Mintaka - Revision history

Overthink: accidental self edit conflict

2026-02-09T23:09:04Z

accidental self edit conflict

← Older revision		Revision as of 23:09, 9 February 2026
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	\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)		\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)
	\| Edo join 1 = b17 \| Edo join 2 = b22		\| Edo join 1 = b17 \| Edo join 2 = b22
	\| ~~Generator~~ = 11/7 \| ~~Generator~~ tuning = 780.~~428~~ \| Optimization method = CWE		\| Mapping = 1; 6 -3 -2 13
			\| Generators = 11/7 \| Generators tuning = 780.4 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]
	~~\| Mapping = 1; 6 -3 -2 13~~		\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 12
	\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22		\| Odd limit 2 = 3.5.7.11.13 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 17
	\| Odd limit 2 = (13~~-limited)~~ 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 39
	}}		}}
	For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.		For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.

Overthink: slight fix

2026-02-09T23:07:07Z

slight fix

← Older revision		Revision as of 23:07, 9 February 2026
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	\| Generators = 11/7 \| Generators tuning = 778.7 \| Optimization method = CWE		\| Generators = 11/7 \| Generators tuning = 778.7 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]
			\| Ploidacot = alpha-trigem
	\| Odd limit 1 = 3.7.11 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7		\| Odd limit 1 = 3.7.11 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7
	}}		}}
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	\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)		\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)
	\| Edo join 1 = b17 \| Edo join 2 = b22		\| Edo join 1 = b17 \| Edo join 2 = b22
			\| Generator = 11/7 \| Generator tuning = 780.428 \| Optimization method = CWE
			\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]
	\| Mapping = 1; 6 -3 -2 13		\| Mapping = 1; 6 -3 -2 13
	~~\| Generators = 11/7 \| Generators tuning = 780.4 \| Optimization method = CWE~~		\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22
	~~\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]~~		\| Odd limit 2 = (13-limited) 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 39
	\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 12
	\| Odd limit 2 = ~~3.5.7.11.~~13 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 17
	}}		}}
	For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.		For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.

Overthink: /* Mintra */ missed a spot

2026-02-09T23:06:45Z

Mintra: missed a spot

← Older revision		Revision as of 23:06, 9 February 2026
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	\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)		\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)
	\| Edo join 1 = b17 \| Edo join 2 = b22		\| Edo join 1 = b17 \| Edo join 2 = b22
	\| ~~Generator~~ = 11/7 \| ~~Generator~~ tuning = 780.~~428~~ \| Optimization method = CWE		\| Mapping = 1; 6 -3 -2 13
			\| Generators = 11/7 \| Generators tuning = 780.4 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]
	~~\| Mapping = 1; 6 -3 -2 13~~		\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 12
	\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22		\| Odd limit 2 = 3.5.7.11.13 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 17
	\| Odd limit 2 = (13~~-limited)~~ 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 39
	}}		}}
	For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.		For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.

FloraC: Cleanup on infobox

2026-02-09T10:03:39Z

Cleanup on infobox

← Older revision		Revision as of 10:03, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Subgroups = 3.7.11		\| Subgroups = 3.7.11
	\| Comma basis = [[1331/1323]]		\| Comma basis = [[1331/1323]]
	\| Edo join 1 = b5 \| Edo join 2 = b17		\| Edo join 1 = b5 \| Edo join 2 = b17
	\| ~~Generator~~ = 11/7 \| ~~Generator~~ tuning = 778.~~703~~ \| Optimization method = CWE		\| Mapping = 1; -3 -2
			\| Generators = 11/7 \| Generators tuning = 778.7 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]
	~~\| Mapping = 1; -3 -2~~		\| Odd limit 1 = 3.7.11 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7
	\| Odd limit 1 = (3.7.11) 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7
	}}		}}
	'''Mintaka''' is a [[non-octave]] [[temperament]] in the 3.7.11 [[subgroup]] where [[~]][[11/7]] is a [[generator]], and the comma [[1331/1323]] is [[tempering out\|tempered out]], so a stack of two generators represents [[27/11]] in addition to 121/49, and a stack of three generators, [[3/1\|tritave]]-reduced, represents [[9/7]]. As 11/7 as a generator against the tritave produces a [[5L 2s (3/1-equivalent)\|5L 2s]] (macrodiatonic) scale, with the generator here occupying the role of a [[4/3\|perfect fourth]], it is possible to use an analogue of the [[chain-of-fifths notation]] that is standardly used for [[diatonic]] scales, with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭) and that all intervals are extremely stretched, though the [[5L 7s (3/1-equivalent)\|5L 7s]] macrochromatic scale is suggested for musical use due to the hardness of the macrodiatonic and the increased breadth of the tritave. [[22edt\|9\22]]edt is a very good tuning for the generator, and 22edt overall excels in the 3.7.11 subgroup, but other tunings such as [[17edt\|7\17]]edt and [[39edt\|16\39]]edt are also useful, especially for extensions involving primes 5 and 13 (see below).		'''Mintaka''' is a [[non-octave]] [[temperament]] in the 3.7.11 [[subgroup]] where [[~]][[11/7]] is a [[generator]], and the comma [[1331/1323]] is [[tempering out\|tempered out]], so a stack of two generators represents [[27/11]] in addition to 121/49, and a stack of three generators, [[3/1\|tritave]]-reduced, represents [[9/7]]. As 11/7 as a generator against the tritave produces a [[5L 2s (3/1-equivalent)\|5L 2s]] (macrodiatonic) scale, with the generator here occupying the role of a [[4/3\|perfect fourth]], it is possible to use an analogue of the [[chain-of-fifths notation]] that is standardly used for [[diatonic]] scales, with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭) and that all intervals are extremely stretched, though the [[5L 7s (3/1-equivalent)\|5L 7s]] macrochromatic scale is suggested for musical use due to the hardness of the macrodiatonic and the increased breadth of the tritave. [[22edt\|9\22]]edt is a very good tuning for the generator, and 22edt overall excels in the 3.7.11 subgroup, but other tunings such as [[17edt\|7\17]]edt and [[39edt\|16\39]]edt are also useful, especially for extensions involving primes 5 and 13 (see below).

