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Gamelismic clan: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The [[2.3.7 subgroup|2.3.7-subgroup]] [[comma]] for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with [[monzo]] {{monzo| -10 1 0 3 }}. For any member of the clan, for the rank-3 [[gamelismic family #Gamelismic|gamelismic temperament]] itself, and for the rank-2 2.3.7 temperament [[slendric]] (a.k.a. gamelic), this means three [[~]][[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that {{nowrap| 3/2 {{=}} (8/7)<sup>3</sup>⋅(1029/1024) }}. From this it follows that gamelismic temperaments tend to flatten both the fifth and the harmonic seventh, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for slendric, though if the full 7-limit is desired, [[72edo]], [[77edo]], or [[118edo]] might be preferred.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-12-21 12:33:16 UTC</tt>.<br>
: The original revision id was <tt>570593495</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]]
The 2.3.7-[[Just intonation subgroups|subgroup]] comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3&gt;. For any member of the clan, for the rank three [[Gamelismic family#Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[slendric]], this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.


7-limit minimax
== Slendric ==
[|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,
{{Main| Slendric }}
|5/2 -1/4 1 -3/4&gt;, |5/2 -1/4 0 1/4&gt;]
Eigenmonzos: 2, 7/6, 6/5


9-limit minimax
[[Subgroup]]: 2.3.7
[|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
|10/7 -1/7 1 -3/7&gt;, |20/7 -2/7 0 1/7&gt;]
Eigenmonzos: 2, 6/5, 9/7


Lattice basis: 8/7 0.5192 5/4 2.3219
[[Comma list]]: 1029/1024
Angle(8/7, 5/4) = 90 degrees
Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]


Map: [&lt;1 1 0 3|, &lt;0 3 0 -1|, &lt; 0 0 1 0|]
{{Mapping|legend=2| 1 1 3 | 0 3 -1 }}
Generators: 2, 5, 7


No-fives [[POTE tuning|POTE generator]]: 233.688
{{Mapping|legend=3| 1 1 0 3 | 0 3 0 -1 }}
EDOs: 5, 36, 77, 190
: mapping generators: ~2, ~8/7


==Full seven limit children==
[[Optimal tuning]]s:
To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.
* [[WE]]: ~2 = 1200.4859{{c}}, ~8/7 = 233.7822{{c}}
: [[error map]]: {{val| +0.486 -0.123 -1.151 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~8/7 = 233.7474{{c}}
: error map: {{val| 0.000 -0.713 -2.573 }}


=Miracle=  
{{Optimal ET sequence|legend=1| 5, 21, 26, 31, 36, 77, 113, 190 }}
[[Comma|Commas]]: 1029/1024, 225/224
 
[[Badness]] (Sintel): 0.158
 
=== Overview to extensions ===
==== Full 7-limit extensions ====
To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]] for the full 7-limit. The second comma on the list for mothra is [[81/80]], for rodan [[245/243]], for guiron [[32805/32768]], for gorgo [[36/35]], and for gidorah [[256/245]]. These all use ~8/7 as a generator, though in the case of gidorah that is the same as ~[[6/5]].
 
Miracle adds [[33075/32768]] and uses the [[secor]], half an ~8/7, as generator. Lemba adds [[525/512]] to the list, and has a half-octave [[period]]. Valentine adds [[6144/6125]] with a generator of ~[[21/20]] and superkleismic adds [[875/864]] with a generator of ~6/5. Unidec adds [[4375/4374]], and has a generator of ~[[10/9]] with a half-octave period. Hemithirds adds [[65625/65536]] with a generator half of a classical major third. Finally, tritikleismic adds [[15625/15552]] and has a generator of 6/5 with a 1/3-octave period.
 
Full 7-limit temperaments discussed elsewhere are:
* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]
* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
* [[Trisected]] (+128/125) → [[Augmented family #Trisected|Augmented family]]
* ''[[Echidnic]]'' (+686/675) → [[Diaschismic family #Echidnic|Diaschismic family]]
* [[Trismegistus]] (+3125/3072) → [[Magic family #Trismegistus|Magic family]]
* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]
* ''[[Gamity]]'' (+1071875/1062882) → [[Amity family #Gamity|Amity family]]
* ''[[Tritikleismic]]'' (+15625/15552) → [[Kleismic family #Tritikleismic|Kleismic family]]
* ''[[Heinz]]'' (+78732/78125) → [[Sensipent family #Heinz|Sensipent family]]
* ''[[Triwell]]'' (+235298/234375) → [[Semicomma family #Triwell|Semicomma family]]
* ''[[Gamelstearn]]'' (+118098/117649) → [[Compton family #Gamelstearn|Compton family]]
 
The rest are considered below.
 
==== Subgroup extensions ====
No-five subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-five rodan, considered below, euslendric, a 2.3.7.13-subgroup extension, baladic, a weak 2.3.7.13.17-subgroup extension, and gigapyth, a 2.3.7.85-subgroup extension, considered in [[#Other subgroup extensions]]. Dicussed elsewhere is [[Subgroup temperaments #Trisect|trisect]] in the 2.3.7.11/5 subgroup.
 
=== Radon ===
{{See also|Chromatic pairs #Radon}}
 
Radon is the no-fives version of [[rodan]], equating the diatonic major third to [[14/11]].
 
Subgroup: 2.3.7.11
 
Comma list: 896/891, 1029/1024
 
Subgroup-val mapping: {{mapping| 1 1 3 6 | 0 3 -1 -13 }}
 
Gencom mapping: {{mapping| 1 1 0 3 6 | 0 3 0 -1 -13 }}
 
Optimal tunings:
* WE: ~2 = 1199.9708{{c}}, ~8/7 = 234.3748{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.3813{{c}}
 
{{Optimal ET sequence|legend=0| 5, …, 36, 41, 87, 128 }}
 
Badness (Sintel): 0.619
 
== Mothra ==
{{Main| Mothra }}
 
Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. It can be described as the {{nowrap| 26 & 31 }}. Using [[31edo]] with a generator of 6\31 is an excellent tuning choice. However, a pure mos mothra scale is often described as directionless and has limited chord-building potential<ref>[https://www.youtube.com/watch?v=uH3ahBzDSrs 31-EDO Music Theory: Supermajor Hexatonic Scale] by [[Zhea Erose]]</ref>, so something other than a mos may be used as a scale to get the most out of mothra. There are examples of non-mos mothra scales in 31edo [[Strictly proper 7-tone 31edo scales|in the article on strictly proper 7-tone 31edo scales]].
 
Note that mothra is also called '''cynder''' in the 7-limit, which can be a little confusing sometimes.
 
Its [[S-expression]]-based comma list is {[[1728/1715|S6/S7]], [[1029/1024|S7/S8]], ([[81/80|S6/S8 = S9]])}, taking advantage of the fact that [[81/80]] is a [[semiparticular]].
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 81/80, 1029/1024
 
{{Mapping|legend=1| 1 1 0 3 | 0 3 12 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.9303{{c}}, ~8/7 = 232.3733{{c}}
: [[error map]]: {{val| +0.930 -3.905 +2.165 +1.592 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 232.2514{{c}}
: error map: {{val| 0.000 -5.520 +0.703 -1.077 }}
 
[[Algebraic generator]]: Rabrindanath, largest real root of ''x''<sup>8</sup> - 3''x''<sup>2</sup> + 1, or 232.0774 cents.
 
[[Minimax tuning]]:
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 0 0 1/12 }}
: {{monzo list| 1 0 0 0 | 1 0 1/4 0 | 0 0 1 0 | 3 0 -1/12 0 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
 
{{Optimal ET sequence|legend=1| 5, 21c, 26, 31 }}
 
[[Badness]] (Sintel): 0.940
 
=== Undecimal mothra ===
Undecimal mothra is the extension of 7-limit cynder which tempers out 385/384 as is natural in slendric temperaments. It is the simplest extension, supported within a reasonable tuning range (between [[26edo]] and 31edo), and is supported by the patent val of [[5edo]], which implies that it is better behaved as a cluster temperament. It is also notable for being supported by the just tuning of 8/7, and has a restriction to the 2.7.11 subgroup, namely [[amaranthine]], that is a microtemperament.
 
