Myna - Revision history

Lériendil: replaced quasitemp with superkleismic, since it's generated by 6/5 like myna and demonstrates the keemic equivalence better; also I believe it to be more known than quasitemp

2026-05-14T06:29:52Z

replaced quasitemp with superkleismic, since it's generated by 6/5 like myna and demonstrates the keemic equivalence better; also I believe it to be more known than quasitemp

← Older revision		Revision as of 06:29, 14 May 2026
Line 11:		Line 11:
	\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58		\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58
	}}		}}
	'''Myna''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a flattened minor third of [[~]][[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]]–[[7/6]]–6/5–[[49/40]]–[[5/4]]–[[9/7]]–[[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[edo]]s of medium size – the other one being [[keemic temperaments]], such as [[~~quasitemp~~]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. In either case, by tempering the septimal dieses together, there is an exact neutral third in between 6/5 and 5/4. [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.		'''Myna''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a flattened minor third of [[~]][[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]]–[[7/6]]–6/5–[[49/40]]–[[5/4]]–[[9/7]]–[[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[edo]]s of medium size – the other one being [[keemic temperaments]], such as [[superkleismic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. In either case, by tempering the septimal dieses together, there is an exact neutral third in between 6/5 and 5/4. [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.

	[[27edo\|27e-edo]] and [[31edo]] represent natural endpoints of myna's tuning range, and 27 + 31 = [[58edo]] and 58 + 31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35~50/49 chroma. Additionally, [[1728/1715]] ([[S-expression\|S6/S7]]), the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40~60/49). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.		[[27edo\|27e-edo]] and [[31edo]] represent natural endpoints of myna's tuning range, and 27 + 31 = [[58edo]] and 58 + 31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35~50/49 chroma. Additionally, [[1728/1715]] ([[S-expression\|S6/S7]]), the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40~60/49). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.

Lériendil at 00:50, 14 May 2026

2026-05-14T00:50:01Z

← Older revision		Revision as of 00:50, 14 May 2026
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	\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58		\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58
	}}		}}
	'''Myna''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a flattened minor third of [[~]][[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]]–[[7/6]]–6/5–[[49/40]]–[[5/4]]–[[9/7]]–[[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[edo]]s of medium size – the other one being [[keemic temperaments]], ~~in particular~~ [[quasitemp]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. In either case, by tempering the septimal dieses together, there is an exact neutral third in between 6/5 and 5/4. [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.		'''Myna''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a flattened minor third of [[~]][[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]]–[[7/6]]–6/5–[[49/40]]–[[5/4]]–[[9/7]]–[[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[edo]]s of medium size – the other one being [[keemic temperaments]], such as [[quasitemp]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. In either case, by tempering the septimal dieses together, there is an exact neutral third in between 6/5 and 5/4. [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.

	[[27edo\|27e-edo]] and [[31edo]] represent natural endpoints of myna's tuning range, and 27 + 31 = [[58edo]] and 58 + 31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35~50/49 chroma. Additionally, [[1728/1715]] ([[S-expression\|S6/S7]]), the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40~60/49). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.		[[27edo\|27e-edo]] and [[31edo]] represent natural endpoints of myna's tuning range, and 27 + 31 = [[58edo]] and 58 + 31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35~50/49 chroma. Additionally, [[1728/1715]] ([[S-expression\|S6/S7]]), the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40~60/49). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.

FloraC: Myna should be compared with quasitemp (since both are rank-2)

2026-02-19T16:07:14Z

Myna should be compared with quasitemp (since both are rank-2)

← Older revision		Revision as of 16:07, 19 February 2026
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	\| Title = Myna		\| Title = Myna
	\| Subgroups = 2.3.5.7, 2.3.5.7.11		\| Subgroups = 2.3.5.7, 2.3.5.7.11
	\| Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br> [[126/125]], [[176/175]], [[243/242]] (11-limit)		\| Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br>[[126/125]], [[176/175]], [[243/242]] (11-limit)
	\| Edo join 1 = 27 \| Edo join 2 = 31		\| Edo join 1 = 27e \| Edo join 2 = 31
	\| Mapping = 1; 10 9 7 25		\| Mapping = 1; 10 9 7 25
	\| Generators = 6/5 \| Generators tuning = 310.1 \| Optimization method = CWE		\| Generators = 6/5 \| Generators tuning = 310.1 \| Optimization method = CWE
Line 11:		Line 11:
	\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58		\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58
	}}		}}
	'''Myna''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a flattened minor third of [[~]][[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]]–[[7/6]]–6/5–[[49/40]]–[[5/4]]–[[9/7]]–[[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[edo]]s of medium size – the other one being [[keemic temperaments]], ~~such as [[superkleismic]] and~~ [[~~magic~~]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. ~~Both have their characteristic sets of damage~~, ~~but myna leaves space for~~ an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.		'''Myna''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a flattened minor third of [[~]][[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]]–[[7/6]]–6/5–[[49/40]]–[[5/4]]–[[9/7]]–[[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[edo]]s of medium size – the other one being [[keemic temperaments]], in particular [[quasitemp]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. In either case, by tempering the septimal dieses together, there is an exact neutral third in between 6/5 and 5/4. [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.