FloraC: Fix ET joins

2025-12-06T14:13:16Z

Fix ET joins

← Older revision		Revision as of 14:13, 6 December 2025
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	\| Subgroups = 3.7.11		\| Subgroups = 3.7.11
	\| Comma basis = [[1331/1323]]		\| Comma basis = [[1331/1323]]
	\| Edo join 1 = 5 \| Edo join 2 = 17		\| Edo join 1 = b5 \| Edo join 2 = b17
	\| Generator = 11/7 \| Generator tuning = 778.703 \| Optimization method = CWE		\| Generator = 11/7 \| Generator tuning = 778.703 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]
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	\| Title = Mintra		\| Title = Mintra
	\| Subgroups = 3.5.7.11, 3.5.7.11.13		\| Subgroups = 3.5.7.11, 3.5.7.11.13
	\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br />[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)		\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)
	\| Edo join 1 = 17 \| Edo join 2 = 22		\| Edo join 1 = b17 \| Edo join 2 = b22
	\| Generator = 11/7 \| Generator tuning = 780.428 \| Optimization method = CWE		\| Generator = 11/7 \| Generator tuning = 780.428 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]

Lériendil: reverted stuff that caused broken lua

2025-05-20T02:02:25Z

reverted stuff that caused broken lua

← Older revision		Revision as of 02:02, 20 May 2025
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	\| Edo join 1 = 5 \| Edo join 2 = 17		\| Edo join 1 = 5 \| Edo join 2 = 17
	\| Generator = 11/7 \| Generator tuning = 778.703 \| Optimization method = CWE		\| Generator = 11/7 \| Generator tuning = 778.703 \| Optimization method = CWE
	\| MOS scales = ~~{{mos scalesig\|~~2L 3s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 2s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 7s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 12s<3/1>\|~~link=1}}~~		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]
	\| Mapping = 1; -3 -2		\| Mapping = 1; -3 -2
	\| Odd limit 1 = (3.7.11) 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7		\| Odd limit 1 = (3.7.11) 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7
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	\| Edo join 1 = 17 \| Edo join 2 = 22		\| Edo join 1 = 17 \| Edo join 2 = 22
	\| Generator = 11/7 \| Generator tuning = 780.428 \| Optimization method = CWE		\| Generator = 11/7 \| Generator tuning = 780.428 \| Optimization method = CWE
	\| MOS scales = ~~{{mos scalesig\|~~2L 3s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 2s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 7s<3/1>\|~~link=1}}~~,~~<br />{{mos scalesig\|~~5L 12s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~17L 5s<3/1>\|~~link=1}}~~		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]
	\| Mapping = 1; 6 -3 -2 13		\| Mapping = 1; 6 -3 -2 13
	\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22		\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22

