Myna: Difference between revisions

| 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)

| Generator = 6/5 | Generator tuning = 310.1 | Optimization method = POTE

| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], ... [[4L 23s]], [[27L 4s]]

| 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 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.

 

 

 

! &#35;

| 36/35, 40/39, 45/44, 49/48, 50/49

 

 

; MOS scales

 

; Transversal scales

 

! ET<br />generator

! Minor<br />third (¢)

| 5-, 7-, 9- and 11-odd-imit minimax; <br>5-, 7-, 11- and 13-limit POTT

 

* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3 Myna Music]'' by [[Igliashon Jones]]

 

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