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**Imported revision 466845546 - Original comment: **
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
 
(44 intermediate revisions by 9 users not shown)
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox regtemp
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Title = Myna
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-11-07 01:37:23 UTC</tt>.<br>
| Subgroups = 2.3.5.7, 2.3.5.7.11
: The original revision id was <tt>466845546</tt>.<br>
| Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br>[[126/125]], [[176/175]], [[243/242]] (11-limit)
: The revision comment was: <tt></tt><br>
| Edo join 1 = 27e | Edo join 2 = 31
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Mapping = 1; 10 9 7 25
<h4>Original Wikitext content:</h4>
| Generators = 6/5 | Generators tuning = 310.1 | Optimization method = CWE
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">See [[Starling temperaments#Myna temperament]].
| 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.


=Spectrum of Myna Tunings by Eigenmonzos=  
[[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.
||~ Eigenmonzo ||~ Minor Third ||
|| 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 limit minimax) ||
|| 11/10 || 310.313 ||
|| 15/13 || 310.323 (15 limit minimax) ||
|| 15\58 || 310.345 ||
|| 13/11 || 310.360 (13 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 ||
|| 16/13 || 311.894 ||
|| 6/5 || 315.641 ||</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Myna&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Starling%20temperaments#Myna temperament"&gt;Starling temperaments&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Spectrum of Myna Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Spectrum of Myna Tunings by Eigenmonzos&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
Note: "myna" is pronounced /'maɪnə/, like {{w|myna|the bird}}, but is also as a pun on "minor".  
    &lt;tr&gt;
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Minor Third&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;308.744&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.482&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.590&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.677&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.832&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.909&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.953&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.958&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.053&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23\89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.112&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.138&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.196 (5, 7, 9 and 11 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.313&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.323 (15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15\58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.345&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.360 (13 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.391&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.413&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.508&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.535&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22\85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.588&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.691&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.692&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.762&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;311.043&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;311.894&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;315.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
See [[Starling temperaments #Myna]] for more technical data.
 
== Interval chain ==
In the following table, prime harmonics are in '''bold'''.
 
{| class="wikitable center-1 right-2"
|-
! #
! Cents*
! Approximate ratios
|-
| 0
| 0.0
| '''1/1'''
|-
| 1
| 310.2
| 6/5
|-
| 2
| 620.4
| 10/7
|-
| 3
| 930.7
| 12/7
|-
| 4
| 40.9
| 36/35, 40/39, 45/44, 49/48, 50/49
|-
| 5
| 351.1
| 11/9, '''16/13'''
|-
| 6
| 661.3
| 22/15, 35/24
|-
| 7
| 971.6
| '''7/4'''
|-
| 8
| 81.8
| 21/20, 22/21, 25/24
|-
| 9
| 392.0
| '''5/4'''
|-
| 10
| 702.2
| '''3/2'''
|-
| 11
| 1012.4
| 9/5
|-
| 12
| 122.7
| 14/13, 15/14, 27/25
|-
| 13
| 432.7
| 9/7
|-
| 14
| 743.1
| 20/13
|-
| 15
| 1053.3
| 11/6, 24/13
|-
| 16
| 163.5
| 11/10
|-
| 17
| 473.8
| 21/16
|-
| 18
| 784.0
| 11/7
|-
| 19
| 1094.2
| 15/8
|-
| 20
| 204.4
| 9/8
|-
| 21
| 514.7
| 27/20
|-
| 22
| 824.9
| 21/13
|-
| 23
| 1135.1
| 27/14
|-
| 24
| 245.3
| 15/13
|-
| 25
| 555.5
| '''11/8''', 18/13
|-
| 26
| 865.6
| 33/20
|-
| 27
| 1176.0
| 55/28, 63/32, 77/39, 99/50
|}
<nowiki/>* In 13-limit CWE tuning
 
== Chords and harmony ==
{{See also| Chords of myna | Chords of tridecimal myna }}
 
== Scales ==
; Mos scales
* [[Myna7]]
* [[Myna11]]
* [[Myna15]]
 
; Transversal scales
* [[Myna19trans]]
* [[Myna19trans37]]
* [[Myna23trans]]
* [[Myna23trans37]]
* [[Myna27trans]]
* [[Myna27trans37]]
 
== Tunings ==
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]
! Generator (¢)
! Comments
|-
|
| 7/5
| 308.744
|
|-
|
| 11/9
| 309.482
|
|-
|
| 5/4
| 309.590
|
|-
| 8\31
|
| 309.677
|
|-
|
| 7/4
| 309.832
|
|-
|
| 15/8
| 309.909
|
|-
|
| 15/14
| 309.953
|
|-
|
| 11/6
| 309.958
|
|-
|
| 11/8
| 310.053
|
|-
| 23\89
|
| 310.112
| 89f val
|-
|
| 11/7
| 310.138
|
|-
|
| 3/2
| 310.196
| 5-, 7-, 9- and 11-odd-imit minimax; <br>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
|
|-
|
| 13/9
| 310.535
|
|-
| 22\85
|
| 310.588
| 85ce val
|-
|
| 9/5
| 310.691
|
|-
|
| 13/7
| 310.692
|
|-
|
| 13/12
| 310.762
|
|-
|
| 7/6
| 311.043
|
|-
| 7\27
|
| 311.111
| 27e val
|-
|
| 13/8
| 311.894
|
|-
|
| 5/3
| 315.641
|
|}
 
== Music ==
; [[Igliashon Jones]]
* [https://web.archive.org/web/20201129182056/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3 ''Myna Music'']
 
[[Category:Myna| ]] <!-- Main article -->
[[Category:Rank-2 temperaments]]
[[Category:Starling temperaments]]
[[Category:Orwellismic temperaments]]
[[Category:Breedsmic temperaments]]

Latest revision as of 06:29, 14 May 2026

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]
ET join 27e & 31
Generators (CWE) ~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, 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.

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 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 (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 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
1 310.2 6/5
2 620.4 10/7
3 930.7 12/7
4 40.9 36/35, 40/39, 45/44, 49/48, 50/49
5 351.1 11/9, 16/13
6 661.3 22/15, 35/24
7 971.6 7/4
8 81.8 21/20, 22/21, 25/24
9 392.0 5/4
10 702.2 3/2
11 1012.4 9/5
12 122.7 14/13, 15/14, 27/25
13 432.7 9/7
14 743.1 20/13
15 1053.3 11/6, 24/13
16 163.5 11/10
17 473.8 21/16
18 784.0 11/7
19 1094.2 15/8
20 204.4 9/8
21 514.7 27/20
22 824.9 21/13
23 1135.1 27/14
24 245.3 15/13
25 555.5 11/8, 18/13
26 865.6 33/20
27 1176.0 55/28, 63/32, 77/39, 99/50

* In 13-limit CWE tuning

Chords and harmony

See also: Chords of myna and Chords of tridecimal myna

Scales

Mos scales
Transversal scales

Tunings

Tuning spectrum

Edo
generator 		Eigenmonzo
(unchanged interval) 		Generator (¢) Comments
7/5 308.744
11/9 309.482
5/4 309.590
8\31 309.677
7/4 309.832
15/8 309.909
15/14 309.953
11/6 309.958
11/8 310.053
23\89 310.112 89f val
11/7 310.138
3/2 310.196 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
13/9 310.535
22\85 310.588 85ce val
9/5 310.691
13/7 310.692
13/12 310.762
7/6 311.043
7\27 311.111 27e val
13/8 311.894
5/3 315.641

Music

Igliashon Jones
Retrieved from "https://en.xen.wiki/index.php?title=Myna&oldid=230321"