Xenharmonic Wiki

Myna: Difference between revisions

← Older edit
VisualWikitext
→Interval chain: improvements
mNo edit summary
 
(24 intermediate revisions by 5 users not shown)
Line 1: Line 1:
{{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 7: Line 24:


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
! #
|-
! &#35;
! Cents*
! Cents*
! Approximate Ratios
! Approximate Ratios
Line 123: 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 ==
; MOS scales
; MOS scales
* [[Myna7]]
* [[Myna11]]
* [[Myna11]]
* [[Myna15]]
* [[Myna15]]
Line 141: 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
Line 265: Line 312:
* ''[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:Temperament]]
[[Category:Rank-2 temperaments]]
[[Category:Starling]]
[[Category:Starling temperaments]]
[[Category:Orwellismic]]
[[Category:Orwellismic temperaments]]
[[Category:Breed]]
[[Category:Breedsmic temperaments]]
Retrieved from "https://en.xen.wiki/w/Myna"