Lériendil at 02:01, 20 May 2025

2025-05-20T02:01:52Z

← Older revision		Revision as of 02:01, 20 May 2025
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	\| Odd limit 1 = (3.7.11) 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7		\| Odd limit 1 = (3.7.11) 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7
	}}		}}
	'''Mintaka''' is a [[non-octave]] [[temperament]] in the 3.7.11 [[subgroup]] where [[~]][[11/7]] is a [[generator]], and the comma [[1331/1323]] is [[tempering out\|tempered out]], so a stack of two generators represents [[27/11]] in addition to 121/49, and a stack of three generators, [[3/1\|tritave]]-reduced, represents [[9/7]]. As 11/7 as a generator against the tritave produces a ~~{{mos scalesig\|~~5L 2s<3/1>\|~~link=1}}~~ (macrodiatonic) scale, with the generator here occupying the role of a [[4/3\|perfect fourth]], it is possible to use an analogue of the [[chain-of-fifths notation]] that is standardly used for [[diatonic]] scales, with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭) and that all intervals are extremely stretched, though the ~~{{mos scalesig\|~~5L 7s<3/1>\|~~link=1}}~~ macrochromatic scale is suggested for musical use due to the hardness of the macrodiatonic and the increased breadth of the tritave. [[22edt\|9\22]]edt is a very good tuning for the generator, and 22edt overall excels in the 3.7.11 subgroup, but other tunings such as [[17edt\|7\17]]edt and [[39edt\|16\39]]edt are also useful, especially for extensions involving primes 5 and 13 (see below).		'''Mintaka''' is a [[non-octave]] [[temperament]] in the 3.7.11 [[subgroup]] where [[~]][[11/7]] is a [[generator]], and the comma [[1331/1323]] is [[tempering out\|tempered out]], so a stack of two generators represents [[27/11]] in addition to 121/49, and a stack of three generators, [[3/1\|tritave]]-reduced, represents [[9/7]]. As 11/7 as a generator against the tritave produces a [[5L 2s (3/1-equivalent)\|5L 2s]] (macrodiatonic) scale, with the generator here occupying the role of a [[4/3\|perfect fourth]], it is possible to use an analogue of the [[chain-of-fifths notation]] that is standardly used for [[diatonic]] scales, with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭) and that all intervals are extremely stretched, though the [[5L 7s (3/1-equivalent)\|5L 7s]] macrochromatic scale is suggested for musical use due to the hardness of the macrodiatonic and the increased breadth of the tritave. [[22edt\|9\22]]edt is a very good tuning for the generator, and 22edt overall excels in the 3.7.11 subgroup, but other tunings such as [[17edt\|7\17]]edt and [[39edt\|16\39]]edt are also useful, especially for extensions involving primes 5 and 13 (see below).

	As perhaps the simplest temperament of this subgroup delivering decent accuracy—and, in particular, the simplest supported by tunings such as 17edt and 22edt—Mintaka can be considered the 3.7.11 analog of 3.5.7 [[Bohlen–Pierce–Stearns]] or 2.3.5 [[meantone]], using [[7:9:11]] as its fundamental consonant chord in the place of [[3:5:7]] or of [[4:5:6]].		As perhaps the simplest temperament of this subgroup delivering decent accuracy—and, in particular, the simplest supported by tunings such as 17edt and 22edt—Mintaka can be considered the 3.7.11 analog of 3.5.7 [[Bohlen–Pierce–Stearns]] or 2.3.5 [[meantone]], using [[7:9:11]] as its fundamental consonant chord in the place of [[3:5:7]] or of [[4:5:6]].

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:26:30Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:26, 29 April 2025
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	[[Category:Mintaka\| ]] <!-- main article -->		[[Category:Mintaka\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup temperaments]]~~		[[Category:Non-octave temperaments]]
	~~[[Category:Tritave~~-~~equivalent~~ temperaments]]

FloraC: - parent category

2025-04-28T14:24:53Z

- parent category

← Older revision		Revision as of 14:24, 28 April 2025
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	[[Mos scale]]s of reasonable tunings have cardinalities of 5 (2L 3s), 7 (5L 2s), 12 (5L 7s), or 17 (5L 12s).		[[Mos scale]]s of reasonable tunings have cardinalities of 5 (2L 3s), 7 (5L 2s), 12 (5L 7s), or 17 (5L 12s).

	{{~~tdlink~~\|No-twos subgroup temperaments#Mintaka}}		{{Tdlink\|No-twos subgroup temperaments #Mintaka}}


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	* [https://archive.org/details/TuneIn22Edt Tune in 22edt] – [[Peter Kosmorsky]] (2011) – uses the LssLssLsssLssLsss MOS (Mintaka[17])		* [https://archive.org/details/TuneIn22Edt Tune in 22edt] – [[Peter Kosmorsky]] (2011) – uses the LssLssLsssLssLsss MOS (Mintaka[17])

	[[Category:~~Temperaments~~]]		[[Category:Mintaka\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
			[[Category:Subgroup temperaments]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

Lériendil at 23:16, 19 April 2025

2025-04-19T23:16:29Z

← Older revision		Revision as of 23:16, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

← Older revision		Revision as of 23:09, 9 February 2026
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	\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)		\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)
	\| Edo join 1 = b17 \| Edo join 2 = b22		\| Edo join 1 = b17 \| Edo join 2 = b22
	\| ~~Generator~~ = 11/7 \| ~~Generator~~ tuning = 780.~~428~~ \| Optimization method = CWE		\| Mapping = 1; 6 -3 -2 13
			\| Generators = 11/7 \| Generators tuning = 780.4 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]
	~~\| Mapping = 1; 6 -3 -2 13~~		\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 12
	\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22		\| Odd limit 2 = 3.5.7.11.13 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 17
	\| Odd limit 2 = (13~~-limited)~~ 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 39
	}}		}}
	For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.		For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.

