Xenharmonic Wiki

Myna: Difference between revisions

← Older edit
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,164 edits
unchanged interval → unchanged-interval
Lériendil (talk | contribs)
8,033 edits
m replaced quasitemp with superkleismic, since it's generated by 6/5 like myna and demonstrates the keemic equivalence better; also I believe it to be more known than quasitemp
 
(23 intermediate revisions by 3 users not shown)
Line 1: Line 1:
'''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 scale]]s of cardinality 7, 11, 15, 19, 23, 27 and 31.  
{{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 = 27e | Edo join 2 = 31
| Mapping = 1; 10 9 7 25
| Generators = 6/5 | Generators tuning = 310.1 | Optimization method = CWE
| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], …, [[4L 23s]], [[27L 4s]]
| 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]] [[regular temperament|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]], 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. In either case, by tempering the septimal dieses together, there is 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.


Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia: Myna|the bird]], but is also as a pun on "minor".  
[[27edo|27e-edo]] and [[31edo]] represent natural endpoints of myna's 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, [[1728/1715]] ([[S-expression|S6/S7]]), 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 49/40~60/49). 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 {{w|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.
Line 9: Line 23:


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! #
! #
! Cents*
! Cents*
! Approximate Ratios
! Approximate ratios
|-
|-
| 0
| 0
Line 18: Line 33:
|-
|-
| 1
| 1
| 310.3
| 310.2
| 6/5
| 6/5
|-
|-
| 2
| 2
| 620.6
| 620.4
| 10/7
| 10/7
|-
|-
| 3
| 3
| 930.8
| 930.7
| 12/7
| 12/7
|-
|-
| 4
| 4
| 41.1
| 40.9
| 36/35, 40/39, 45/44, 49/48, 50/49
| 36/35, 40/39, 45/44, 49/48, 50/49
|-
|-
| 5
| 5
| 351.4
| 351.1
| 11/9, '''16/13'''
| 11/9, '''16/13'''
|-
|-
| 6
| 6
| 661.7
| 661.3
| 22/15, 35/24
| 22/15, 35/24
|-
|-
| 7
| 7
| 971.9
| 971.6
| '''7/4'''
| '''7/4'''
|-
|-
| 8
| 8
| 82.2
| 81.8
| 21/20, 22/21, 25/24
| 21/20, 22/21, 25/24
|-
|-
| 9
| 9
| 392.5
| 392.0
| '''5/4'''
| '''5/4'''
|-
|-
| 10
| 10
| 702.8
| 702.2
| '''3/2'''
| '''3/2'''
|-
|-
| 11
| 11
| 1013.0
| 1012.4
| 9/5
| 9/5
|-
|-
| 12
| 12
| 123.3
| 122.7
| 14/13, 15/14, 27/25
| 14/13, 15/14, 27/25
|-
|-
| 13
| 13
| 433.6
| 432.7
| 9/7
| 9/7
|-
|-
| 14
| 14
| 743.9
| 743.1
| 20/13
| 20/13
|-
|-
| 15
| 15
| 1054.1
| 1053.3
| 11/6, 24/13
| 11/6, 24/13
|-
|-
| 16
| 16
| 164.4
| 163.5
| 11/10
| 11/10
|-
|-
| 17
| 17
| 474.7
| 473.8
| 21/16
| 21/16
|-
|-
| 18
| 18
| 785.0
| 784.0
| 11/7
| 11/7
|-
|-
| 19
| 19
| 1095.3
| 1094.2
| 15/8
| 15/8
|-
|-
| 20
| 20
| 205.5
| 204.4
| 9/8
| 9/8
|-
|-
| 21
| 21
| 515.8
| 514.7
| 27/20
| 27/20
|-
|-
| 22
| 22
| 826.1
| 824.9
| 21/13
| 21/13
|-
|-
| 23
| 23
| 1136.4
| 1135.1
| 27/14
| 27/14
|-
|-
| 24
| 24
| 246.6
| 245.3
| 15/13
| 15/13
|-
|-
| 25
| 25
| 556.9
| 555.5
| '''11/8''', 18/13
| '''11/8''', 18/13
|-
|-
| 26
| 26
| 867.1
| 865.6
| 33/20
| 33/20
|-
|-
| 27
| 27
| 1177.5
| 1176.0
| 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 CWE tuning


== Chords ==
== Chords and harmony ==
{{main| Chords of myna }}
{{See also| Chords of myna | Chords of tridecimal myna }}


== Scales ==
== Scales ==
; MOS scales
; Mos scales
* [[Myna7]]
* [[Myna7]]
* [[Myna11]]
* [[Myna11]]
Line 144: Line 159:
* [[Myna27trans37]]
* [[Myna27trans37]]


== Tuning spectrum ==
== Tunings ==
 
=== Tuning spectrum ===
{| class="wikitable center-all"
{| class="wikitable center-all left-4"
|-
|-
! ET<br>generator
! Edo<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]
! minor<br>third (¢)
! Generator (¢)
! comments
! Comments
|-
|-
|  
|  
Line 174: Line 189:
|-
|-
|  
|  
| 8/7
| 7/4
| 309.832
| 309.832
|  
|  
|-
|-
|  
|  
| 16/15
| 15/8
| 309.909
| 309.909
|  
|  
Line 189: Line 204:
|-
|-
|  
|  
| 12/11
| 11/6
| 309.958
| 309.958
|  
|  
Line 201: Line 216:
|  
|  
| 310.112
| 310.112
|  
| 89f val
|-
|-
|  
|  
| 14/11
| 11/7
| 310.138
| 310.138
|  
|  
|-
|-
|  
|  
| 4/3
| 3/2
| 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
Line 249: Line 264:
|-
|-
|  
|  
| 18/13
| 13/9
| 310.535
| 310.535
|  
|  
Line 256: Line 271:
|  
|  
| 310.588
| 310.588
|  
| 85ce val
|-
|-
|  
|  
| 10/9
| 9/5
| 310.691
| 310.691
|  
|  
|-
|-
|  
|  
| 14/13
| 13/7
| 310.692
| 310.692
|  
|  
Line 281: Line 296:
|  
|  
| 311.111
| 311.111
|  
| 27e val
|-
|-
|  
|  
| 16/13
| 13/8
| 311.894
| 311.894
|  
|  
|-
|-
|  
|  
| 6/5
| 5/3
| 315.641
| 315.641
|  
|  
Line 295: Line 310:


== Music ==
== Music ==
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3 Myna Music]'' by [[Igliashon Jones]]
; [[Igliashon Jones]]
* [https://web.archive.org/web/20201129182056/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3 ''Myna Music'']


[[Category:Temperaments]]
[[Category:Myna| ]] <!-- Main article -->
[[Category:Myna| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Starling temperaments]]
[[Category:Starling temperaments]]
[[Category:Orwellismic temperaments]]
[[Category:Orwellismic temperaments]]
[[Category:Breedsmic temperaments]]
[[Category:Breedsmic temperaments]]
Retrieved from "https://en.xen.wiki/w/Myna"