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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''hemimean clan''' [[Tempering out|tempers out]] the hemimean comma, [[3136/3125]], with [[monzo]] {{monzo| 6 0 -5 2 }}, such that [[7/4]] is split into five steps, of which two make [[5/4]] and three make [[7/5]]; this defines the [[2.5.7 subgroup]] temperament [[didacus]], generated by a tempered hemithird of [[28/25]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-11 12:04:40 UTC</tt>.<br>
: The original revision id was <tt>300769016</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]


The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwuerschmidt, parakleismic, hemithirds, clyde, hemischismic, passion, hexe and sycamore considered elsewhere.
The second comma of the comma list determines which 7-limit family member we are looking at. These [[extension]]s, in general, split the [[syntonic comma]] into two, each for [[126/125]]~[[225/224]], as 3136/3125 = (126/125)/(225/224). Hemiwürschmidt adds [[2401/2400]]; hemithirds adds [[1029/1024]]; spell adds [[49/48]]. These all use the same nominal generator as didacus.  


Comma: 3136/3125
Septimal passion adds [[64/63]], splitting the hemithird into a further two. Septimal meantone adds [[81/80]] as well as [[126/125]] and [[225/224]], splitting an octave plus the hemithird into two perfect fifths. Sycamore adds [[686/675]], splitting the hemithird into three. Semisept adds [[1728/1715]], splitting an octave plus the hemithird into three. Mohavila adds [[135/128]], whereas cohemimabila adds [[65536/64827]], both splitting two octaves plus the hemithird into three. Emka adds [[84035/82944]], splitting two octaves plus the hemithird into four. Bidia adds [[2048/2025]] with a 1/4-octave period. Misty adds [[5120/5103]] with a 1/3-octave period. Bischismic adds [[32805/32768]] with a semioctave period. Hexe adds [[50/49]] with a 1/6-octave period. Clyde adds [[245/243]] with a generator of ~9/7, five of which make the original. Parakleismic adds [[4375/4374]] with a generator of ~6/5. Arch adds [[5250987/5242880]] with a generator of ~64/63. For these seven generators make the original. Sengagen adds [[420175/419904]] with a generator of ~686/675, splitting the hemithird into eight. Subpental adds [[19683/19600]] with a generator of ~56/45, nine of which make the original.


No-threes [[POTE tuning|POTE generator]] (~28/25): 193.772
Didacus has canonical subgroup extensions to primes 11 and 13, at [[#Undecimal didacus|undecimal didacus]]. Other subgroup extensions include rectified hebrew and isra.


Map: [&lt;1 0 0 -3|, &lt;0 0 2 5|]
Temperaments considered below are hemiwürschmidt, hemithirds, spell, semisept, emka, decipentic, sengagen, subpental, mowglic, and undetrita. Discussed elsewhere are
EDOs: [[6edo|6]], [[12edo|12]], [[19edo|12]], [[31edo|31]], [[68edo|68]], [[80edo|80]], [[87edo|87]], [[99edo|99]], [[130edo|130]], [[217edo|217]], [[229edo|229]], [[328edo|328]], [[347edo|347]], [[446edo|446]], [[545edo|545c]], [[675edo|675]]
* ''[[Passion]]'' (+64/63 or 3125/3087) → [[Passion family #Septimal passion|Passion family]]
* [[Meantone]] (+81/80, 126/125, 225/224) → [[Meantone family #Septimal meantone|Meantone family]]
* ''[[Mohavila]]'' (+135/128 or 1323/1250) → [[Mavila family #Mohavila|Mavila family]]
* ''[[Cohemimabila]]'' (+65536/64827) → [[Mabila family #Cohemimabila|Mabila family]]
* ''[[Sycamore]]'' (+686/675 or 875/864) → [[Sycamore family #Septimal sycamore|Sycamore family]]
* ''[[Bidia]]'' (+2048/2025) → [[Diaschismic family #Bidia|Diaschismic family]]
* ''[[Hexe]]'' (+50/49 or 128/125) → [[Augmented family #Hexe|Augmented family]]
* [[Misty]] (+5120/5103) → [[Misty family #Septimal misty|Misty family]]
* ''[[Bischismic]]'' (+32805/32768) → [[Schismatic family #Bischismic|Schismatic family]]
* ''[[Clyde]]'' (+245/243) → [[Kleismic family #Clyde|Kleismic family]]
* [[Parakleismic]] (+4375/4374) → [[Parakleismic family #Parakleismic|Parakleismic family]]
* ''[[Arch]]'' (+5250987/5242880) → [[Escapade family #Arch|Escapade family]]
* ''[[Subpental]]'' (+19683/19600) → [[Sensipent family #Sensipent|Sensipent family]]
* ''[[Doubloon]]'' (+33756345/33554432) → [[Vavoom family #Doubloon|Vavoom family]]
* ''[[Decistearn]]'' (+118098/117649) → [[Stearnsmic clan #Decistearn|Stearnsmic clan]]
* ''[[Quintagar]]'' (+33554432/33480783) → [[Quindromeda family #Quintagar|Quindromeda family]]
* ''[[Rubidium]]'' (+4194304/4117715) → [[37th-octave temperaments]]


=Misty=
= 2.5.7 subgroup =
Commas: 3136/3125, 5120/5103
== Didacus ==
{{main|Didacus}}


[[POTE tuning|POTE generator]]: 703.021
See also its canonical extension to the 2.5.7.11 subgroup, [[#Undecimal didacus]].


Map: [&lt;3 0 26 56|, &lt;0 1 -4 -10|]
[[Subgroup]]: 2.5.7
Wedgie: &lt;&lt;3 -12 -30 -26 -56 -36||
EDOs: [[12edo|12]], [[87edo|87]], [[99edo|99]]


==11-limit==
[[Comma list]]: [[3136/3125]]
Commas: 441/440, 3136/3125, 4375/4356


[[POTE tuning|POTE generator]]: 703.210
{{Mapping|legend=2| 1 0 -3 | 0 2 5 }}


Map: [&lt;3 0 26 56 77|, &lt;0 1 -4 -10 -14|]
: sval mapping generators: ~2, ~56/25
EDOs: 12, 87, 99e, 186e


==13-limit==
{{Mapping|legend=3| 1 0 0 -3 | 0 0 2 5 }}
Commas: 196/195, 352/351, 364/363, 625/624


[[POTE tuning|POTE generator]]: 703.303
: [[gencom]]: [2 56/25; 3136/3125]