Subgroup: 2.3.5.7.11
 
Comma list: 81/80, 99/98, 385/384
 
Mapping: {{mapping| 1 1 0 3 5 | 0 3 12 -1 -8 }}
 
Optimal tunings:
* WE: ~2 = 1201.3979{{c}}, ~8/7 = 232.3010{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 232.0621{{c}}
 
{{Optimal ET sequence|legend=0| 5, 26, 31, 88, 119be, 150be }}
 
Badness (Sintel): 0.848
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 81/80, 99/98, 105/104, 144/143
 
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 }}
 
Optimal tunings:
* WE: ~2 = 1201.0985{{c}}, ~8/7 = 232.0231{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 231.8425{{c}}
 
{{Optimal ET sequence|legend=0| 5, 26, 31, 57, 88 }}
 
Badness (Sintel): 0.990
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 81/80, 99/98, 105/104, 120/119, 144/143
 
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 16 }}
 
Optimal tunings:
* WE: ~2 = 1200.9734{{c}}, ~8/7 = 231.8960{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 231.7392{{c}}
 
{{Optimal ET sequence|legend=0| 5g, 26, 31, 57, 88 }}
 
Badness (Sintel): 1.00
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 81/80, 99/98, 105/104, 120/119, 144/143, 153/152
 
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 16 22 }}
 
Optimal tunings:
* WE: ~2 = 1200.9663{{c}}, ~8/7 = 231.8393{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 231.6842{{c}}
 
{{Optimal ET sequence|legend=0| 26, 31, 57 }}
 
Badness (Sintel): 1.05
 
=== Mosura ===
The [[S-expression]]-based comma list of mosura suggests it might be the most natural extension of 7-limit cynder to the 11-limit: {[[1728/1715|S6/S7]], [[1029/1024|S7/S8]], ([[81/80|S6/S8 = S9]]), [[176/175|S8/S10]]}.
 
Subgroup: 2.3.5.7.11
 
Comma list: 81/80, 176/175, 540/539
 
Mapping: {{mapping| 1 1 0 3 -1 | 0 3 12 -1 23 }}
 
Optimal tunings:
* WE: ~2 = 1200.7675{{c}}, ~8/7 = 232.5673{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 232.4567{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 26e, 31, 129 }}
 
Badness (Sintel): 1.04
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 81/80, 144/143, 176/175, 196/195
 
Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 }}
 
Optimal tunings:
* WE: ~2 = 1199.9347{{c}}, ~8/7 = 232.6275{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 232.6392{{c}}
 
{{Optimal ET sequence|legend=0| 31, 67, 98 }}
 
Badness (Sintel): 1.52
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 81/80, 144/143, 176/175, 189/187, 196/195
 
Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 -15 }}
 
Optimal tunings:
* WE: ~2 = 1199.7124{{c}}, ~8/7 = 232.6376{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 232.6917{{c}}
 
{{Optimal ET sequence|legend=0| 31, 67, 98 }}
 
Badness (Sintel): 1.53
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 81/80, 96/95, 144/143, 153/152, 176/175, 196/195
 
Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 -15 -9 }}
 
Optimal tunings:
* WE: ~2 = 1199.4885{{c}}, ~8/7 = 232.6310{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 232.7287{{c}}
 
{{Optimal ET sequence|legend=0| 31, 67, 98h }}
 
Badness (Sintel): 1.50
 
=== Cyndra ===
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 81/80, 1029/1024
 
Mapping: {{mapping| 1 1 0 3 0 | 0 3 12 -1 18 }}
 
Optimal tunings:
* WE: ~2 = 1201.1585{{c}}, ~8/7 = 231.5404{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 231.3850{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 21ce, 26 }}
 
Badness (Sintel): 1.84
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 45/44, 78/77, 81/80, 640/637
 
Mapping: {{mapping| 1 1 0 3 0 1 | 0 3 12 -1 18 14 }}
 
Optimal tunings:
* WE: ~2 = 1201.1152{{c}}, ~8/7 = 231.5079{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 231.3612{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 21cef, 26 }}
 
Badness (Sintel): 1.41
 
== Rodan ==
{{Main| Rodan }}
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Rodan (5-limit)]].''
 
Rodan tempers out 245/243 and can be described as the {{nowrap| 41 & 46 }} temperament. This temperament is more accurate than mothra and extends neatly to the 13-limit, though the perfect fifth is sharper than ideal for slendric. [[87edo]] is excellent for this, with the 17\87 generator missing the 13-limit CWE tuning by less than a millicent.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 245/243, 1029/1024
 
{{Mapping|legend=1| 1 1 -1 3 | 0 3 17 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.2146{{c}}, ~8/7 = 234.4587{{c}}
: [[error map]]: {{val| +0.215 +1.636 -0.731 -2.641 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 234.4259{{c}}
: error map: {{val| 0.000 +1.323 -1.073 -3.252 }}
 
[[Minimax tuning]]:
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 2/9 0 1/18 -1/18 }}
: {{monzo list| 1 0 0 0 | 5/3 0 1/6 -1/6 | 25/9 0 17/18 -17/18 | 25/9 0 -1/18 1/18 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
 
[[Algebraic generator]]: larger root of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10.
 
{{Optimal ET sequence|legend=1| 41, 87, 128, 215d }}
 
[[Badness]] (Sintel): 0.939
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 245/243, 385/384, 441/440
 
Mapping: {{mapping| 1 1 -1 3 6 | 0 3 17 -1 -13 }}
 
Optimal tunings:
* WE: ~2 = 1200.0553{{c}}, ~8/7 = 234.4695{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.4594{{c}}
 
Minimax tuning:
* 11-odd-limit: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
: unchanged-interval (eigenmonzo) basis: 2.11/9
 
Algebraic generator: positive root of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.
 
{{Optimal ET sequence|legend=0| 41, 87 }}
 
Badness (Sintel): 0.763
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 245/243, 352/351, 364/363
 
Mapping: {{mapping| 1 1 -1 3 6 8 | 0 3 17 -1 -13 -22 }}
 
Optimal tunings:
* WE: ~2 = 1199.9868{{c}}, ~8/7 = 234.4796{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.4822{{c}}
 
Minimax tuning:
* 13- and 15-odd-limit: ~8/7 = {{monzo| 3/14 1/14 0 0 0 -1/28 }}
: unchanged-interval (eigenmonzo) basis: 2.13/9
 
Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly.
 
{{Optimal ET sequence|legend=0| 41, 46, 87 }}
 
Badness (Sintel): 0.762
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 154/153, 196/195, 245/243, 256/255, 273/272
 
Mapping: {{mapping| 1 1 -1 3 6 8 8 | 0 3 17 -1 -13 -22 -20 }}
 
Optimal tunings:
* WE: ~2 = 1199.8331{{c}}, ~8/7 = 234.4919{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.5254{{c}}
 
Minimax tuning:
* 17-odd-limit: ~8/7 = {{monzo| 3/13 1/13 0 0 0 0 -1/26 }}
: unchanged-interval (eigenmonzo) basis: 2.17/9
 
{{Optimal ET sequence|legend=0| 41, 46, 87 }}
 
Badness (Sintel): 0.853
 
==== Aerodactyl ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 91/90, 245/243, 385/384, 441/440
 
Mapping: {{mapping| 1 1 -1 3 6 -1 | 0 3 17 -1 -13 24 }}
 
Optimal tunings:
* WE: ~2 = 1200.2997{{c}}, ~8/7 = 234.6972{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.6439{{c}}
 
{{Optimal ET sequence|legend=0| 5, 41f, 46 }}
 
Badness (Sintel): 1.40
 
=== Aerodino ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 245/243, 1029/1024
 
Mapping: {{mapping| 1 1 -1 3 -3 | 0 3 17 -1 33 }}
 
Optimal tunings:
* WE: ~2 = 1199.9179{{c}}, ~8/7 = 234.7123{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.7256{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 41e, 46 }}
 
Badness (Sintel): 1.79
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 91/90, 176/175, 245/243, 847/845
 
