Xenharmonic Wiki

Myna: Difference between revisions

← Older edit
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
re-categorized: not a redirect any more
mNo edit summary
 
(29 intermediate revisions by 6 users not shown)
Line 1: Line 1:
See also [[Starling temperaments #Myna]].
{{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".  
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.


== Interval chain ==
== Interval chain ==
{| class="wikitable center-all right-2"
In the following table, prime harmonics are in '''bold'''.
! #
 
{| class="wikitable center-1 right-2"
|-
! &#35;
! Cents*
! Cents*
! Approximate Ratios
! Approximate Ratios
|-
|-
| 0
| 0
| 0.000
| 0.0
| 1/1
| '''1/1'''
|-
|-
| 1
| 1
| 310.276
| 310.3
| 6/5
| 6/5
|-
|-
| 2
| 2
| 620.552
| 620.6
| 10/7
| 10/7
|-
|-
| 3
| 3
| 930.828
| 930.8
| 12/7
| 12/7
|-
|-
| 4
| 4
| 41.104
| 41.1
| 36/35~49/48~50/49~40/39
| 36/35, 40/39, 45/44, 49/48, 50/49
|-
|-
| 5
| 5
| 351.380
| 351.4
| 11/9~16/13
| 11/9, '''16/13'''
|-
|-
| 6
| 6
| 661.657
| 661.7
| 35/24
| 22/15, 35/24
|-
|-
| 7
| 7
| 971.933
| 971.9
| 7/4
| '''7/4'''
|-
|-
| 8
| 8
| 82.209
| 82.2
| 25/24~21/20
| 21/20, 22/21, 25/24
|-
|-
| 9
| 9
| 392.485
| 392.5
| 5/4
| '''5/4'''
|-
|-
| 10
| 10
| 702.761
| 702.8
| 3/2
| '''3/2'''
|-
|-
| 11
| 11
| 1013.037
| 1013.0
| 9/5
| 9/5
|-
|-
| 12
| 12
| 123.313
| 123.3
| 27/25~15/14~14/13
| 14/13, 15/14, 27/25
|-
|-
| 13
| 13
| 433.589
| 433.6
| 9/7
| 9/7
|-
|-
| 14
| 14
| 743.865
| 743.9
| 20/13
| 20/13
|-
|-
| 15
| 15
| 1054.141
| 1054.1
| 11/6~24/13
| 11/6, 24/13
|-
|-
| 16
| 16
| 164.418
| 164.4
| 11/10
| 11/10
|-
|-
| 17
| 17
| 474.694
| 474.7
| 21/16
| 21/16
|-
|-
| 18
| 18
| 784.970
| 785.0
| 11/7
| 11/7
|-
|-
| 19
| 19
| 1095.256
| 1095.3
| 15/8
| 15/8
|-
|-
| 20
| 20
| 205.522
| 205.5
| 9/8
| 9/8
|-
|-
| 21
| 21
| 515.798
| 515.8
| 27/20
| 27/20
|-
|-
| 22
| 22
| 826.074
| 826.1
| 21/13
| 21/13
|-
|-
| 23
| 23
| 1136.350
| 1136.4
| 27/14
| 27/14
|-
|-
| 24
| 24
| 246.626
| 246.6
| 15/13
| 15/13
|-
|-
| 25
| 25
| 556.902
| 556.9
| 11/8~18/13
| '''11/8''', 18/13
|-
| 26
| 867.1
| 33/20
|-
| 27
| 1177.5
| 55/28, 63/32, 77/39, 99/50
|}
|}
<nowiki>*</nowiki> In 13-limit POTE tuning
<nowiki />* In 13-limit POTE tuning
 
== Chords ==
: ''Main article: [[Chords of myna]] and [[Chords of tridecimal myna]]''
 
== Scales ==
; MOS scales
* [[Myna7]]
* [[Myna11]]
* [[Myna15]]


== Spectrum of Myna Tunings by Eigenmonzos ==
; Transversal scales
* [[Myna19trans]]
* [[Myna19trans37]]
* [[Myna23trans]]
* [[Myna23trans37]]
* [[Myna27trans]]
* [[Myna27trans37]]


{| class="wikitable center-all left-3"
== Tuning spectrum ==
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! ET<br />generator
! Minor Third
! [[Eigenmonzo|Eigenmonzo<br />(unchanged interval)]])
! Comment
! 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 limit 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 limit minimax
| 15-odd-limit minimax
|-
|-
| (15\58)
| 15\58
|
| 310.345
| 310.345
|  
|  
|-
|-
|
| 13/11
| 13/11
| 310.360
| 310.360
| 13 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
|
|}
|}


[[Category:Myna| ]] <!-- main article -->
== Music ==
[[Category:Temperament]]
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3 Myna Music]'' by [[Igliashon Jones]]
 
[[Category:Myna| ]] <!-- Main article -->
[[Category:Rank-2 temperaments]]
[[Category:Starling temperaments]]
[[Category:Orwellismic temperaments]]
[[Category:Breedsmic temperaments]]
Retrieved from "https://en.xen.wiki/w/Myna"