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{{todo|add introduction}}
{{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
}}
 
'''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".


See [[Starling temperaments #Myna]] for more technical data.
See [[Starling temperaments #Myna]] for more technical data.
Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia: Myna|the bird]], but is also as a pun on "minor".


== Interval chain ==
== Interval chain ==
Line 9: Line 24:


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
! #
|-
! &#35;
! Cents*
! Cents*
! Approximate Ratios
! Approximate Ratios
Line 125: Line 141:
| 55/28, 63/32, 77/39, 99/50
| 55/28, 63/32, 77/39, 99/50
|}
|}
<nowiki>*</nowiki> in 13-limit POTE tuning
<nowiki />* In 13-limit POTE tuning


== Chords ==
== Chords ==
{{main| Chords of myna }}
: ''Main article: [[Chords of myna]] and [[Chords of tridecimal myna]]''


== Scales ==
== Scales ==
Line 144: Line 160:
* [[Myna27trans37]]
* [[Myna27trans37]]


== Spectrum of myna tunings by eigenmonzos ==
== Tuning spectrum ==
 
{| class="wikitable center-all"
{| class="wikitable center-1 center-2"
|-
|-
! Eigenmonzo
! ET<br />generator
! Minor Third
! [[Eigenmonzo|Eigenmonzo<br />(unchanged interval)]])
! Minor<br />third (¢)
! Comments
! Comments
|-
|-
|
| 7/5
| 7/5
| 308.744
| 308.744
|  
|  
|-
|-
|
| 11/9
| 11/9
| 309.482
| 309.482
|  
|  
|-
|-
|
| 5/4
| 5/4
| 309.590
| 309.590
|  
|  
|-
|-
| (8\31)
| 8\31
|
| 309.677
| 309.677
|  
|  
|-
|-
|
| 8/7
| 8/7
| 309.832
| 309.832
|  
|  
|-
|-
|
| 16/15
| 16/15
| 309.909
| 309.909
|  
|  
|-
|-
|
| 15/14
| 15/14
| 309.953
| 309.953
|  
|  
|-
|-
|
| 12/11
| 12/11
| 309.958
| 309.958
|  
|  
|-
|-
|
| 11/8
| 11/8
| 310.053
| 310.053
|  
|  
|-
|-
| (23\89)
| 23\89
|
| 310.112
| 310.112
|  
|  
|-
|-
|
| 14/11
| 14/11
| 310.138
| 310.138
|  
|  
|-
|-
|
| 4/3
| 4/3
| 310.196
| 310.196
| 5-, 7-, 9- and 11-odd-imit minimax; <br>5-, 7-, 11- and 13-limit POTT
| 5-, 7-, 9- and 11-odd-imit minimax; <br>5-, 7-, 11- and 13-limit POTT
|-
|-
|
| 11/10
| 11/10
| 310.313
| 310.313
|  
|  
|-
|-
|
| 15/13
| 15/13
| 310.323
| 310.323
| 15-odd-limit minimax
| 15-odd-limit minimax
|-
|-
| (15\58)
| 15\58
|
| 310.345
| 310.345
|  
|  
|-
|-
|
| 13/11
| 13/11
| 310.360
| 310.360
| 13-odd-limit minimax
| 13-odd-limit minimax
|-
|-
|
| 9/7
| 9/7
| 310.391
| 310.391
|  
|  
|-
|-
|
| 13/10
| 13/10
| 310.413
| 310.413
|  
|  
|-
|-
|
| 15/11
| 15/11
| 310.508
| 310.508
|  
|  
|-
|-
|
| 18/13
| 18/13
| 310.535
| 310.535
|  
|  
|-
|-
| (22\85)
| 22\85
|
| 310.588
| 310.588
|  
|  
|-
|-
|
| 10/9
| 10/9
| 310.691
| 310.691
|  
|  
|-
|-
|
| 14/13
| 14/13
| 310.692
| 310.692
|  
|  
|-
|-
|
| 13/12
| 13/12
| 310.762
| 310.762
|  
|  
|-
|-
|
| 7/6
| 7/6
| 311.043
| 311.043
|  
|  
|-
|-
| (7\27)
| 7\27
|
| 311.111
| 311.111
|  
|  
|-
|-
|
| 16/13
| 16/13
| 311.894
| 311.894
|  
|  
|-
|-
|
| 6/5
| 6/5
| 315.641
| 315.641
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* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3 Myna Music]'' by [[Igliashon Jones]]
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3 Myna Music]'' by [[Igliashon Jones]]


[[Category:Myna| ]] <!-- main article -->
[[Category:Myna| ]] <!-- Main article -->
[[Category:Starling]]
[[Category:Rank-2 temperaments]]
[[Category:Orwellismic]]
[[Category:Starling temperaments]]
[[Category:Breed]]
[[Category:Orwellismic temperaments]]
{{IoT}}
[[Category:Breedsmic temperaments]]

Latest revision as of 03:35, 6 August 2025

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)
Reduced mapping ⟨1; 10 9 7 25]
Edo join 27 & 31
Generator (POTE) ~6/5 = 310.1 ¢
MOS scales 3L 1s, 4L 3s, 4L 7s, ... 4L 23s, 27L 4s
Ploidacot beta-decacot
Pergen (P8, ccP5/10)
Minimax error (7-odd limit) ? ¢;
((2.3.5.7.11) 21-odd limit) ? ¢
Target scale size (7-odd limit) 23 notes;
((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

Music

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