Myna: Difference between revisions

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→Spectrum of myna tunings by eigenmonzos: improve and standardize tuning spectra tables
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* [[Myna27trans37]]
* [[Myna27trans37]]


== Spectrum of myna tunings by eigenmonzos ==
== Tuning spectrum ==


{| class="wikitable center-1 center-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! ET<br>generator
! Minor Third
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! Comments
! minor<br>third (¢)
! 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

Revision as of 00:28, 30 September 2021

Myna is the rank-2 temperament that tempers out the starling comma (126/125) and the orwellisma (1728/1715). It is supported by 27edo, 31edo and 58edo, with MOS scales of cardinality 7, 11, 15, 19, 23, 27 and 31.

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

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

Template:IoT

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