	~~It can be described as the 27e & 31 temperament;~~ [[27edo]] and [[31edo]] represent natural endpoints of ~~its~~ tuning range, and 27 + 31 = [[58edo]] and 58 + 31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35~50/49 chroma. Additionally, [[1728/1715]] ([[S-expression\|S6/S7]]), the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40~60/49). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.		[[27edo\|27e-edo]] and [[31edo]] represent natural endpoints of myna's tuning range, and 27 + 31 = [[58edo]] and 58 + 31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35~50/49 chroma. Additionally, [[1728/1715]] ([[S-expression\|S6/S7]]), the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40~60/49). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.

	Note: "myna" is pronounced /'maɪnə/, like {{w\|myna\|the bird}}, but is also as a pun on "minor".		Note: "myna" is pronounced /'maɪnə/, like {{w\|myna\|the bird}}, but is also as a pun on "minor".

FloraC: Cleanup on infobox

2026-02-09T09:30:10Z

Cleanup on infobox

← Older revision		Revision as of 09:30, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Myna		\| Title = Myna
	\| Subgroups = 2.3.5.7, 2.3.5.7.11		\| Subgroups = 2.3.5.7, 2.3.5.7.11
	\| Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br> [[126/125]], [[176/175]], [[243/242]] (11-limit)		\| Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br> [[126/125]], [[176/175]], [[243/242]] (11-limit)
	\| Edo join 1 = 27 \| Edo join 2 = 31		\| Edo join 1 = 27 \| Edo join 2 = 31
	\| ~~Generator~~ = 6/5 \| ~~Generator~~ tuning = 310.1 \| Optimization method = CWE		\| Mapping = 1; 10 9 7 25
			\| Generators = 6/5 \| Generators tuning = 310.1 \| Optimization method = CWE
	\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], …, [[4L 23s]], [[27L 4s]]		\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], …, [[4L 23s]], [[27L 4s]]
	~~\| Mapping = 1; 10 9 7 25~~
	\| Pergen = (P8, ccP5/10)		\| Pergen = (P8, ccP5/10)
	\| Odd limit 1 = 7 \| Mistuning 1 = ? \| Complexity 1 = 23		\| Odd limit 1 = 7 \| Mistuning 1 = ? \| Complexity 1 = 23
	\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58		\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58
	}}		}}

	'''Myna''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a flattened minor third of [[~]][[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]]–[[7/6]]–6/5–[[49/40]]–[[5/4]]–[[9/7]]–[[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[edo]]s of medium size – the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.		'''Myna''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a flattened minor third of [[~]][[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]]–[[7/6]]–6/5–[[49/40]]–[[5/4]]–[[9/7]]–[[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[edo]]s of medium size – the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.

FloraC: /* Tunings */ + notes

2025-10-13T10:33:55Z

Tunings: + notes

← Older revision		Revision as of 10:33, 13 October 2025
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	\|-		\|-
	! Edo<br>generator		! Edo<br>generator
	! [[Eigenmonzo\|Eigenmonzo<br>(unchanged interval)]])		! [[Eigenmonzo\|Eigenmonzo<br>(unchanged interval)]]
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
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	\|		\|
	\| 310.112		\| 310.112
	\|		\| 89f val
	\|-		\|-
	\|		\|
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	\|		\|
	\| 310.588		\| 310.588
	\|		\| 85ce val
	\|-		\|-
	\|		\|
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	\|		\|
	\| 311.111		\| 311.111
	\|		\| 27e val
	\|-		\|-
	\|		\|

FloraC: Adopt CWE tuning. Simplify the ratios in the tuning spectrum. Misc. cleanup. Fix the dead link

2025-10-13T10:28:31Z

Adopt CWE tuning. Simplify the ratios in the tuning spectrum. Misc. cleanup. Fix the dead link

Show changes

Lériendil at 03:35, 6 August 2025

2025-08-06T03:35:49Z

← Older revision		Revision as of 03:35, 6 August 2025
Line 12:		Line 12:
	}}		}}

	'''Myna''' is a [[rank-2]] [[temperament]] that is [[generator\|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how ~~septimal harmony is~~ organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.		'''Myna''' is a [[rank-2]] [[temperament]] that is [[generator\|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.