Map: [&lt;3 0 26 56 77 92|, &lt;0 1 -4 -10 -14 -17|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/25 = 193.772
EDOs: 12, 87, 186ef, 273ef


=Mystic=
{{Optimal ET sequence|legend=1| 6, 19, 25, 31, 99, 130, 161, 353, 514c, 867c }}
Commas: 325/324, 441/440, 896/891, 1001/1000


[[POTE tuning|POTE generator]]: 703.311
[[Tp tuning #T2 tuning|RMS error]]: 0.2138 cents


Map: [&lt;3 0 26 56 77 -46|, &lt;0 1 -4 -10 -14 12|]
[[Badness]] (Sintel): 0.091
EDOs: 12, 87, 186e, 273e, 633bde


==17-limit==
= Strong extensions =
Commas: 196/195, 352/351, 364/363, 625/624
{| class="wikitable center-all"
|+ style="font-size: 105%;" | Map to strong extensions
|-
! rowspan="2" | Extension !! colspan="2" | 5-limit re-restriction !! rowspan="2" | Mapping of 3 !! rowspan="2" | Tuning range*
|-
! Temperament !! 5-limit generator location
|-
| [[#Hemiwürschmidt|Hemiwürschmidt]] || [[Würschmidt family#Würschmidt|Würschmidt]] || +2 || +16 || ↓ [[31edo|31]]
|-
| [[#Hemithirds|Hemithirds]] || [[Luna family#Luna|Luna]] || +1 || -15 || ↑ 31 <br /> ↓ [[25edo|25]]
|-
| [[#Spell|Spell]] || [[Magic family#Magic|Magic]] || +2 || +10 || ↑ 25
|}
<nowiki />* Defined by intersection with other documented extensions


[[POTE tuning|POTE generator]]: 703.233
== Hemiwürschmidt ==
''[[#Strong extensions|Return to the map]]''


Map: [&lt;3 0 26 56 77 92 -2|, &lt;0 1 -4 -10 -14 -17 3|]
{{See also| Würschmidt family }}
EDOs: 87, 186ef, 273ef


==19-limit==
'''Hemiwürschmidt''' (sometimes spelled '''hemiwuerschmidt''') is not only one of the more accurate extensions of didacus, but also the most important extension of 5-limit [[würschmidt]], even with the rather large complexity for the fifth. It tempers out [[2401/2400]], [[3136/3125]], and [[6144/6125]]. [[68edo]], [[99edo]] and [[130edo]] can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwürschmidt extends to a higher limit temperament, mapping 11 to 40 generators and 13 to -39.
Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324


[[POTE tuning|POTE generator]]: 703.253
[[Subgroup]]: 2.3.5.7


Map: [&lt;3 0 26 56 77 92 -2 8|, &lt;0 1 -4 -10 -14 -17 3 1|]
[[Comma list]]: 2401/2400, 3136/3125
EDOs: 46, 87, 133, 326de, 413degh


=Semisept=
{{Mapping|legend=1| 1 15 4 7 | 0 -16 -2 -5 }}
Commas: 3136/3126, 1728/1715


[[POTE tuning|POTE generator]]: (~75/49) 735.155
Mapping generators: ~2, ~25/14


Map: [&lt;1 12 6 12|, &lt;0 -17 -6 -15|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/25 = 193.898
Wedgie: &lt;&lt;17 6 15 -30 -24 18||
EDOs: [[18edo|18]], 31, [[80edo|80]], 111


11-limit
{{Optimal ET sequence|legend=1| 31, 68, 99, 229, 328, 557c, 885cc }}
Commas: 176/175, 540/539, 1331/1323


[[POTE tuning|POTE generator]]: (~55/36) 735.125
[[Badness]]: 0.020307


Map: [&lt;1 12 6 12 20|, &lt;0 -17 -6 -15 -27|]
=== 2.3.5.7.23 subgroup ===
EDOs: 18, 31, 80, 111, 364cd,  
As described at the page for [[würschmidt]], there is an extension to prime 23 with essentially no damage, which maps the prime to 28 generators (or 14 generators of würschmidt).


13-limit
Subgroup: 2.3.5.7.23
Commas: 176/175, 351/350, 540/539, 1375/1372


[[POTE tuning|POTE generator]]: 735.126
[[Comma list]]: 576/575, 736/735, 1127/1125


Map: [&lt;1 12 6 12 20 -11|, &lt;0 -17 -6 -15 -27 24|]
{{Mapping|legend=1| 1 15 4 7 28 | 0 -16 -2 -5 -28 }}
EDOs: 31, 80, 111


17-limit
Mapping generators: ~2, ~25/14
Commas: 176/175, 256/255, 351/350, 640/637, 715/714


[[POTE tuning|POTE generator]]: (~26/17) 735.125
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/25 = 193.901


Map: [&lt;1 12 6 12 20 -11 -10|, &lt;0 -17 -6 -15 -27 24 23|]
{{Optimal ET sequence|legend=1| 31, 68, 99, 229, 328 }}
EDOs: 31, 80, 111


19-limit
Badness (Sintel): 0.304
Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323


[[POTE tuning|POTE generator]]: 735.116
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 12 6 12 20 -11 -10 -8|, &lt;0 -17 -6 -15 -27 24 23 20|]
Comma list: 243/242, 441/440, 3136/3125
EDOs: 31, 80, 111


23-limit
Mapping: {{mapping| 1 15 4 7 37 | 0 -16 -2 -5 -40 }}
Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459


[[POTE tuning|POTE generator]]: 435.106
Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.840


Map: [&lt;1 12 6 12 20 -11 -10 -8 18|,
{{Optimal ET sequence|legend=1| 31, 99e, 130, 811ce }}
&lt;0 -17 -6 -15 -27 24 23 20 -22|]
EDOs: 31, 80, 111, 191cdh, 302cdgh


=Sengagen=
Badness: 0.021069
Commas: 3136/3125, 420175/419904


POTE generator: ~686/675 = 24.217
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 1 2 2|, &lt;0 29 16 40|]
Comma list: 243/242, 351/350, 441/440, 3584/3575
Wedgie: &lt;&lt;29 16 40 -42 -18 48||
EDOs: 49, 50, 99, 248, 347, 446
Badness: 0.0580


=Subpental=
Mapping: {{mapping| 1 15 4 7 37 -29 | 0 -16 -2 -5 -40 39 }}
Commas: 3136/3125, 19683/19600


POTE generator: ~56/45 = 378.467
Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.829


