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 = 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 [[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". | Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia:Myna|the bird]], but is also as a pun on "minor". | ||
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== Chords == | == Chords == | ||
: ''Main article: [[Chords of myna]] and [[Chords of tridecimal myna]]'' | |||
== Scales == | == Scales == | ||
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|- | |- | ||
! ET<br />generator | ! ET<br />generator | ||
! [[Eigenmonzo|Eigenmonzo<br />(unchanged | ! [[Eigenmonzo|Eigenmonzo<br />(unchanged interval)]]) | ||
! Minor<br />third (¢) | ! Minor<br />third (¢) | ||
! Comments | ! Comments | ||
Latest revision as of 03:35, 6 August 2025
| Myna |
126/125, 176/175, 243/242 (11-limit)
((2.3.5.7.11) 21-odd limit) ? ¢
((2.3.5.7.11) 21-odd limit) 58 notes
Myna is a rank-2 temperament that is 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 EDOs 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 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, S6/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 the bird, but is also as a pun on "minor".
See Starling temperaments #Myna for more technical data.
Interval chain
In the following table, prime harmonics are in bold.
| # | Cents* | Approximate Ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 310.3 | 6/5 |
| 2 | 620.6 | 10/7 |
| 3 | 930.8 | 12/7 |
| 4 | 41.1 | 36/35, 40/39, 45/44, 49/48, 50/49 |
| 5 | 351.4 | 11/9, 16/13 |
| 6 | 661.7 | 22/15, 35/24 |
| 7 | 971.9 | 7/4 |
| 8 | 82.2 | 21/20, 22/21, 25/24 |
| 9 | 392.5 | 5/4 |
| 10 | 702.8 | 3/2 |
| 11 | 1013.0 | 9/5 |
| 12 | 123.3 | 14/13, 15/14, 27/25 |
| 13 | 433.6 | 9/7 |
| 14 | 743.9 | 20/13 |
| 15 | 1054.1 | 11/6, 24/13 |
| 16 | 164.4 | 11/10 |
| 17 | 474.7 | 21/16 |
| 18 | 785.0 | 11/7 |
| 19 | 1095.3 | 15/8 |
| 20 | 205.5 | 9/8 |
| 21 | 515.8 | 27/20 |
| 22 | 826.1 | 21/13 |
| 23 | 1136.4 | 27/14 |
| 24 | 246.6 | 15/13 |
| 25 | 556.9 | 11/8, 18/13 |
| 26 | 867.1 | 33/20 |
| 27 | 1177.5 | 55/28, 63/32, 77/39, 99/50 |
* In 13-limit POTE tuning
Chords
- Main article: Chords of myna and Chords of tridecimal myna
Scales
- MOS scales
- Transversal scales
Tuning spectrum
| ET generator |
Eigenmonzo (unchanged interval)) |
Minor third (¢) |
Comments |
|---|---|---|---|
| 7/5 | 308.744 | ||
| 11/9 | 309.482 | ||
| 5/4 | 309.590 | ||
| 8\31 | 309.677 | ||
| 8/7 | 309.832 | ||
| 16/15 | 309.909 | ||
| 15/14 | 309.953 | ||
| 12/11 | 309.958 | ||
| 11/8 | 310.053 | ||
| 23\89 | 310.112 | ||
| 14/11 | 310.138 | ||
| 4/3 | 310.196 | 5-, 7-, 9- and 11-odd-imit minimax; 5-, 7-, 11- and 13-limit POTT | |
| 11/10 | 310.313 | ||
| 15/13 | 310.323 | 15-odd-limit minimax | |
| 15\58 | 310.345 | ||
| 13/11 | 310.360 | 13-odd-limit minimax | |
| 9/7 | 310.391 | ||
| 13/10 | 310.413 | ||
| 15/11 | 310.508 | ||
| 18/13 | 310.535 | ||
| 22\85 | 310.588 | ||
| 10/9 | 310.691 | ||
| 14/13 | 310.692 | ||
| 13/12 | 310.762 | ||
| 7/6 | 311.043 | ||
| 7\27 | 311.111 | ||
| 16/13 | 311.894 | ||
| 6/5 | 315.641 |