	It can be described as the 27e & 31 temperament; [[27edo]] and [[31edo]] represent natural endpoints of its tuning range, and 27+31 = [[58edo]] and 58+31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35[[~]]50/49 chroma. Additionally, {{S\|6/S7}} = [[1728/1715]], the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.		It can be described as the 27e & 31 temperament; [[27edo]] and [[31edo]] represent natural endpoints of its tuning range, and 27+31 = [[58edo]] and 58+31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35[[~]]50/49 chroma. Additionally, {{S\|6/S7}} = [[1728/1715]], the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.

Lériendil at 20:39, 1 July 2025

2025-07-01T20:39:51Z

← Older revision		Revision as of 20:39, 1 July 2025
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	'''Myna''' is a [[rank-2]] [[temperament]] that is [[generator\|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how septimal harmony is organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.		'''Myna''' is a [[rank-2]] [[temperament]] that is [[generator\|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how septimal harmony is organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.

	It can be described as the 27e & 31 temperament; [[27edo]] and [[31edo]] represent natural endpoints of its tuning range, and 27+31 = [[58edo]] and 58+31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35[[~]]50/49 chroma. Additionally, {{S\|6/S7}} = [[1728/1715]], the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are tempered out.		It can be described as the 27e & 31 temperament; [[27edo]] and [[31edo]] represent natural endpoints of its tuning range, and 27+31 = [[58edo]] and 58+31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35[[~]]50/49 chroma. Additionally, {{S\|6/S7}} = [[1728/1715]], the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.

	Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia:Myna\|the bird]], but is also as a pun on "minor".		Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia:Myna\|the bird]], but is also as a pun on "minor".

Lériendil: pot we

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pot we

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	\| Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br> [[126/125]], [[176/175]], [[243/242]] (11-limit)		\| Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br> [[126/125]], [[176/175]], [[243/242]] (11-limit)
	\| Edo join 1 = 27 \| Edo join 2 = 31		\| Edo join 1 = 27 \| Edo join 2 = 31
	\| Generator = 6/5 \| Generator tuning = 310.1 \| Optimization method = ~~POTWE~~		\| Generator = 6/5 \| Generator tuning = 310.1 \| Optimization method = POTE
	\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], ... [[4L 23s]], [[27L 4s]]		\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], ... [[4L 23s]], [[27L 4s]]
	\| Mapping = 1; 10 9 7 25		\| Mapping = 1; 10 9 7 25

Lériendil: added infobox

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added infobox

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			{{Infobox Regtemp
			\| Title = Myna
			\| Subgroups = 2.3.5.7, 2.3.5.7.11
			\| Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br> [[126/125]], [[176/175]], [[243/242]] (11-limit)
			\| Edo join 1 = 27 \| Edo join 2 = 31
			\| Generator = 6/5 \| Generator tuning = 310.1 \| Optimization method = POTWE
			\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], ... [[4L 23s]], [[27L 4s]]
			\| Mapping = 1; 10 9 7 25
			\| Pergen = (P8, ccP5/10)
			\| Odd limit 1 = 7 \| Mistuning 1 = ? \| Complexity 1 = 23
			\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = ? \| Complexity 2 = 58
			}}

	'''Myna''' is a [[rank-2]] [[temperament]] that is [[generator\|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how septimal harmony is organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.		'''Myna''' is a [[rank-2]] [[temperament]] that is [[generator\|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how septimal harmony is organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.

← Older revision		Revision as of 20:39, 1 July 2025
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	'''Myna''' is a [[rank-2]] [[temperament]] that is [[generator\|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how septimal harmony is organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.		'''Myna''' is a [[rank-2]] [[temperament]] that is [[generator\|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how septimal harmony is organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well.

	It can be described as the 27e & 31 temperament; [[27edo]] and [[31edo]] represent natural endpoints of its tuning range, and 27+31 = [[58edo]] and 58+31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35[[~]]50/49 chroma. Additionally, {{S\|6/S7}} = [[1728/1715]], the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are tempered out.		It can be described as the 27e & 31 temperament; [[27edo]] and [[31edo]] represent natural endpoints of its tuning range, and 27+31 = [[58edo]] and 58+31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out\|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35[[~]]50/49 chroma. Additionally, {{S\|6/S7}} = [[1728/1715]], the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out.

	Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia:Myna\|the bird]], but is also as a pun on "minor".		Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia:Myna\|the bird]], but is also as a pun on "minor".