Map: [&lt;1 6 8 17|, &lt;0 -14 -18 -45|]
{{Optimal ET sequence|legend=1| 31, 99e, 130, 291, 421e, 551ce }}
Wedgie: &lt;&lt;14 18 45 -4 32 54||
EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc
Badness: 0.0543


==11-limit==
Badness: 0.023074
Commas: 540/539, 3136/3125, 8019/8000


POTE generator: ~56/45 = 378.440
==== Hemithir ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 6 8 17 -6|, &lt;0 -14 -18 -45 30|]
Comma list: 121/120, 176/175, 196/195, 275/273
EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde
Badness: 0.0453


==13-limit==
Mapping: {{mapping| 1 15 4 7 37 -3 | 0 -16 -2 -5 -40 8 }}
Commas: 351/350, 540/539, 676/675, 3136/3125


POTE generator: ~56/45 = 378.437
Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.918


Map: [&lt;1 6 8 17 -6 16|, &lt;0 -14 -18 -45 30 -39|]
{{Optimal ET sequence|legend=1| 31, 68e, 99ef }}
EDOs: 19, 111, 130, 241, 371ce
Badness: 0.0239


Badness: 0.031199


</pre></div>
=== Hemiwur ===
<h4>Original HTML content:</h4>
Subgroup: 2.3.5.7.11
<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;Hemimean clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:22:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;a href="#Misty"&gt;Misty&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Mystic"&gt;Mystic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Semisept"&gt;Semisept&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Sengagen"&gt;Sengagen&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Subpental"&gt;Subpental&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;
 
&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;br /&gt;
Comma list: 121/120, 176/175, 1375/1372
The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwuerschmidt, parakleismic, hemithirds, clyde, hemischismic, passion, hexe and sycamore considered elsewhere.&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 15 4 7 11 | 0 -16 -2 -5 -9 }}
Comma: 3136/3125&lt;br /&gt;
 
&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.884
No-threes &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt; (~28/25): 193.772&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 31, 68, 99, 130e, 229e }}
Map: [&amp;lt;1 0 0 -3|, &amp;lt;0 0 2 5|]&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/6edo"&gt;6&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/80edo"&gt;80&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130&lt;/a&gt;, &lt;a class="wiki_link" href="/217edo"&gt;217&lt;/a&gt;, &lt;a class="wiki_link" href="/229edo"&gt;229&lt;/a&gt;, &lt;a class="wiki_link" href="/328edo"&gt;328&lt;/a&gt;, &lt;a class="wiki_link" href="/347edo"&gt;347&lt;/a&gt;, &lt;a class="wiki_link" href="/446edo"&gt;446&lt;/a&gt;, &lt;a class="wiki_link" href="/545edo"&gt;545c&lt;/a&gt;, &lt;a class="wiki_link" href="/675edo"&gt;675&lt;/a&gt;&lt;br /&gt;
Badness: 0.029270
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Misty"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Misty&lt;/h1&gt;
==== 13-limit ====
Commas: 3136/3125, 5120/5103&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.021&lt;br /&gt;
Comma list: 121/120, 176/175, 196/195, 275/273
&lt;br /&gt;
 
Map: [&amp;lt;3 0 26 56|, &amp;lt;0 1 -4 -10|]&lt;br /&gt;
Mapping: {{mapping| 1 15 4 7 11 -3 | 0 -16 -2 -5 -9 8 }}
Wedgie: &amp;lt;&amp;lt;3 -12 -30 -26 -56 -36||&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt;&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 194.004
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Misty-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=1| 31, 68, 99f, 167ef }}
Commas: 441/440, 3136/3125, 4375/4356&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.028432
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.210&lt;br /&gt;
 
&lt;br /&gt;
==== Hemiwar ====
Map: [&amp;lt;3 0 26 56 77|, &amp;lt;0 1 -4 -10 -14|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: 12, 87, 99e, 186e&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 66/65, 105/104, 121/120, 1375/1372
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Misty-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
 
Commas: 196/195, 352/351, 364/363, 625/624&lt;br /&gt;
Mapping: {{mapping| 1 15 4 7 11 23 | 0 -16 -2 -5 -9 -23 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.303&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.698
&lt;br /&gt;
 
Map: [&amp;lt;3 0 26 56 77 92|, &amp;lt;0 1 -4 -10 -14 -17|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 6f, 31 }}
EDOs: 12, 87, 186ef, 273ef&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.044886
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Mystic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Mystic&lt;/h1&gt;
 
Commas: 325/324, 441/440, 896/891, 1001/1000&lt;br /&gt;
=== Quadrawürschmidt ===
&lt;br /&gt;
This has been documented in Graham Breed's temperament finder as ''semihemiwürschmidt'', but ''quadrawürschmidt'' arguably makes more sense.
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.311&lt;br /&gt;
 
&lt;br /&gt;
The generator of quadrawürschmidt is essentially a [[septimal meantone]] fifth. However, it is not used to represent [[3/2]], as 3/2 is found at the hemiwürschmidt position, 16 wholetones up. The small comma between the generator and 3/2 is taken to represent [[441/440]].
Map: [&amp;lt;3 0 26 56 77 -46|, &amp;lt;0 1 -4 -10 -14 12|]&lt;br /&gt;
 
EDOs: 12, 87, 186e, 273e, 633bde&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Mystic-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;17-limit&lt;/h2&gt;
Comma list: 2401/2400, 3025/3024, 3136/3125
Commas: 196/195, 352/351, 364/363, 625/624&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 15 4 7 24 | 0 -32 -4 -10 -49 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.233&lt;br /&gt;
 
&lt;br /&gt;
: mapping generators: ~2, ~147/110
Map: [&amp;lt;3 0 26 56 77 92 -2|, &amp;lt;0 1 -4 -10 -14 -17 3|]&lt;br /&gt;
 
EDOs: 87, 186ef, 273ef&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~147/110 = 503.0404
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Mystic-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;19-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=1| 31, 105be, 136e, 167, 198, 427c }}
Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.034814
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.253&lt;br /&gt;
 
&lt;br /&gt;
=== Semihemiwür ===
Map: [&amp;lt;3 0 26 56 77 92 -2 8|, &amp;lt;0 1 -4 -10 -14 -17 3 1|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: 46, 87, 133, 326de, 413degh&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 2401/2400, 3136/3125, 9801/9800
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Semisept"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Semisept&lt;/h1&gt;
 
