Myna: Difference between revisions

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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~~ [[7/6]] - ~~6/5 -~~ [[49/40]] - [[5/4]] - [[9/7]] ~~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 to organize septimal harmony 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~~. ~~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.~~

{{Infobox Regtemp

| Title = Myna

| Subgroups = 2.3.5.7, 2.3.5.7.11

| Comma basis = [[126/125]], [[1728/1715]] (7-limit); [[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 = POTE

| 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

}}

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, and so is [[2401/2400]], the breedsma. In the 11-limit, [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are tempered out.

'''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.

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

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== Chords ==

~~{{main|~~ Chords of myna }}

: ''Main article: [[Chords of myna]] and [[Chords of tridecimal myna]]''

== Scales ==

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|-

! ET generator

! [[Eigenmonzo|Eigenmonzo (unchanged-interval)]])

! [[Eigenmonzo|Eigenmonzo (unchanged interval)]])

! Minor third (¢)

! Comments

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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 [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] 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 to organize septimal harmony 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. 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.
+{{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 = POTE
+| 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
+}}
-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, and so is [[2401/2400]], the breedsma. In the 11-limit, [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are tempered out.
+'''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.
 Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia:Myna|the bird]], but is also as a pun on "minor".
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 == Chords ==
-{{main| Chords of myna }}
+: ''Main article: [[Chords of myna]] and [[Chords of tridecimal myna]]''
 == Scales ==
@@ Line 151: / Line 164: @@
 |-
 ! ET<br />generator
-! [[Eigenmonzo|Eigenmonzo<br />(unchanged-interval)]])
+! [[Eigenmonzo|Eigenmonzo<br />(unchanged interval)]])
 ! Minor<br />third (¢)
 ! Comments