Mapping: {{mapping| 1 1 -1 3 -3 -1 | 0 3 17 -1 33 24 }}
 
Optimal tunings:
* WE: ~2 = 1200.0242{{c}}, ~8/7 = 234.7863{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.7824{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 41ef, 46 }}
 
Badness (Sintel): 1.48
 
=== Varan ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 245/243, 1029/1024
 
Mapping: {{mapping| 1 1 -1 3 -2 | 0 3 17 -1 28 }}
 
Optimal tunings:
* WE: ~2 = 1200.3738{{c}}, ~8/7 = 234.2174{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.1586{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 36ce, 41 }}
 
Badness (Sintel): 1.49
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 105/104, 245/243, 352/351
 
Mapping: {{mapping| 1 1 -1 3 -2 0 | 0 3 17 -1 28 19 }}
 
Optimal tunings:
* WE: ~2 = 1200.1389{{c}}, ~8/7 = 234.1162{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.0946{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 36ce, 41 }}
 
Badness (Sintel): 1.33
 
== Guiron ==
Guiron tempers out the [[schisma]], and finds the prime 5 at the diminished fourth as does any temperament in the [[schismatic family]]. It can be described as the {{nowrap| 36 & 41 }} temperament. It is more complex than rodan, but the optimal tuning is closer to optimal slendric.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 10976/10935
 
{{Mapping|legend=1| 1 1 7 3 | 0 3 -24 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3395{{c}}, ~8/7 = 233.9963{{c}}
: [[error map]]: {{val| +0.340 +0.374 +0.151 -1.804 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.9239{{c}}
: error map: {{val| 0.000 -0.183 -0.487 -2.750 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
7-limit: [|1 0 0 0&gt;, |25/13 6/13 -6/13 0&gt;,
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }}
|25/13 -7/13 7/13 0&gt;, |35/13 -2/13 2/13 0&gt;]
: {{monzo list| 1 0 0 0 | 15/8 0 -1/8 0 | 0 0 1 0 | 65/24 0 1/24 0 }}
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
 
{{Optimal ET sequence|legend=1| 36, 41, 77, 118, 277d }}
 
[[Badness]] (Sintel): 1.20
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 10976/10935
 
Mapping: {{mapping| 1 1 7 3 -2 | 0 3 -24 -1 28 }}
 
Optimal tunings:
* WE: ~2 = 1200.3453{{c}}, ~8/7 = 233.9988{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.9312{{c}}
 
Minimax tuning:
* 11-odd-limit: ~8/7 = {{monzo| 7/24 0 -1/24 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}]
: unchanged-interval (eigenmonzo) basis: 2.5
 
{{Optimal ET sequence|legend=0| 36e, 41, 77, 118, 159, 277d }}
 
Badness (Sintel): 0.881
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 385/384, 729/728
 
Mapping: {{mapping| 1 1 7 3 -2 0 | 0 3 -24 -1 28 19 }}
 
Optimal tunings:
* WE: ~2 = 1200.1222{{c}}, ~8/7 = 233.9228{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.8994{{c}}
 
{{Optimal ET sequence|legend=0| 36e, 41, 77, 118 }}
 
Badness (Sintel): 1.18
 
== Gorgo ==
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Laconic]].''
{{See also| Llywelynsmic clan }}
 
Gorgo tempers the generator of ~8/7 together with ~10/9. It can be described as the {{nowrap| 16 & 21 }} temperament.
 
If we discard the inaccurate mapping of prime 3, we get [[shoe]], so that the large commas of gorgo are explained practically entirely by the inaccurate 3.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 36/35, 1029/1024
 
{{Mapping|legend=1| 1 1 1 3 | 0 3 7 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.9847{{c}}, ~8/7 = 228.5210{{c}}
: [[error map]]: {{val| +0.985 -15.407 +14.318 +5.607 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 228.4371{{c}}
: error map: {{val| 0.000 -16.644 +12.746 +2.737 }}
 
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21 }}
 
[[Badness]] (Sintel): 1.54
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 36/35, 45/44, 1029/1024
 
Mapping: {{mapping| 1 1 1 3 1 | 0 3 7 -1 13 }}
 
Optimal tunings:
* WE: ~2 = 1201.3609{{c}}, ~8/7 = 227.6312{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.4955{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 16, 21, 37b }}
 
Badness (Sintel): 1.64
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 36/35, 45/44, 507/500
 
Mapping: {{mapping| 1 1 1 3 1 2 | 0 3 7 -1 13 9 }}
 
Optimal tunings:
* WE: ~2 = 1201.0996{{c}}, ~8/7 = 227.4378{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.3327{{c}}
 
{{Optimal ET sequence|legend=0| 5e, 16, 21, 37b }}
 
Badness (Sintel): 1.35
 
=== Spartan ===
Subgroup: 2.3.5.7.11
 
Comma list: 36/35, 56/55, 1029/1024
 
Mapping: {{mapping| 1 1 1 3 5 | 0 3 7 -1 -8 }}
 
Optimal tunings:
* WE: ~2 = 1198.9344{{c}}, ~8/7 = 229.3316{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 229.5124{{c}}
 
{{Optimal ET sequence|legend=0| 5, 16e, 21 }}
 
Badness (Sintel): 2.07
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 36/35, 56/55, 507/500
 
Mapping: {{mapping| 1 1 1 3 5 2 | 0 3 7 -1 -8 9 }}
 
Optimal tunings:
* WE: ~2 = 1198.3002{{c}}, ~8/7 = 228.7341{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 229.0044{{c}}
 
{{Optimal ET sequence|legend=0| 5, 16e, 21 }}
 
Badness (Sintel): 1.95
 
; Music
* [https://web.archive.org/web/20201127012514/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 ''Gorgo Example''] by [[Herman Miller]]
 
== Gidorah ==
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #University]].''
 
Gidorah is a very low-accuracy temperament where the generator of ~8/7 is lumped together with ~6/5. 16c-, 21cc-, and 26ccc-edo are among the possible tunings.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 21/20, 144/125
 
{{Mapping|legend=1| 1 1 2 3 | 0 3 2 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1192.4932{{c}}, ~8/7 = 229.3187{{c}}
: [[error map]]: {{val| -7.507 -21.506 +57.310 -20.665 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 229.6649{{c}}
: error map: {{val| 0.000 -12.960 +73.016 +1.509 }}
 
{{Optimal ET sequence|legend=1| 1b, 5 }}
 
[[Badness]] (Sintel): 1.58
 
== Oncle ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Oncle]].''
 
Oncle can be described as the {{nowrap| 31 & 36c }} temperament.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 2430/2401
 
{{Mapping|legend=1| 1 1 6 3 | 0 3 -19 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.2246{{c}}, ~8/7 = 232.7354{{c}}
: [[error map]]: {{val| +1.225 -2.524 -0.939 +2.112 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 232.4718{{c}}
: error map: {{val| 0.000 -4.539 -3.279 -1.298 }}
 
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc }}
 
[[Badness]] (Sintel): 2.24
 
== Archaeotherium ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Archaeotherium]].''
 
Archaeotherium can be described as the {{nowrap| 21 & 26 }} temperament.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 405/392, 1029/1024
 
{{Mapping|legend=1| 1 1 5 3 | 0 3 -14 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1202.7179{{c}}, ~8/7 = 230.7800{{c}}
: [[error map]]: {{val| +2.718 -6.897 -3.644 +8.548 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 230.1909{{c}}
: error map: {{val| 0.000 -11.382 -8.986 +0.983 }}
 
{{Optimal ET sequence|legend=1| 21, 26, 47, 73bc }}


9-limit: [|1 0 0 0&gt;, |25/19 12/19 -6/19 0&gt;,
[[Badness]] (Sintel): 3.70
|50/19 -14/19 7/19 0&gt;, |55/19 -4/19 2/19 0&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9


[[POTE tuning|POTE generator]]: 116.675
== Clyndro ==
Algebraic generator: Secor59, [[Algebraic number|positive root]] of 15x^6-8x^4-12
Clyndro tempers out [[135/128]] and finds the interval class of 5 at a stack of -3 fifths as does any temperament in the [[mavila family]]. It can be described as the {{nowrap| 11 & 16 }} temperament.