Commas: 3136/3126, 1728/1715&lt;br /&gt;
Mapping: {{mapping| 2 14 6 9 -10 | 0 -16 -2 -5 25 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: (~75/49) 735.155&lt;br /&gt;
: mapping generators: ~99/70, ~495/392
&lt;br /&gt;
 
Map: [&amp;lt;1 12 6 12|, &amp;lt;0 -17 -6 -15|]&lt;br /&gt;
Optimal tuning (POTE): ~99/70 = 1\2, ~28/25 = 193.9021
Wedgie: &amp;lt;&amp;lt;17 6 15 -30 -24 18||&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, 31, &lt;a class="wiki_link" href="/80edo"&gt;80&lt;/a&gt;, 111&lt;br /&gt;
{{Optimal ET sequence|legend=1| 62e, 68, 130, 198, 328 }}
&lt;br /&gt;
 
11-limit&lt;br /&gt;
Badness: 0.044848
Commas: 176/175, 540/539, 1331/1323&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: (~55/36) 735.125&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
Map: [&amp;lt;1 12 6 12 20|, &amp;lt;0 -17 -6 -15 -27|]&lt;br /&gt;
Comma list: 676/675, 1001/1000, 1716/1715, 3136/3125
EDOs: 18, 31, 80, 111, 364cd, &lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 14 6 9 -10 25 | 0 -16 -2 -5 25 -26 }}
13-limit&lt;br /&gt;
 
Commas: 176/175, 351/350, 540/539, 1375/1372&lt;br /&gt;
Optimal tuning (POTE): ~99/70 = 1\2, ~28/25 = 193.9035
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 735.126&lt;br /&gt;
{{Optimal ET sequence|legend=1| 62e, 68, 130, 198, 328 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 12 6 12 20 -11|, &amp;lt;0 -17 -6 -15 -27 24|]&lt;br /&gt;
Badness: 0.023388
EDOs: 31, 80, 111&lt;br /&gt;
 
&lt;br /&gt;
===== Semihemiwürat =====
17-limit&lt;br /&gt;
Subgroup: 2.3.5.7.11.13.17
Commas: 176/175, 256/255, 351/350, 640/637, 715/714&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 289/288, 442/441, 561/560, 676/675, 1632/1625
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: (~26/17) 735.125&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 14 6 9 -10 25 19 | 0 -16 -2 -5 25 -26 -16 }}
Map: [&amp;lt;1 12 6 12 20 -11 -10|, &amp;lt;0 -17 -6 -15 -27 24 23|]&lt;br /&gt;
 
EDOs: 31, 80, 111&lt;br /&gt;
Optimal tuning (POTE): ~17/12 = 1\2, ~28/25 = 193.9112
&lt;br /&gt;
 
19-limit&lt;br /&gt;
{{Optimal ET sequence|legend=1| 62e, 68, 130, 198, 328g, 526cfgg }}
Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.028987
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 735.116&lt;br /&gt;
 
&lt;br /&gt;
====== 19-limit ======
Map: [&amp;lt;1 12 6 12 20 -11 -10 -8|, &amp;lt;0 -17 -6 -15 -27 24 23 20|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13.17.19
EDOs: 31, 80, 111&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 289/288, 442/441, 456/455, 476/475, 561/560, 627/625
23-limit&lt;br /&gt;
 
Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459&lt;br /&gt;
Mapping: {{mapping| 2 14 6 9 -10 25 19 20 | 0 -16 -2 -5 25 -26 -16 -17 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 435.106&lt;br /&gt;
Optimal tuning (POTE): ~17/12 = 1\2, ~19/17 = 193.9145
&lt;br /&gt;
 
Map: [&amp;lt;1 12 6 12 20 -11 -10 -8 18|, &lt;br /&gt;
{{Optimal ET sequence|legend=1| 62e, 68, 130, 198, 328g, 526cfgg }}
&amp;lt;0 -17 -6 -15 -27 24 23 20 -22|]&lt;br /&gt;
 
EDOs: 31, 80, 111, 191cdh, 302cdgh&lt;br /&gt;
Badness: 0.021707
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Sengagen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Sengagen&lt;/h1&gt;
===== Semihemiwüram =====
Commas: 3136/3125, 420175/419904&lt;br /&gt;
Subgroup: 2.3.5.7.11.13.17
&lt;br /&gt;
 
POTE generator: ~686/675 = 24.217&lt;br /&gt;
Comma list: 256/255, 676/675, 715/714, 1001/1000, 1225/1224
&lt;br /&gt;
 
Map: [&amp;lt;1 1 2 2|, &amp;lt;0 29 16 40|]&lt;br /&gt;
Mapping: {{mapping| 2 14 6 9 -10 25 -4 | 0 -16 -2 -5 25 -26 18 }}
Wedgie: &amp;lt;&amp;lt;29 16 40 -42 -18 48||&lt;br /&gt;
 
EDOs: 49, 50, 99, 248, 347, 446&lt;br /&gt;
Optimal tuning (POTE): ~99/70 = 1\2, ~28/25 = 193.9112
Badness: 0.0580&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 62eg, 68, 130g, 198g }}
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Subpental"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Subpental&lt;/h1&gt;
 
Commas: 3136/3125, 19683/19600&lt;br /&gt;
Badness: 0.029718
&lt;br /&gt;
 
POTE generator: ~56/45 = 378.467&lt;br /&gt;
====== 19-limit ======
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13.17.19
Map: [&amp;lt;1 6 8 17|, &amp;lt;0 -14 -18 -45|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;14 18 45 -4 32 54||&lt;br /&gt;
Comma list: 256/255, 286/285, 400/399, 476/475, 495/494, 1225/1224
EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc&lt;br /&gt;
 
Badness: 0.0543&lt;br /&gt;
Mapping: {{mapping| 2 14 6 9 -10 25 -4 -3 | 0 -16 -2 -5 25 -26 18 17 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Subpental-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
Optimal tuning (POTE): ~99/70 = 1\2, ~19/17 = 193.9428
Commas: 540/539, 3136/3125, 8019/8000&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 62egh, 68, 130gh, 198gh }}
POTE generator: ~56/45 = 378.440&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.029545
Map: [&amp;lt;1 6 8 17 -6|, &amp;lt;0 -14 -18 -45 30|]&lt;br /&gt;
 
EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde&lt;br /&gt;
== Hemithirds ==
Badness: 0.0453&lt;br /&gt;
''[[#Strong extensions|Return to the map]]''
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Subpental-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h2&gt;
{{Main| Hemithirds }}
Commas: 351/350, 540/539, 676/675, 3136/3125&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
POTE generator: ~56/45 = 378.437&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 1029/1024, 3136/3125
Map: [&amp;lt;1 6 8 17 -6 16|, &amp;lt;0 -14 -18 -45 30 -39|]&lt;br /&gt;
 
EDOs: 19, 111, 130, 241, 371ce&lt;br /&gt;
{{Mapping|legend=1| 1 4 2 2 | 0 -15 2 5 }}
Badness: 0.0239&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/25 = 193.244
 
[[Minimax tuning]]:
* [[7-odd-limit]]: ~28/25 = {{monzo| 1/10 -1/20 0 1/20 }}
: {{monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 11/5 -1/10 0 1/10 | 5/2 -1/4 0 1/4 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3
* [[9-odd-limit]]: ~28/25 = {{monzo| 6/35 -2/35 0 1/35 }}
: {{monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 82/35 -4/35 0 2/35 | 20/7 -2/7 0 1/7 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
 
{{Optimal ET sequence|legend=1| 25, 31, 87, 118 }}
 
[[Badness]]: 0.044284
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 3136/3125
 
Mapping: {{mapping| 1 4 2 2 7 | 0 -15 2 5 -22 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.227
 
Minimax tuning:
* 11-odd-limit: ~28/25 = {{monzo| 5/27 0 0 1/27 -1/27 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}]
: Eigenmonzos (unchanged-intervals): 2, 11/7
 
{{Optimal ET sequence|legend=1| 25e, 31, 87, 118 }}
 
Badness: 0.019003
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 385/384, 625/624
 
Mapping: {{mapping| 1 4 2 2 7 0 | 0 -15 2 5 -22 23 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.166
 
{{Optimal ET sequence|legend=1| 31, 56, 87, 118, 205d }}
 
Badness: 0.021738
 
== Spell ==
''[[#Strong extensions|Return to the map]]''
 
{{See also| Magic family }}
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 49/48, 3125/3072
 
{{Mapping|legend=1| 1 0 2 2 | 0 10 2 5 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/25 = 189.927
 
{{Optimal ET sequence|legend=1| 6, 19, 82dd }}
 
[[Badness]]: 0.080958
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 49/48, 56/55, 125/121
 
Mapping: {{mapping| 1 0 2 2 3 | 0 10 2 5 3 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 190.285
 
{{Optimal ET sequence|legend=1| 6, 19, 44de, 63dee, 82ddee }}
 
Badness: 0.059791
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 56/55, 78/77, 125/121
 
Mapping: {{mapping| 1 0 2 2 3 4 | 0 10 2 5 3 -2 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 189.928
 
{{Optimal ET sequence|legend=1| 6, 19, 82ddeeff }}
 
Badness: 0.045591
 
==== Cantrip ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 56/55, 91/90, 125/121
 
Mapping: {{mapping| 1 0 2 2 3 1 | 0 10 2 5 3 17 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 190.360
 
{{Optimal ET sequence|legend=1| 19, 44de, 63dee, 82ddee }}
 
Badness: 0.041603
 
= Weak extensions =
 
== Semisept ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semisept]].''
 
The minimal generator of semisept is half a tempered septimal major sixth (12/7), hence the name. Three such generator steps minus an octave give the hemithird, and six give the classical major third. It can be described as the 31 & 80 temperament, and as one may expect, [[111edo]] makes for a great tuning.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1728/1715, 3136/3125
 
{{Mapping|legend=1| 1 12 6 12 | 0 -17 -6 -15 }}
 
: mapping generators: ~2, ~75/49
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/49 = 735.155
 
{{Optimal ET sequence|legend=1| 18, 31, 80, 111 }}
 
[[Badness]]: 0.050472
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 540/539, 1331/1323
 
Mapping: {{mapping| 1 12 6 12 20 | 0 -17 -6 -15 -27 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~55/36 = 735.125
 
{{Optimal ET sequence|legend=1| 18e, 31, 80, 111, 364cd }}
 
Badness: 0.022476
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 176/175, 351/350, 540/539, 1375/1372
 
Mapping: {{mapping| 1 12 6 12 20 -11 | 0 -17 -6 -15 -27 24 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~55/36 = 735.126
 
{{Optimal ET sequence|legend=1| 31, 80, 111 }}
 
Badness: 0.025204
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 176/175, 256/255, 351/350, 640/637, 715/714
 
Mapping: {{mapping| 1 12 6 12 20 -11 -10 | 0 -17 -6 -15 -27 24 23 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~26/17 = 735.125
 
{{Optimal ET sequence|legend=1| 31, 80, 111 }}
 
Badness: 0.019919
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323
 
Mapping: {{mapping| 1 12 6 12 20 -11 -10 -8 | 0 -17 -6 -15 -27 24 23 20 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~26/17 = 735.116
 
{{Optimal ET sequence|legend=1| 31, 80, 111 }}
 
Badness: 0.016301
 
===== 23-limit =====
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459
 
Mapping: {{mapping| 1 12 6 12 20 -11 -10 -8 18 | 0 -17 -6 -15 -27 24 23 20 -22 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~26/17 = 735.106
 
{{Optimal ET sequence|legend=1| 31, 80, 111, 191cdh, 302cdgh }}
 
Badness: 0.014957
 
==== Semishly ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 144/143, 176/175, 196/195, 275/273
 
Mapping: {{mapping| 1 12 6 12 20 8 | 0 -17 -6 -15 -27 -7 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 464.980
 
{{Optimal ET sequence|legend=1| 31, 49f, 80f }}
 
Badness: 0.028408
 
== Emka ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Emka]].''
 
