Myna: Difference between revisions

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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.

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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.