Map: [&lt;1 1 3 3|, &lt;0 6 -7 -2|]
[[Subgroup]]: 2.3.5.7
Wedgie: &lt;&lt;6 -7 -2 -25 -20 15||
EDOs: 10, 21, 31, 41, 72, [[175edo|175]]
Badness: 0.0167


==11-limit==  
[[Comma list]]: 135/128, 360/343
[[Comma|Commas]]: 1029/1024, 225/224, 243/242
 
{{Mapping|legend=1| 1 1 4 3 | 0 3 -9 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1205.6135{{c}}, ~8/7 = 227.5283{{c}}
: [[error map]]: {{val| +5.613 -13.757 -11.614 +20.486 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.3207{{c}}
: error map: {{val| 0.000 -22.993 -23.200 +4.853 }}
 
{{Optimal ET sequence|legend=1| 5c, 11, 16 }}
 
[[Badness]] (Sintel): 4.03
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 45/44, 352/343
 
Mapping: {{mapping| 1 1 4 3 4 | 0 3 -9 -1 -3 }}
 
Optimal tunings:
* WE: ~2 = 1206.2134{{c}}, ~8/7 = 227.6004{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.2421{{c}}
 
{{Optimal ET sequence|legend=0| 5c, 11, 16 }}
 
Badness (Sintel): 2.30
 
== Miracle ==
{{Main| Miracle }}
: ''For the 5-limit version, see [[Syntonic–31 equivalence continuum #Ampersand]].''
 
Miracle is one of the most important entries of this temperament clan. It tempers out [[225/224]], splitting the ~8/7 generator of slendric into [[15/14]]~[[16/15]], and can be described as the {{nowrap| 31 & 41 }} temperament. Its ploidacot is hexacot. It is then extremely natural to equate the neutral third, three generators up, to [[11/9]] and thereby extend miracle to the full [[11-limit]] with essentially no further damage. [[72edo]] makes for an excellent tuning.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 1029/1024
 
{{Mapping|legend=1| 1 1 3 3 | 0 6 -7 -2 }}
: mapping generator: ~2, ~15/14
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.8209{{c}}, ~15/14 = 116.7550{{c}}
: [[error map]]: {{val| +0.821 -0.604 -1.136 +0.127 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 116.6756{{c}}
: error map: {{val| 0.000 -1.901 -3.043 -2.177 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
[|1 0 0 0 0&gt;, |25/19 12/19 -6/19 0 0&gt;,
* [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }}
|50/19 -14/19 7/19 0 0&gt;, |55/19 -4/19 2/19 0 0&gt;,
: {{monzo list| 1 0 0 0 | 25/13 6/13 -6/13 0 | 25/13 -7/13 7/13 0 | 35/13 -2/13 2/13 0 }}
|53/19 30/19 -15/19 0 0&gt;]
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9
* [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: {{monzo list| 1 0 0 0 | 25/19 12/19 -6/19 0 | 50/19 -14/19 7/19 0 | 55/19 -4/19 2/19 0 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5
 
[[Tuning ranges]]:
* 7-odd-limit [[diamond monotone]]: ~15/14 = [114.286, 120.000] (2\21 to 1\10)
* 9-odd-limit diamond monotone: ~15/14 = [116.129, 120.000] (3\31 to 1\10)
* 7- and 9-odd-limit [[diamond tradeoff]]: ~15/14 = [115.587, 116.993]
 
[[Algebraic generator]]: Secor59, positive root of 15''x''<sup>6</sup> - 8''x''<sup>4</sup> - 12
 
{{Optimal ET sequence|legend=1| 10, 21, 31, 41, 72 }}
 
[[Badness]] (Sintel): 0.424
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 243/242, 385/384
 
Mapping: {{mapping| 1 1 3 3 2 | 0 6 -7 -2 15 }}
 
Optimal tunings:
* WE: ~2 = 1200.7626{{c}}, ~15/14 = 116.7069{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.6469{{c}}
 
Minimax tuning:
* 11-odd-limit: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}]
: unchanged-interval (eigenmonzo) basis: 2.9/5
 
Tuning ranges:
* 11-odd-limit diamond monotone: ~15/14 = [116.129, 117.073] (3\31 to 4\41)
* 11-odd-limit diamond tradeoff: ~15/14 = [115.587, 116.993]


[[POTE tuning|POTE generator]]: 116.633
Algebraic generator: Secor59
Algebraic generator: Secor59


Map: [&lt;1 1 3 3 2|, &lt;0 6 -7 -2 15|]
{{Optimal ET sequence|legend=0| 10, 21e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}
[[edo|EDOs]]: 10, 31, 41, [[72edo|72]], 247c, 319bcde, [[391edo|391bcde]], 463bcde
 
Badness: 0.0107
Badness (Sintel): 0.353
 
==== Miraculous ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 144/143, 196/195, 243/242
 
Mapping: {{mapping| 1 1 3 3 2 4 | 0 6 -7 -2 15 -3 }}
 
Optimal tunings:
* WE: ~2 = 1200.1267{{c}}, ~15/14 = 116.7596{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.7488{{c}}
 
{{Optimal ET sequence|legend=0| 10, 21e, 31, 41, 72f }}
 
Badness (Sintel): 0.771
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 105/104, 120/119, 144/143, 154/153, 170/169
 
Mapping: {{mapping| 1 1 3 3 2 4 4 | 0 6 -7 -2 15 -3 1 }}
 
Optimal tunings:
* WE: ~2 = 1199.6759{{c}}, ~15/14 = 116.7378{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.7657{{c}}


[[Chords of miracle]]
{{Optimal ET sequence|legend=0| 10, 21e, 31, 41, 72fg }}


==Revelation==
Badness (Sintel): 0.870
Commas: 99/98, 176/175, 1029/1024


POTE generator: ~15/14 = 116.277
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


Map: [&lt;1 1 3 3 5|, &lt;0 6 -7 -2 -16|]
Comma list: 105/104, 120/119, 144/143, 154/153, 170/169, 210/209
EDOs: 10, 21, 31
Badness: 0.0329


===13-limit===
{{Todo|complete temperament data|inline=1}}
Commas: 66/65, 99/98, 105/104, 1001/1000


POTE generator: ~15/14 = 116.268
===== 23-limit =====
Subgroup: 2.3.5.7.11.13.17.19.23


Map: [&lt;1 1 3 3 5 4|, &lt;0 6 -7 -2 -16 -3|]
Comma list: 105/104, 120/119, 144/143, 154/153, 161/160, 170/169, 210/209
EDOs: 10, 21, 31
Badness: 0.0295


==Miraculous==
{{Todo|complete temperament data|inline=1}}
Commas: 105/104, 144/143, 196/195, 275/273


POTE generator: ~15/14 = 116.747
==== Benediction ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 1 3 3 2 4|, &lt;0 6 -7 -2 15 -3|]
Comma list: 225/224, 243/242, 351/350, 385/384
EDOs: 10, 31, 41, 72f, 113f, 185cf
Badness: 0.0187


==Benediction==
Mapping: {{mapping| 1 1 3 3 2 7 | 0 6 -7 -2 15 -34 }}
Commas: 225/224, 243/242, 351/350, 441/440


POTE generator: ~15/14 = 116.574
Optimal tunings:  
* WE: ~2 = 1199.8601{{c}}, ~15/14 = 116.6572{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.5688{{c}}


Map: [&lt;1 1 3 3 2 7|, &lt;0 6 -7 -2 15 -34|]
{{Optimal ET sequence|legend=0| 31, 72, 103, 175f }}
EDOs: 31, 72, 103, [[175edo|175f]]
Badness: 0.0157


===17-limit===
Badness (Sintel): 0.649
Commas: 225/224, 243/242, 273/272, 351/350, 385/384


POTE generator: ~15/14 = 116.585
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 1 3 3 2 7 7|, &lt;0 6 -7 -2 15 -34 -30|]
Comma list: 225/224, 243/242, 273/272, 351/350, 375/374
EDOs: 31, 72, 103, [[175edo|175f]]


==Manna==
Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 6 -7 -2 15 -34 -30 }}
Commas: 225/224, 243/242, 325/324, 385/384