Emka tempers out {{monzo| -50 -8 27 }} in the 5-limit. This temperament can be described as 37 &amp; 50 temperament, which tempers out the hemimean and 84035/82944 (quinzo-ayo). Alternative extension [[Horwell temperaments #Emkay|emkay]] (87 &amp; 224) tempers out the same 5-limit comma as the emka, but with the horwell (65625/65536) rather than the hemimean tempered out.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 3136/3125, 84035/82944
 
{{Mapping|legend=1| 1 14 6 12 | 0 -27 -8 -20 }}
 
: mapping generators: ~2, ~48/35
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 551.782
 
{{Optimal ET sequence|legend=1| 37, 50, 87, 137d, 224d }}
 
[[Badness]]: 0.144338
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 2401/2376, 3136/3125
 
Mapping: {{mapping| 1 14 6 12 3 | 0 -27 -8 -20 1 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 551.765
 
{{Optimal ET sequence|legend=1| 37, 50, 87, 224d, 311d }}
 
Badness: 0.054744
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 364/363, 385/384, 625/624
 
Mapping: {{mapping| 1 14 6 12 3 6 | 0 -27 -8 -20 1 -5 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 551.758
 
{{Optimal ET sequence|legend=1| 37, 50, 87, 224d, 311d, 398d }}
 
Badness: 0.029741
 
== Decipentic ==
The generator for the decipentic temperament (43 &amp; 56) is the tenth root of the [[5/1|5th harmonic (5/1)]], 5<sup>1/10</sup>, tuned between [[75/64]] and [[20/17]] (close to [[27/23]]). Aside from the hemimean comma, this temperament tempers out the [[bronzisma]], 2097152/2083725. [[99edo]] is a good tuning for decipentic, with generator 23\99, and [[mos scale]]s of 9, 13, 17, 30, 43 or 56 notes are available.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 3136/3125, 2097152/2083725
 
{{Mapping|legend=1| 1 6 0 -3 | 0 -19 10 25 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/64 = 278.800
 
{{Optimal ET sequence|legend=1| 13, 43, 56, 99 }}
 
[[Badness]]: 0.087325
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 1344/1331, 3136/3125
 
Mapping: {{mapping| 1 6 0 -3 3 | 0 -19 10 25 2 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~75/64 = 278.799
 
{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
 
Badness: 0.061413
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 441/440, 832/825, 975/968
 
Mapping: {{mapping| 1 6 0 -3 3 3 | 0 -19 10 25 2 3 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 278.802
 
{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
 
Badness: 0.047611
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 221/220, 256/255, 273/272, 375/374
 
Mapping: {{mapping| 1 6 0 -3 3 3 2 | 0 -19 10 25 2 3 9 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 278.798
 
{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
 
Badness: 0.031191
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 169/168, 210/209, 221/220, 256/255, 273/272, 286/285
 
Mapping: {{mapping| 1 6 0 -3 3 3 2 1 | 0 -19 10 25 2 3 9 14 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 278.790
 
{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
 
Badness: 0.023899
 
=== Quasijerome ===
Subgroup: 2.3.5.7.11
 
Comma list: 3136/3125, 15488/15435, 16384/16335
 
Mapping: {{mapping| 1 6 0 -3 3 | 0 -38 20 50 47 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~896/825 = 139.403
 
{{Optimal ET sequence|legend=1| 43, 112, 155, 198, 439cd, 637cd }}
 
Badness: 0.092996
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1001/1000, 3136/3125, 15488/15435
 
Mapping: {{mapping| 1 6 0 -3 3 8 | 0 -38 20 50 47 -37 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 139.403
 
{{Optimal ET sequence|legend=1| 43, 155, 198, 439cdf, 637cdf }}
 
Badness: 0.044328
 
== Sengagen ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 3136/3125, 420175/419904
 
{{Mapping|legend=1| 1 1 2 2 | 0 29 16 40 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~686/675 = 24.217
 
{{Optimal ET sequence|legend=1| 49, 50, 99, 248, 347, 446 }}
 
[[Badness]]: 0.057978
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 1344/1331, 3136/3125
 
Mapping: {{mapping| 1 1 2 2 3 | 0 29 16 40 23 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.235
 
{{Optimal ET sequence|legend=1| 49, 50, 99e }}
 
Badness: 0.053828
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 975/968, 1344/1331
 
Mapping: {{mapping| 1 1 2 2 3 4 | 0 29 16 40 23 -15 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.181
 
{{Optimal ET sequence|legend=1| 49, 50, 99e, 149e }}
 
Badness: 0.053531
 
==== Sengage ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 144/143, 196/195, 364/363, 625/624
 
Mapping: {{mapping| 1 1 2 2 3 3 | 0 29 16 40 23 35 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.234
 
{{Optimal ET sequence|legend=1| 49f, 50, 99ef }}
 
Badness: 0.037416
 
== Mowglic ==
The mowglic temperament (19 &amp; 161) is an extension of the [[Syntonic–kleismic equivalence continuum #Mowgli|mowgli temperament]] which tempers out the hemimean comma and the secanticornisma (177147/175000, laruquingu) in the 7-limit.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 3136/3125, 177147/175000
 
{{Mapping|legend=1| 1 0 0 -3 | 0 15 22 55 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/25 = 126.706
 
{{Optimal ET sequence|legend=1| 19, 123d, 142, 161 }}
 
[[Badness]]: 0.129915
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 3136/3125, 72171/71680
 
Mapping: {{mapping| 1 0 0 -3 8 | 0 15 22 55 -43 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~27/25 = 126.711
 
{{Optimal ET sequence|legend=1| 19, 123de, 142, 161 }}
 
Badness: 0.094032
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 1701/1690, 3136/3125
 
Mapping: {{mapping| 1 0 0 -3 8 -2 | 0 15 22 55 -43 54 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.705
 
{{Optimal ET sequence|legend=1| 19, 123def, 142f, 161 }}
 
Badness: 0.051571
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 351/350, 540/539, 833/832, 1701/1690, 3136/3125
 
Mapping: {{mapping| 1 0 0 -3 8 -2 10 | 0 15 22 55 -43 54 -56 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703
 
{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
 
Badness: 0.041918
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 351/350, 476/475, 495/494, 513/512, 540/539, 1701/1690
 
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 | 0 15 22 55 -43 54 -56 -45 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.705
 
{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
 
Badness: 0.032168
 
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539
 
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 | 0 15 22 55 -43 54 -56 -45 -14 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703
 
{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
 
Badness: 0.026117
 
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
 
Comma list: 261/260, 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539
 
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 0 | 0 15 22 55 -43 54 -56 -45 -14 46 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.704
 
{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
 
Badness: 0.021398
 
=== 31-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
 
Comma list: 261/260, 276/275, 351/350, 435/434, 476/475, 495/494, 513/512, 529/528, 540/539
 
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 0 2 | 0 15 22 55 -43 54 -56 -45 -14 46 28 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703
 
{{Optimal ET sequence|legend=1| 19, 123defgk, 142fk, 161 }}
 
Badness: 0.019331
 
== Tremka ==
The name ''tremka'' was initially used for the [[No-sevens subgroup temperaments|no-sevens version]] of 50 &amp; 111 (especially in the 2.3.5.11.13 subgroup), but extending to full 13-limit or higher prime limit does no significant tuning damage, so for that we keep the 2.3.5.11.13 label tremka.
 
