quadrawell ==		== Quadrawell ==
	Quadrawell tempers out [[2401/2400]] and may be described as the {{nowrap\| 31 & 212 }} temperament. It has a [[7/4]] generator of about 968 cents, four of which minus three octaves give the original generator of orwell. Its ploidacot is 22-sheared-28-cot.		Quadrawell tempers out [[2401/2400]] and may be described as the {{nowrap\| 31 & 212 }} temperament. It has a [[7/4]] generator of about 968 cents, four of which minus three octaves give the original generator of orwell. It can also be viewed as [[2.5.7\|2.5.7-subgroup]] [[mothra]] with a different mapping of prime [[3/1\|3]]. Its ploidacot is 22-sheared-28-cot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:20:59Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:20, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Semicomma family\| ]] <!-- main article -->		[[Category:Semicomma family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]
	[[Category:Orson]]		[[Category:Orson]]
	[[Category:Orwell]]		[[Category:Orwell]]

FloraC: +1

2025-11-02T12:32:32Z

← Older revision		Revision as of 12:32, 2 November 2025
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	== Triwell ==		== Triwell ==
	Triwell may be described as the {{nowrap\| 31 & 159 }} temperament. It slices orwell ~~major sixth ~128/75~~ into three generators, ~~nine of~~ which ~~give~~ the ~~5th harmonic~~. Its ploidacot is 15-sheared-21-cot.		Triwell tempers out the gamelisma, [[1029/1024]], and the triwellisma, [[235298/234375]]. It may be described as the {{nowrap\| 31 & 159 }} temperament. It slices orwell's generator plus two octaves into three generators, and seven generators octave reduced make a ~8/7, which is the generator of [[slendric]]. Its ploidacot is 15-sheared-21-cot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Improve the intros to each temp

2025-11-02T12:20:29Z

Improve the intros to each temp

← Older revision		Revision as of 12:20, 2 November 2025
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	==== Doublethink ====		==== Doublethink ====
	Doublethink is a weak extension of orwell to the 13-limit. It splits the generator of ~7/6 into two [[13/12]]~[[14/13]]'s by tempering out their difference, [[169/168]]. Its ploidacot is alpha-~~tetradecacot~~.		Doublethink is a weak extension of orwell to the 13-limit. It splits the generator of ~7/6 into two [[13/12]]~[[14/13]]'s by tempering out their difference, [[169/168]]. Its ploidacot is alpha-14-cot.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13
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	=== Newspeak ===		=== Newspeak ===
	In ~~Newspeak~~, the simplicity of obtaining ~[[11/8]] by stacking the generator ~[[7/6]] twice (as in basic 11-limit ~~Orwell~~) is sacrificed to gain accuracy for larger equal temperaments (such as [[84edo]] and [[115edo]]), at the cost of much higher complexity: it is reached only after stacking the generator 33 times and octave-reducing. Newspeak intersects with basic 11-limit ~~Orwell~~ at [[31edo]].		In newspeak, the simplicity of obtaining ~[[11/8]] by stacking the generator ~[[7/6]] twice (as in basic 11-limit orwell) is sacrificed to gain accuracy for larger equal temperaments (such as [[84edo]] and [[115edo]]), at the cost of much higher complexity: it is reached only after stacking the generator 33 times and octave-reducing. Newspeak intersects with basic 11-limit orwell at [[31edo]].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11
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	Mapping: {{mapping\| 1 -7 6 -7 -18 \| 0 14 -6 16 35 }}		Mapping: {{mapping\| 1 -7 6 -7 -18 \| 0 14 -6 16 35 }}
	: mapping generators: ~2, ~72/55		: mapping generators: ~2, ~55/36

	Optimal tunings:		Optimal tunings:
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	== Sabric ==		== Sabric ==
	The sabric temperament ({{nowrap\| 53 & 190 }}~~) tempers out the~~ [[~~4375/4374\|ragisma (4375/4374)~~]]~~. It is so named because it is closely related~~ to the ''Sabra2 tuning'' (generator: 271.607278 cents).		The sabric temperament tempers out the ragisma, [[4375/4374]], and may be described as the {{nowrap\| 53 & 190 }} temperament. It was named by [[Xenllium]] in 2021 for its relation to the Sabra2 tuning (generator: 271.607278 cents).

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Triwell ==		== Triwell ==
	~~The triwell temperament (~~{{nowrap\| 31 & 159 }}) slices orwell major sixth ~128/75 into three generators, nine of which give the 5th harmonic.		Triwell may be described as the {{nowrap\| 31 & 159 }} temperament. It slices orwell major sixth ~128/75 into three generators, nine of which give the 5th harmonic. Its ploidacot is 15-sheared-21-cot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Quadrawell ==		== Quadrawell ==
	~~The ''quadrawell'' temperament (~~{{nowrap\| 31 & 212 }}) has an [[8/7]] generator of about ~~232~~ cents, ~~twelve~~ of which give the ~~5th harmonic~~.		Quadrawell tempers out [[2401/2400]] and may be described as the {{nowrap\| 31 & 212 }} temperament. It has a [[7/4]] generator of about 968 cents, four of which minus three octaves give the original generator of orwell. Its ploidacot is 22-sheared-28-cot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Rainwell ==		== Rainwell ==
	The ''rainwell'' temperament ~~({{nowrap\| 31 & 265 }})~~ tempers out the mirkwai comma, 16875/16807 and the [[rainy comma]], 2100875/2097152.		The rainwell temperament tempers out the mirkwai comma, [[16875/16807]], and the rainy comma, [[2100875/2097152]]. It may be described as the {{nowrap\| 31 & 265 }} temperament. Its ploidacot is 22-sheared-35-cot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Quinwell ==		== Quinwell ==
	The quinwell temperament ({{nowrap\| 22 & 243 }}) slices orwell ~~minor third~~ into five ~~generators and tempers out the wizma, 420175/419904~~.		The quinwell temperament tempers out the wizma, [[420175/419904]], and may be described as the {{nowrap\| 22 & 243 }} temperament. It slices orwell's generator into five quartertones. Its ploidacot is alpha-35-cot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: - CTE & POTE tunings

2025-11-02T12:04:38Z

- CTE & POTE tunings

Show changes

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/2)

2025-11-02T12:03:30Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/2)

Show changes

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)

2025-11-02T11:38:00Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)

Show changes

FloraC: Units & misc. cleanup

2025-11-02T11:17:45Z

Units & misc. cleanup

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