POTE generator: ~15/14 = 116.739
Optimal tunings:  
* WE: ~2 = 1200.8328{{c}}, ~15/14 = 116.6661{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.5774{{c}}


Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 38|]
{{Optimal ET sequence|legend=0| 31, 72, 103, 175f, 422bcdefffg }}
EDOs: 10f, 31f, 41, 72, 113, 185cf, 257cf
Badness: 0.0170


==Semimiracle==
Badness (Sintel): 0.639
Commas: 169/168, 225/224, 243/242, 385/384


POTE generator: ~15/14 = 116.624
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


Map: [&lt;2 2 6 6 4 7|, &lt;0 6 -7 -2 15 2|]
Comma list: 210/209, 225/224, 243/242, 273/272, 286/285, 375/374
EDOs: 10, 62, 72
Badness: 0.0246


===17-limit===
{{Todo|complete temperament data|inline=1}}
Commas: 169/168, 221/220, 225/224, 243/242, 385/384


POTE generator: ~15/14 = 116.628
===== 23-limit =====
Subgroup: 2.3.5.7.11.13.17.19.23


Map: [&lt;2 2 6 6 4 7 7|, &lt;0 6 -7 -2 15 2 6|]
Comma list: 162/161, 210/209, 225/224, 231/230, 243/242, 273/272, 286/285
EDOs: 10, 62, 72
Badness: 0.0161


==Hemimiracle==
{{Todo|complete temperament data|inline=1}}
Commas: 225/224, 245/242, 1029/1024


POTE generator: ~33/32 = 58.408
==== Manna ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 1 3 3 4|, &lt;0 12 -14 -4 -11|]
Comma list: 225/224, 243/242, 325/324, 385/384
EDOs: 20, 21, 41, 123c, 144e, 185ce, 226ce
Badness: 0.0592


===13-limit===
Mapping: {{mapping| 1 1 3 3 2 0 | 0 6 -7 -2 15 38 }}
Commas: 105/104, 196/195, 245/242, 512/507


POTE generator: ~33/32 = 58.430
Optimal tunings:  
* WE: ~2 = 1200.7564{{c}}, ~15/14 = 116.8129{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.7528{{c}}


Map: [&lt;1 1 3 3 4 4|, &lt;0 12 -14 -4 -11 -6|]
{{Optimal ET sequence|legend=0| 31f, 41, 72, 185cf, 257cff }}
EDOs: 20, 21, 41, 123cf, 144ef, 185cef
Badness: 0.0432


==Oracle==
Badness (Sintel): 0.703
Commas: 121/120, 225/224, 1029/1024


POTE generator: ~11/8 = 541.668
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 7 -4 1 3|, &lt;0 -12 14 4 1|]
Comma list: 225/224, 243/242, 273/272, 325/324, 385/384
EDOs: 11, 20, 31, 51, 82e, 113e, 144e


==Phicordial==
Mapping: {{mapping| 1 1 3 3 2 0 0 | 0 6 -7 -2 15 38 42 }}
Commas: 225/224, 243/242, 441/440, 2200/2197


POTE generator: ~16/13 = 361.121
Optimal tunings:  
* WE: ~2 = 1200.7570{{c}}, ~15/14 = 116.8011{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.7408{{c}}


Map: [&lt;1 7 -4 1 17 4|, &lt;0 -18 21 6 -45 -1|]
{{Optimal ET sequence|legend=0| 31fg, 41, 72, 185cf, 257cff }}
EDOs: 10, 103, 113, 216c
Badness: 0.0332


===17-limit===
Badness (Sintel): 0.748
Commas: 225/224, 243/242, 273/272, 441/440, 2200/2197


POTE generator: ~16/13 = 361.123
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


Map: [&lt;1 7 -4 1 17 4 8|, &lt;0 -18 21 6 -45 -1 -13|]
Comma list: 210/209, 225/224, 243/242, 273/272, 325/324, 343/342
EDOs: 10, 103, 113, 216c
Badness: 0.0247


==Music==
{{Todo|complete temperament data|inline=1}}
By [[Gene Ward Smith]]
[[http://www.archive.org/details/RachmaninoffPlaysBlackjack|Rachmaninoff Plays Blackjack]] [[http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3|play]]
By [[Joseph Pehrson]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3|Black and Jill]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3|Blacklight]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3|Blackjack]]


=Hemisecordite=  
===== 23-limit =====
Commas: 225/224, 243/242, 441/440, 847/845
Subgroup: 2.3.5.7.11.13.17.19.23


POTE generator: ~27/26 = 58.288
Comma list: 210/209, 225/224, 243/242, 273/272, 300/299, 325/324, 343/342


Map: [&lt;1 1 3 3 2 2|, &lt;0 12 -14 -4 30 35|]
{{Todo|complete temperament data|inline=1}}
EDOs: 41, 62, 103, 247c, 350bcde
Badness: 0.0256


==17-limit==  
==== Semimiracle ====
Commas: 225/224, 243/242, 273/272, 441/440, 847/845
Subgroup: 2.3.5.7.11.13


POTE generator: ~27/26 = 58.261
Comma list: 169/168, 225/224, 243/242, 385/384


Map: [&lt;1 1 3 3 2 2 2|, &lt;0 12 -14 -4 30 35 43|]
Mapping: {{mapping| 2 2 6 6 4 7 | 0 6 -7 -2 15 2 }}
EDOs: 41, 62, 103
: mapping generators: ~55/39, ~15/14
Badness: 0.0225


=Rodan=  
Optimal tunings:
[[Comma|Commas]]: 1029/1024, 245/243
* WE: ~55/39 = 600.4844{{c}}, ~15/14 = 116.7182{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~15/14 = 116.6413{{c}}


7+9 limit minimax tuning: [|1 0 0 0&gt;, |5/3 0 1/6 -1/6&gt;,
{{Optimal ET sequence|legend=0| 10, 62, 72 }}
|25/9 0 17/18 -17/18&gt;, |25/9 0 -1/18 1/18&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5


[[POTE tuning|POTE generator]]: 234.417
Badness (Sintel): 1.02
Algebraic generator: [[Algebraic number|larger root]] of 20x^2-36x+15, or (9+√6)/10.


Map: [&lt;1 1 -1 3|, &lt;0 3 17 -1|]
===== 17-limit =====
EDOs: 41, 87, 128
Subgroup: 2.3.5.7.11.13.17
Badness: 0.0371


==11-limit==
Comma list: 169/168, 221/220, 225/224, 243/242, 273/272
[[Comma|Commas]]: 441/440, 245/243, 385/384


[[Minimax tuning]]: [|1 0 0 0 0&gt;, |31/19 6/19 0 0 -3/19&gt;,
Mapping: {{mapping| 2 2 6 6 4 7 7 | 0 6 -7 -2 15 2 6 }}
|49/19 34/19 0 0 -17/19&gt;, |53/19 -2/19 0 0 1/19&gt;,
|62/19 -26/19 0 0 13/19&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9


[[POTE tuning|POTE generator]]: 234.459
Optimal tunings:  
Algebraic generator: [[Algebraic number|positive root]] of x^2+16x-31, or √95-8.
* WE: ~17/12 = 600.5042{{c}}, ~15/14 = 116.7264{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~15/14 = 116.6485{{c}}


Map: [&lt;1 1 -1 3 6|, &lt;0 3 17 -1 -13|]
{{Optimal ET sequence|legend=0| 10, 62, 72 }}
EDOs: 41, 87, 389d
Badness: 0.0231


[[Chords of rodan]]
Badness (Sintel): 0.822


==13-limit==  
===== 19-limit =====
Commas: 196/195, 245/243, 352/351, 364/363
Subgroup: 2.3.5.7.11.13.17.19


13 and 15 limit minimax
Comma list: 169/168, 210/209, 221/220, 225/224, 243/242, 273/272
[|1 0 0 0 0 0&gt;, |23/14 3/14 0 0 0 -3/28&gt;,
|37/14 17/14 0 0 0 -17/28&gt;, |39/14 -1/14 0 0 0 1/28&gt;,
|45/14 -13/14 0 0 0 13/28&gt;, |23/7 -11/7 0 0 0 11/14&gt;]
Eigenmonzos: 2, 13/9


[[POTE tuning|POTE generator]]: 234.482
{{Todo|complete temperament data|inline=1}}
Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly.