=== 7-limit ===
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 3136/3125, 2125764/2100875
 
{{Mapping|legend=1| 1 -4 -2 -8 | 0 31 24 60 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~4375/3888 = 216.173
 
{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
 
[[Badness]]: 0.179925
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 3136/3125, 35937/35840
 
Mapping: {{mapping| 1 -4 -2 -8 4 | 0 31 24 60 -3 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~112/99 = 216.168
 
{{Optimal ET sequence|legend=1| 50, 111, 161, 272, 433c }}
 
Badness: 0.068825
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 847/845, 3136/3125
 
Mapping: {{mapping| 1 -4 -2 -8 4 1 | 0 31 24 60 -3 15 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~112/99 = 216.172
 
{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
 
Badness: 0.036070
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 351/350, 540/539, 561/560, 847/845, 1089/1088
 
Mapping: {{mapping| 1 -4 -2 -8 4 1 -6 | 0 31 24 60 -3 15 56 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~17/15 = 216.172
 
{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
 
Badness: 0.022528
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 324/323, 351/350, 456/455, 476/455, 495/494, 540/539
 
Mapping: {{mapping| 1 -4 -2 -8 4 1 -6 -8 | 0 31 24 60 -3 15 56 68 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~17/15 = 216.170
 
{{Optimal ET sequence|legend=1| 50, 111, 161, 272h, 433cfh, 705ccdffhh }}
 
Badness: 0.016900
 
== Undetrita ==
: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Undetrita (5-limit)]].''
 
The undetrita temperament (111 &amp; 118) tempers out the hemimean comma (3136/3125) and [[scheme comma]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It is also related to the [[Subgroup temperaments #No-sevens subgroup|twentcufo temperament]], which is no-sevens version of 111 &amp; 118.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 3136/3125, 14348907/14336000
 
{{Mapping|legend=1| 1 0 -2 -8 | 0 11 30 75 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~448/405 = 172.917
 
{{Optimal ET sequence|legend=1| 111, 118, 229, 347, 576c }}
 
[[Badness]]: 0.114188
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 3136/3125, 8019/8000
 
Mapping: {{mapping| 1 0 -2 -8 0 | 0 11 30 75 24 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~400/363 = 172.912
 
{{Optimal ET sequence|legend=1| 111, 118, 229, 347 }}
 
Badness: 0.043883
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 729/728, 1001/1000, 3025/3024
 
Mapping: {{mapping| 1 0 -2 -8 0 5 | 0 11 30 75 24 -9 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 172.930
 
{{Optimal ET sequence|legend=1| 111, 229f }}
 
Badness: 0.038771
 
==== Undetritoid ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 1573/1568, 2080/2079, 3136/3125
 
Mapping: {{mapping| 1 0 -2 -8 0 -11 | 0 11 30 75 24 102 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~400/363 = 172.933
 
{{Optimal ET sequence|legend=1| 111, 229 }}
 
Badness: 0.042744
 
= Subgroup extensions =
 
== Undecimal didacus ==
In the no-3's [[11-limit]], there is a natural extension with prime 11 by equating [[25/16]] (which is already tuned sharp anyways) with [[11/7]] by tempering out [[176/175]], which is the same route that [[undecimal meantone]] uses, as this is essentially a no-3's restriction of undecimal meantone in the 11-limit, except that undecimal meantone finds ~[[28/25]] at 2 generators (as a flat ~[[9/8]]) while here it is the generator. This is equivalent to finding [[11/4]] as ([[7/5]])<sup>3</sup>. In the no-3's 19-limit extension "mediantone", this whole tone generator serves as the two simplest [[mediant]]s of [[9/8]] and [[10/9]], namely [[19/17]] and [[28/25]], while in undecimal didacus and its extension to the no-3's 13-limit only the latter interpretation is relevant.
 
Subgroup: 2.5.7.11
 
Comma list: [[176/175]], [[1375/1372]]
 
Sval mapping: {{mapping| 1 0 -3 -7 | 0 2 5 9 }}
 
: sval mapping generators: ~2, ~56/25
 
Optimal tuning (CWE): 2 = 1\1, ~28/25 = 194.428
 
Optimal ET sequence: {{Optimal ET sequence| 6, 19e, 25, 31, 37 }}
 
RMS error: 0.5567 cents
 
Badness (Sintel): 0.195
 
=== Tridecimal didacus ===
Tridecimal didacus (formerly ''roulette''; that name has now been reassigned to the no-threes 19-limit extension 37 & 68) is equivalent to [[hemiwur]] or [[grosstone]] with no mapping for prime 3. The mapping of prime 13 is somewhat strange, because it is the only mapping that requires a negative amount of generators (and a large amount of them), but it can be rationalized in a variety of ways, such as that because [[~]][[8/7]] is already tuned almost 3{{cent}} flat, it makes sense to equate two of it with [[~]][[13/10]] (tempering out the 8{{cent}} [[huntma]]). This mapping of 13 increases the [[badness]] of the temperament, but as it does not noticeably affect the optimal generators, it is usually a safe extension to didacus if prime 3 is not included.
 
Subgroup: 2.5.7.11.13
 
Comma list: 176/175, 640/637, 1375/1372
 
Sval mapping: {{mapping| 1 0 -3 -7 13 | 0 2 5 9 -8 }}
 
: sval mapping generators: ~2, ~56/25
 
Gencom mapping: {{mapping| 1 0 2 2 2 5 | 0 0 2 5 9 -8 }}
 
: gencom: [2 28/25; 176/175 1375/1372 640/637]
 
Optimal tuning (POTE): 2 = 1\1, ~28/25 = 194.594
 
Optimal ET sequence: {{Optimal ET sequence| 6, 25, 31, 37 }}
 
Badness (Sintel): 0.324
 
==== Mediantone ====
Mediantone is named after its whole tone generator serving as the [[mediant]] of [[9/8]] and [[10/9]], namely [[19/17]], in addition to [[28/25]], as well as by the observation that this temperament seems to have been repeatedly rediscovered in parts in a variety of contexts, so that it seems to exist as a "median" of all of these temperaments' logics. It is also an intentional play on "[[meantone]]", as the context one is most likely to first discover this logic is when the tone also represents [[~]][[10/9]][[~]][[9/8]].
 