← Older revision		Revision as of 23:07, 9 February 2026
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	\| Generators = 11/7 \| Generators tuning = 778.7 \| Optimization method = CWE		\| Generators = 11/7 \| Generators tuning = 778.7 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]
			\| Ploidacot = alpha-trigem
	\| Odd limit 1 = 3.7.11 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7		\| Odd limit 1 = 3.7.11 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7
	}}		}}
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	\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)		\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)
	\| Edo join 1 = b17 \| Edo join 2 = b22		\| Edo join 1 = b17 \| Edo join 2 = b22
			\| Generator = 11/7 \| Generator tuning = 780.428 \| Optimization method = CWE
			\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]
	\| Mapping = 1; 6 -3 -2 13		\| Mapping = 1; 6 -3 -2 13
	~~\| Generators = 11/7 \| Generators tuning = 780.4 \| Optimization method = CWE~~		\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22
	~~\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]~~		\| Odd limit 2 = (13-limited) 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 39
	\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 12
	\| Odd limit 2 = ~~3.5.7.11.~~13 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 17
	}}		}}
	For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.		For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.

← Older revision		Revision as of 23:06, 9 February 2026
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	\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)		\| Comma basis = [[245/243]], [[1331/1323]] (3.5.7.11);<br>[[245/243]], [[275/273]], [[1331/1323]] (3.5.7.11.13)
	\| Edo join 1 = b17 \| Edo join 2 = b22		\| Edo join 1 = b17 \| Edo join 2 = b22
	\| ~~Generator~~ = 11/7 \| ~~Generator~~ tuning = 780.~~428~~ \| Optimization method = CWE		\| Mapping = 1; 6 -3 -2 13
			\| Generators = 11/7 \| Generators tuning = 780.4 \| Optimization method = CWE
	\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]
	~~\| Mapping = 1; 6 -3 -2 13~~		\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 12
	\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22		\| Odd limit 2 = 3.5.7.11.13 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 17
	\| Odd limit 2 = (13~~-limited)~~ 25 \| Mistuning 2 = 8.77 \| Complexity 2 = 39
	}}		}}
	For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.		For tunings of the generator that possess a sharp 9/7 (sharper than {{frac\|1\|3}}-comma, or effectively between [[17edt]] and [[22edt]] tuning), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. A good tuning for this temperament is [[39edt]], the triple BP equalized scale, though others such as [[95edt]] are possible.

← Older revision		Revision as of 02:02, 20 May 2025
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	\| Edo join 1 = 5 \| Edo join 2 = 17		\| Edo join 1 = 5 \| Edo join 2 = 17
	\| Generator = 11/7 \| Generator tuning = 778.703 \| Optimization method = CWE		\| Generator = 11/7 \| Generator tuning = 778.703 \| Optimization method = CWE
	\| MOS scales = ~~{{mos scalesig\|~~2L 3s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 2s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 7s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 12s<3/1>\|~~link=1}}~~		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]]
	\| Mapping = 1; -3 -2		\| Mapping = 1; -3 -2
	\| Odd limit 1 = (3.7.11) 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7		\| Odd limit 1 = (3.7.11) 11 \| Mistuning 1 = 3.48 \| Complexity 1 = 7
Line 41:		Line 41:
	\| Edo join 1 = 17 \| Edo join 2 = 22		\| Edo join 1 = 17 \| Edo join 2 = 22
	\| Generator = 11/7 \| Generator tuning = 780.428 \| Optimization method = CWE		\| Generator = 11/7 \| Generator tuning = 780.428 \| Optimization method = CWE
	\| MOS scales = ~~{{mos scalesig\|~~2L 3s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 2s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~5L 7s<3/1>\|~~link=1}}~~,~~<br />{{mos scalesig\|~~5L 12s<3/1>\|~~link=1}}~~, ~~{{mos scalesig\|~~17L 5s<3/1>\|~~link=1}}~~		\| MOS scales = [[2L 3s (3/1-equivalent)\|2L 3s]], [[5L 2s (3/1-equivalent)\|5L 2s]], [[5L 7s (3/1-equivalent)\|5L 7s]], [[5L 12s (3/1-equivalent)\|5L 12s]], [[17L 5s (3/1-equivalent)\|17L 5s]]
	\| Mapping = 1; 6 -3 -2 13		\| Mapping = 1; 6 -3 -2 13
	\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22		\| Odd limit 1 = 11 \| Mistuning 1 = 6.16 \| Complexity 1 = 22