Map: [&lt;1 1 -1 3 6 8|, &lt;0 3 17 -1 -13 -22|]
===== 23-limit =====
Generators: 2, 8/7
Subgroup: 2.3.5.7.11.13.17.19.23
[[edo|Edos]]: 41, 46, [[87edo|87]]
Badness: 0.0184


==17-limit==
Comma list: 169/168, 208/207, 210/209, 221/220, 225/224, 243/242, 273/272
Commas: 154/153, 196/195, 245/243, 273/272, 364/363


Eigenmonzos: 2, 18/17
{{Todo|complete temperament data|inline=1}}
[[POTE tuning|POTE generator]]: ~8/7 = 234.524


Map: [&lt;1 1 -1 3 6 8 8|, &lt;0 3 17 -1 -13 -22 -20|]
==== Hemisecordite ====
Edos: 41, 46, 87, 220dg, 307dg
Subgroup: 2.3.5.7.11.13
Badness: 0.0167


===Music===
Comma list: 225/224, 243/242, 385/384, 847/845
By [[Gene Ward Smith]]
[[http://www.archive.org/details/Pianodactyl|Pianodactyl]] [[http://www.archive.org/download/Pianodactyl/pianodactyl.mp3|play]]


==Aerodactyl==
Mapping: {{mapping| 1 1 3 3 2 2 | 0 12 -14 -4 30 35 }}
Commas: 91/90, 245/243, 385/384, 441/440
: mapping generators: ~2, ~27/26


[[POTE tuning|POTE generator]]: ~8/7 = 234.639
Optimal tunings:  
* WE: ~2 = 1200.6969{{c}}, ~27/26 = 58.3217{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~27/26 = 58.2964{{c}}


Map: [&lt;1 1 -1 3 6 -1|, &lt;0 3 17 -1 -13 24|
{{Optimal ET sequence|legend=0| 41, 62, 103, 247c, 350bcde }}
EDOs: 41f, 46, 51c
Badness: 0.0340


==Aerodino==
Badness (Sintel): 1.06
Commas: 176/175, 245/243, 1029/1024


POTE generator: ~8/7 = 234.728
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 1 -1 3 -3|, &lt;0 3 17 -1 33|
Comma list: 225/224, 243/242, 273/272, 385/384, 847/845
EDOS: 46
Badness: 0.0543


===13-limit===
Mapping: {{mapping| 1 1 3 3 2 2 2 | 0 12 -14 -4 30 35 43 }}
Commas: 91/90, 176/175, 245/243, 847/845


POTE generator: ~8/7 = 234.782
Optimal tunings:  
* WE: ~2 = 1200.6557{{c}}, ~27/26 = 58.2932{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~27/26 = 58.2702{{c}}


Map: [&lt;1 1 -1 3 -3 -1|, &lt;0 3 17 -1 33 24|
{{Optimal ET sequence|legend=0| 41, 62, 103 }}
EDOs: 46
Badness: 0.0358


==Varan==
Badness (Sintel): 1.15
Commas: 100/99, 245/243, 2835/2816


POTE generator: ~8/7 = 234.145
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


Map: [&lt;1 1 -1 3 -2|, &lt;0 3 17 -1 28|
Comma list:  
EDOs: 41, 46e
Badness: 0.0449


===13-limit===
{{Todo|complete temperament data|inline=1}}
Commas: 100/99, 105/104, 245/243, 352/351


POTE generator: ~8/7 = 234.089
===== 23-limit =====
Subgroup: 2.3.5.7.11.13.17.19.23


Map: [&lt;1 1 -1 3 -2 0|, &lt;0 3 17 -1 28 19|
Comma list:  
EDOs: 41
Badness: 0.0323


=Valentine=  
{{Todo|complete temperament data|inline=1}}
==7-limit==  
 
[[Comma|Commas]]: 1029/1024, 126/125
===== Semihemisecordite =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 225/224, 243/242, 289/288, 385/384, 847/845
 
Mapping: {{mapping| 2 2 6 6 4 4 7 | 0 12 -14 -4 30 35 12 }}
: mapping generators: ~17/12, ~27/26
 
Optimal tunings:
* WE: ~17/12 = 600.3951{{c}}, ~27/26 = 58.3260{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~27/26 = 58.2974{{c}}
 
{{Optimal ET sequence|legend=0| 62, 144g, 206begg }}
 
Badness (Sintel): 2.39
 
====== 19-limit ======
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 209/208, 225/224, 243/242, 289/288, 361/360, 385/384
 
Mapping: {{mapping| 2 2 6 6 4 4 7 8 | 0 12 -14 -4 30 35 12 5 }}
 
Optimal tunings:
* WE: ~17/12 = 600.4418{{c}}, ~27/26 = 58.3255{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~27/26 = 58.2928{{c}}
 
{{Optimal ET sequence|legend=0| 62, 144gh, 206begghh }}
 
Badness (Sintel): 2.13
 
====== 23-limit ======
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 209/208, 225/224, 243/242, 289/288, 323/322, 361/360, 385/384
 
Mapping: {{mapping| 2 2 6 6 4 4 7 8 7 | 0 12 -14 -4 30 35 12 5 21 }}
 
Optimal tunings:
* WE: ~17/12 = 600.4451{{c}}, ~27/26 = 58.3264{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~27/26 = 58.2942{{c}}
 
{{Optimal ET sequence|legend=0| 62, 144gh, 206begghhi }}
 
Badness (Sintel): 1.89
 
==== Phicordial ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 243/242, 385/384, 2200/2197
 
Mapping: {{mapping| 1 -11 17 7 -28 3 | 0 18 -21 -6 45 1 }}
: mapping generators: ~2, ~13/8
 
Optimal tunings:
* WE: ~2 = 1200.7056{{c}}, ~13/8 = 839.3726{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 838.8831{{c}}
 
{{Optimal ET sequence|legend=0| 103, 216c, 319bcde, 535bccdef }}
 
Badness (Sintel): 1.37
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 225/224, 243/242, 273/272, 385/384, 2200/2197
 
Mapping: {{mapping| 1 -11 17 7 -28 3 -5 | 0 18 -21 -6 45 1 13 }}
 
Optimal tunings:
* WE: ~2 = 1200.5918{{c}}, ~13/8 = 839.2912{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 838.8809{{c}}
 
{{Optimal ET sequence|legend=0| 103, 216c, 319bcde }}
 
Badness (Sintel): 1.26
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 210/209, 225/224, 243/242, 273/272, 385/384, 2200/2197
 
{{Todo|complete temperament data|inline=1}}
 
===== 23-limit =====
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 210/209, 225/224, 243/242, 273/272, 300/299, 385/384, 1105/1104
 
{{Todo|complete temperament data|inline=1}}
 
=== Revelation ===
Subgroup: 2.3.5.7.11
 
Comma list: 99/98, 176/175, 1029/1024
 
Mapping: {{mapping| 1 1 3 3 5 | 0 6 -7 -2 -16 }}
 
Optimal tunings:
* WE: ~2 = 1201.3320{{c}}, ~15/14 = 116.4057{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.2524{{c}}
 
{{Optimal ET sequence|legend=0| 10e, 21, 31 }}
 
Badness (Sintel): 1.09
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 66/65, 99/98, 105/104, 512/507
 
Mapping: {{mapping| 1 1 3 3 5 4 | 0 6 -7 -2 -16 -3 }}
 
Optimal tunings:
* WE: ~2 = 1200.6059{{c}}, ~15/14 = 116.3263{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 116.2564{{c}}
 
{{Optimal ET sequence|legend=0| 10e, 21, 31 }}
 
Badness (Sintel): 1.22
 
=== Hemimiracle ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 245/242, 1029/1024
 
Mapping: {{mapping| 1 1 3 3 4 | 0 12 -14 -4 -11 }}
: mapping generators: ~2, ~33/32
 
Optimal tunings:
* WE: ~2 = 1200.2902{{c}}, ~33/32 = 58.4217{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 58.4062{{c}}
 
{{Optimal ET sequence|legend=0| 20, 21, 41 }}
 
Badness (Sintel): 1.96
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 196/195, 245/242, 512/507
 
Mapping: {{mapping| 1 1 3 3 4 4 | 0 12 -14 -4 -11 -6 }}
 
Optimal tunings:
* WE: ~2 = 1199.8454{{c}}, ~33/32 = 58.4220{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 58.4305{{c}}
 
{{Optimal ET sequence|legend=0| 20, 21, 41 }}
 
Badness (Sintel): 1.78
 
=== Oracle ===
The name is a portmanteau of [[orwell]] and [[miracle]]: Oracle is a weak extension of 7-limit miracle, splitting its ~[[16/15]] generator and an octave into two ~[[16/11]] generators. Additionally, when [[restriction|restricted]] to the 2.15.7.11 subgroup, oracle's generator corresponds to 2 stacked orwell generators.
 