In the full no-3's [[19-limit]], this temperament is a structure common to quite a few temperaments. It is a rank-2 version of [[orion]] with a mapping for primes 11 and 13. It is a no-3's version of 19-limit [[grosstone]] which can be seen as an extension of [[undecimal meantone]] according to the "mediant-tone" logic of this temperament, and which as aforementioned effectively doubles the complexity of the temperament as a result of finding the generator of [[~]][[19/17]][[~]][[28/25]] as ([[~]][[3/2]])<sup>2</sup>/[[2/1|2]]. It does not work so well as an extension for [[hemiwur]] to the full 19-limit, but if you want to try anyway (at the cost of primes 17 and 19), a notable patent-val tuning is [[37edo]], which finds prime 3 through the [[würschmidt]] mapping so that [[6/1]] is found at 16 generators.
 
Subgroup: 2.5.7.11.13.17.19
 
Comma list: [[176/175]], [[640/637]], [[221/220]], [[476/475]], [[1375/1372]]
 
Sval mapping: {{mapping| 1 0 -3 -7 13 -18 -19 | 0 2 5 9 -8 19 20 }}
 
: sval mapping generators: ~2, ~56/25
 
Optimal tuning (CWE): ~2 = 1\1, ~19/17 = 194.927
 
Optimal ET sequence: {{Optimal ET sequence| 6h, 31gh, 37, 80, 117d* }}
 
<nowiki />* 117d only appears without prime 19
 
Badness (Sintel): 0.618
 
==== Roulette ====
{{See also | Chromatic pairs #Roulette }}
 
Roulette is an alternative no-threes 19-limit extension of tridecimal didacus to mediantone (the two mappings converging at [[37edo]]), equating (8/7)<sup>2</sup> to [[17/13]] in addition to 13/10, tempering out [[170/169]] and [[833/832]]; in doing so, it also tempers out the micro-comma [[2000033/2000000]] so that ([[50/49]])<sup>3</sup> is equated to [[17/16]]. The generator is then equated to 19/17 in the same way as in mediantone.
 
Subgroup: 2.5.7.11.13.17.19
 
Comma list: [[170/169]], [[176/175]], [[476/475]], [[640/637]], [[1375/1372]]
 
Sval mapping: {{mapping| 1 2 2 2 5 7 7 | 0 2 5 9 -8 -18 -17 }}
 
: sval mapping generators: ~2, ~28/25
 
Optimal tuning (CWE): ~2 = 1\1, ~19/17 = 194.259
 
Optimal ET sequence: {{Optimal ET sequence| 6g, ... 31, 37, 68, 105 }}
 
Badness (Sintel): 0.676
 
== Rectified hebrew ==
{{Main| Rectified hebrew }}
 
Rectified hebrew (37 &amp; 56) is derived from the [https://individual.utoronto.ca/kalendis/hebrew/rect.htm#353 calendar by the same name]. It is leap year pattern takes a stack of 18 Metonic cycle diatonic major scales and truncates the 19th one down to its generator, 11. It adds harmonic 13 through tempering out [[4394/4375]] and spliting the generator of didacus in three. Notably, it is the no-threes restriction of [[Sycamore family#Septimal sycamore|sycamore]].
 
Subgroup: 2.5.7.13
 
Comma list: 3136/3125, 4394/4375
 
Sval mapping: {{mapping| 1 2 2 3 | 0 6 15 13 }}
 
: sval mapping generators: ~2, ~26/25
 
Optimal tuning (POTE): ~2 = 1\1, ~26/25 = 64.6086
 
{{Optimal ET sequence|legend=1| 18, 19, 37, 93, 130 }}
 
== Isra ==
Isra (''iss-RAH'') results from taking every other generator of [[septimal meantone]], or from [[didacus]] if the generator is interpreted as 9/8. It is named after the Isrāʾ night journey in the Qur'an, because it is similar to [[luna]] (septimal [[hemithirds]], a didacus extension).
 
[[Subgroup]]: 2.9.5.7
 
[[Comma list]]: 81/80, 126/125
 
{{Mapping|legend=2| 1 0 -4 -13 | 0 1 2 5 }}
 
: sval mapping generators: ~2, ~9
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.9898
 
{{Optimal ET sequence|legend=1| 6, 19, 25, 31, 56b, 87b }}
 
=== Tutone ===
Tutone is every other step of [[Meantone vs meanpop|undecimal meantone]], or undecimal [[didacus]] with the generator interpreted as 9/8.
 
[[Subgroup]]: 2.9.5.7.11
 
[[Comma list]]: 81/80, 99/98, 126/125
 
{{Mapping|legend=2| 1 0 -4 -13 -25 | 0 1 2 5 9 }}
 
{{Mapping|legend=3| 1 3/2 2 2 2 | 0 1/2 2 5 9 }}
 
: [[gencom]]: [2 9/8; 81/80 99/98 126/125]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 193.937
 
{{Optimal ET sequence|legend=1| 6, 19e, 25, 31, 68b, 99b }}
 
[[Badness]]: 0.00536
 
=== Leantone ===
{{See also| Chromatic pairs #Leantone }}
 
Leantone is every other step of [[vincenzo]].
 
[[Subgroup]]: 2.9.5.7.11
 
[[Comma list]]: 45/44, 56/55, 81/80
 
{{Mapping|legend=2| 1 0 -4 -13 -6 | 0 1 2 5 3 }}
 
{{Mapping|legend=3| 1 3/2 2 2 3 | 0 1/2 2 5 3 }}
 
: [[gencom]]: [2 9/8; 45/44 56/55 81/80]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.500
 
{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25e, 31e, 56bee, 81beee }}
 
[[Tp tuning #T2 tuning|RMS error]]: 3.882 cents
 
=== Deutone ===
{{See also| Chromatic pairs #Deutone }}
 
Deutone is (also) every other step of [[vincenzo]].
 
[[Subgroup]]: 2.9.5.7.13
 
[[Comma list]]: 65/64, 81/80, 91/90
 
{{Mapping|legend=2| 1 0 -4 -13 10 | 0 1 2 5 -2 }}
 
{{Mapping|legend=3| 1 3/2 2 2 0 4 | 0 1/2 2 5 0 -2 }}
 
: [[gencom]]: [2 9/8; 65/64 81/80 91/90]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 191.059
 
{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25f, 44df }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.003 cents
 
[[Category:Temperament clans]]
[[Category:Hemimean clan| ]] <!-- main article -->
[[Category:Hemimean| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Hemimean_clan"