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 225/224, 1029/1024
 
Mapping: {{mapping| 1 -5 10 5 4 | 0 12 -14 -4 -1 }}
: mapping generators: ~2, ~16/11
 
Optimal tunings:
* WE: ~2 = 1201.2122{{c}}, ~16/11 = 658.9974{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 658.3320{{c}}
 
{{Optimal ET sequence|legend=0| 11, 20, 31, 82e, 113e, 144ee }}
 
Badness (Sintel): 1.41
 
== Hemiseven ==
Unlike miracle which splits 8/7, hemiseven splits ~16/7, an octave above. It can be described as the {{nowrap| 72 & 77 }} temperament; its ploidacot is gamma-hexacot. [[149edo]] is an obvious tuning.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 19683/19600
 
{{Mapping|legend=1| 1 -2 -15 4 | 0 6 29 -2 }}
: mapping generators: ~2, ~243/160
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.5612{{c}}, ~243/160 = 717.0687{{c}}
: [[error map]]: {{val| +0.561 -0.665 +0.260 -0.718 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/160 = 716.7478{{c}}
: error map: {{val| 0.000 -1.468 -0.629 -2.321 }}
 
{{Optimal ET sequence|legend=1| 72, 149, 221, 514bd, 735bcdd }}
 
[[Badness]] (Sintel): 1.43
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 19683/19600
 
Mapping: {{mapping| 1 -2 -15 4 16 | 0 6 29 -2 -21 }}
 
Optimal tunings:
* WE: ~2 = 1200.6243{{c}}, ~243/160 = 717.0969{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~243/160 = 716.7292{{c}}
 
{{Optimal ET sequence|legend=0| 72, 149, 221e, 293de }}
 
Badness (Sintel): 0.941
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 385/384, 441/440, 676/675
 
Mapping: {{mapping| 1 -2 -15 4 16 -19 | 0 6 29 -2 -21 38 }}
 
Optimal tunings:
* WE: ~2 = 1200.6781{{c}}, ~91/60 = 717.1496{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~91/60 = 716.7520{{c}}
 
{{Optimal ET sequence|legend=0| 72, 149, 221ef }}
 
Badness (Sintel): 0.905
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 273/272, 351/350, 385/384, 441/440, 676/675
 
Mapping: {{mapping| 1 -2 -15 4 16 -19 -21 | 0 6 29 -2 -21 38 42 }}
 
Optimal tunings:
* WE: ~2 = 1200.6635{{c}}, ~68/45 = 717.1354{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~68/45 = 716.7472{{c}}
 
{{Optimal ET sequence|legend=0| 72, 149, 221ef }}
 
Badness (Sintel): 0.800
 
== Valentine ==
{{Main| Valentine }}
: ''For the 5-limit version, see [[Syntonic–31 equivalence continuum #Valentine (5-limit)]].''
 
Valentine tempers out [[126/125]] and [[6144/6125]] as well as 1029/1024. It has a generator of [[~]][[21/20]], three of which make the slendric generator ~8/7. 21/20 can be stripped of its 2 and taken as 3 × 7/5. In this respect it resembles miracle, with a generator of 3 × 5/7, and casablanca, with a generator of 5 × 7/3. These three generators are the simplest in terms of the relationship of tetrads in the [[7-limit symmetrical lattices|lattice of 7-limit tetrads]]. Valentine can be described as the {{nowrap| 31 & 46 }} temperament; its ploidacot is enneacot. [[77edo]], [[108edo]], or [[185edo]] make for excellent tunings, which also happen to be excellent tunings for [[starling]], the rank-3 temperament tempering out 126/125. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)<sup>1/9</sup> as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit, tempering out 121/120 and 441/440; 46edo has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, ([[11/7]])<sup>1/10</sup>.
 
Valentine has a very straighforward [[S-expression]]-based comma list in the [[11-limit]] add-23 (i.e. the 2.3.5.7.11.23 subgroup) of {([[176/175|S8/S10 = S22 × S23 × S24]], [[121/120|S11]]), [[441/440|S21]], [[484/483|S22]], [[529/528|S23]], [[576/575|S24]]}, so it is the temperament that equalizes the 20::25 segment of the harmonic series.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 126/125, 1029/1024
 
{{Mapping|legend=1| 1 1 2 3 | 0 9 5 -3 }}
: mapping generators: ~2, ~21/20
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0749{{c}}, ~21/20 = 77.8687{{c}}
: [[error map]]: {{val| +0.075 -1.062 +3.179 -2.207 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 77.8673{{c}}
: error map: {{val| 0.000 -1.149 +3.023 -2.428 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
7-limit: [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,
* [[7-odd-limit]]: ~21/20 = {{monzo| 1/6 1/12 0 -1/12 }}
|17/6 5/12 0 -5/12&gt;, [5/2 -1/4 0 1/4&gt;]
: {{monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 17/6 5/12 0 -5/12 | 5/2 -1/4 0 1/4 }}
Eigenmonzos: 2, 7/6
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3
* [[9-odd-limit]]: ~21/20 = {{monzo| 1/21 2/21 0 -1/21}}
: {{monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 47/21 10/21 0 -5/21 | 20/7 -2/7 0 1/7 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
 
[[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.
 
{{Optimal ET sequence|legend=1| 15, 31, 46, 77, 185 }}
 
[[Badness]] (Sintel): 0.786
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 126/125, 176/175
 
Mapping: {{mapping| 1 1 2 3 3 | 0 9 5 -3 7 }}
 
Optimal tunings:
* WE: ~2 = 1200.3890{{c}}, ~22/21 = 77.9065{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 77.9007{{c}}
 
Minimax tuning:
* 11-odd-limit: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]
: unchanged-interval (eigenmonzo) basis: 2.11/7
 
Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.
 
{{Optimal ET sequence|legend=0| 15, 31, 46, 77 }}
 
Badness (Sintel): 0.552
 
==== Valentino ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 126/125, 176/175, 196/195
 
Mapping: {{mapping| 1 1 2 3 3 5 | 0 9 5 -3 7 -20 }}
 
Optimal tunings:
* WE: ~2 = 1200.1967{{c}}, ~22/21 = 77.9708{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 77.9594{{c}}
 
{{Optimal ET sequence|legend=0| 15f, 31, 46, 77 }}
 
Badness (Sintel): 0.854
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 121/120, 126/125, 154/153, 176/175, 196/195
 
Mapping: {{mapping| 1 1 2 3 3 5 5 | 0 9 5 -3 7 -20 -14 }}
 
Optimal tunings:
* WE: ~2 = 1200.0404{{c}}, ~22/21 = 78.0055{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 78.0029{{c}}
 
{{Optimal ET sequence|legend=0| 15f, 31, 46, 77, 123e }}
 
Badness (Sintel): 0.854
 
==== Lupercalia ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 66/65, 105/104, 121/120, 126/125
 
Mapping: {{mapping| 1 1 2 3 3 3 | 0 9 5 -3 7 11 }}
 
Optimal tunings:
* WE: ~2 = 1199.9143{{c}}, ~22/21 = 77.7039{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 77.7049{{c}}
 
{{Optimal ET sequence|legend=0| 15, 31 }}
 
Badness (Sintel): 0.881
 
==== Dwynwen ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 91/90, 121/120, 126/125, 176/175
 
Mapping: {{mapping| 1 1 2 3 3 2 | 0 9 5 -3 7 26 }}
 
Optimal tunings:
* WE: ~2 = 1200.1306{{c}}, ~22/21 = 78.2273{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 78.2241{{c}}
 
{{Optimal ET sequence|legend=0| 15, 31f, 46 }}
 
Badness (Sintel): 0.969
 
==== Semivalentine ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 126/125, 169/168, 176/175
 
Mapping: {{mapping| 2 2 4 6 6 7 | 0 9 5 -3 7 3 }}
: mapping generators: ~55/39, ~22/21
 
Optimal tunings:
* WE: ~55/39 = 600.3497{{c}}, ~22/21 = 77.8845{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~22/21 = 77.8715{{c}}
 
{{Optimal ET sequence|legend=0| 16, 30, 46, 62, 108ef }}
 
Badness (Sintel): 1.35
 
==== Hemivalentine ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 126/125, 176/175, 343/338
 
Mapping: {{mapping| 1 1 2 3 3 4 | 0 18 10 -6 14 -9 }}
: mapping generators: ~2, ~40/39
 
Optimal tunings:
* WE: ~2 = 1199.6529{{c}}, ~40/39 = 39.0323{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/39 = 39.0383{{c}}
 
{{Optimal ET sequence|legend=0| 30, 31, 61, 92f }}
 
Badness (Sintel): 1.94
 
==== Demivalentine ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 126/125, 176/175, 676/675
 
Mapping: {{mapping| 1 -8 -3 6 -4 -16 | 0 18 10 -6 14 37 }}
: mapping generators: ~2, ~13/9
 
Optimal tunings:
* WE: ~2 = 1200.3929{{c}}, ~13/9 = 639.1320{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/9 = 638.9325{{c}}
 
{{Optimal ET sequence|legend=0| 15, 47ef, 62, 77 }}
 
Badness (Sintel): 1.44
 
=== Hemivalentino ===
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 243/242, 1029/1024
 
Mapping: {{mapping| 1 1 2 3 2 | 0 18 10 -6 45 }}
 
Optimal tunings:
* WE: ~2 = 1200.0816{{c}}, ~45/44 = 38.9236{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~45/44 = 38.9228{{c}}
 
{{Optimal ET sequence|legend=0| 31, 92e, 123, 154, 185 }}
 
Badness (Sintel): 2.03
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 126/125, 196/195, 243/242, 1029/1024
 
Mapping: {{mapping| 1 1 2 3 2 5 | 0 18 10 -6 45 -40 }}
 
Optimal tunings:
* WE: ~2 = 1199.8782{{c}}, ~45/44 = 38.9440{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~45/44 = 38.9472{{c}}
 
{{Optimal ET sequence|legend=0| 31, 123, 154 }}
 
Badness (Sintel): 2.39
 
==== Hemivalentoid ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 126/125, 144/143, 243/242, 343/338
 
Mapping: {{mapping| 1 1 2 3 2 4 | 0 18 10 -6 45 -9 }}
 
Optimal tunings:
* WE: ~2 = 1199.3614{{c}}, ~45/44 = 38.9721{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~45/44 = 38.9839{{c}}
 
{{Optimal ET sequence|legend=0| 31, 92ef }}
 
Badness (Sintel): 2.39
 
== Superkleismic ==
{{Main| Superkleismic }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Shibboleth]].''
 
Superkleismic tempers out the keema, [[875/864]], and can be described as the {{nowrap| 15 & 26 }} temperament. It splits the ~[[7/4]] into three ~6/5 generators of around 322 cents. This is noticeably sharper than the [[kleismic]] generator, hence the name.
 
In the 11-limit, two generator steps can be identified with ~16/11, and in the 13-limit, the same step can be treated as ~13/9. The [[S-expression]]-based comma list of 13-limit superkleismic is {[[875/864|S5/S6]], [[1029/1024|S7/S8]], [[100/99|S10]], [[144/143|S12]], ([[441/440|S21]])}. Through careful observation of the equivalences therein one can derive the mapping of the full 13-limit.
 
Note that the generator is given as 6/5's octave complement, [[5/3]], in the data that follow, since a stack of 9 such generators octave-reduced is the perfect fifth; the [[ploidacot]] of superkleismic is wau-enneacot.
 
Superkleismic also sets two intervals of [[21/20]] equal to [[10/9]]; as {{nowrap| 10/9 {{=}} ([[20/19]])⋅([[19/18]]) }}, we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S|19}}) and [[400/399]] ({{S|20}}). This structure is preserved within the entire superkleismic tuning range between 15edo and 26edo, while extensions for primes 13 and 17 bifurcate and are of higher complexity and lower accuracy.
 
41edo gives an obvious tuning in all the subgroups.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 875/864, 1029/1024
 
{{Mapping|legend=1| 1 -5 -5 5 | 0 9 10 -3 }}
: mapping generators: ~2, ~5/3
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.7640{{c}}, ~5/3 = 878.6289{{c}}
: [[error map]]: {{val| +0.764 +1.885 +3.844 -0.893 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 878.1077{{c}}
: error map: {{val| 0.000 +1.014 -5.237 -3.149 }}
 
{{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}
 
[[Badness]] (Sintel): 1.21
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 245/242, 385/384
 
Mapping: {{mapping| 1 -5 -5 5 2 | 0 9 10 -3 2 }}
 
Optimal tunings:
* WE: ~2 = 1200.1691{{c}}, ~5/3 = 878.2772{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.1606{{c}}
 
{{Optimal ET sequence|legend=0| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
 
Badness (Sintel): 0.848
 
==== 2.3.5.7.11.19 subgroup ====
Subgroup: 2.3.5.7.11.19
 
Comma list: 100/99, 133/132, 190/189, 385/384
 
Mapping: {{mapping| 1 -5 -5 5 2 -6 | 0 9 10 -3 2 14 }}
 
Optimal tunings:
* WE: ~2 = 1200.2289{{c}}, ~5/3 = 878.3409{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.1840{{c}}
 
{{Optimal ET sequence|legend=0| 11c, 15, 26, 41, 138e }}
 
Badness (Sintel): 0.692
 
=== 13-limit ===
Superkleismic in the 13-limit does considerably more damage than in the 11-limit, as indicated by being supported by much fewer [[patent val]]s and having higher Dirichlet badness than its 11-limit counterpart. However, this remains an obvious canonical mapping for prime 13.
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 105/104, 144/143, 245/242
 
Mapping: {{mapping| 1 -5 -5 5 2 -8 | 0 9 10 -3 2 16 }}
 
Optimal tunings:
* WE: ~2 = 1200.0261{{c}}, ~5/3 = 878.0252{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.0073{{c}}
 
{{Optimal ET sequence|legend=0| 11cf, 15, 26, 41 }}
 
Badness (Sintel): 0.887
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 100/99, 105/104, 120/119, 144/143, 245/242
 
Mapping: {{mapping| 1 -5 -5 5 2 -8 -12 | 0 9 10 -3 2 16 22 }}
 
Optimal tunings:
* WE: ~2 = 1200.0488{{c}}, ~5/3 = 877.8872{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 877.8537{{c}}
 
{{Optimal ET sequence|legend=0| 11cfg, 15g, 26, 41 }}
 
Badness (Sintel): 1.01
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 100/99, 105/104, 120/119, 144/143, 133/132, 190/189
 
Mapping: {{mapping| 1 -5 -5 5 2 -8 -12 -6 | 0 9 10 -3 2 16 22 14 }}
 
Optimal tunings:
* WE: ~2 = 1200.2120{{c}}, ~5/3 = 878.0243{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 877.8789{{c}}
 
{{Optimal ET sequence|legend=0| 11cfgh, 15g, 26, 41 }}
 
Badness (Sintel): 0.964
 
=== Superana ===
This extension ({{nowrap| 41 & 56 }}) is the counterpart of canonical superkleismic on the other side of 41edo.
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 196/195, 245/242, 385/384
 
Mapping: {{mapping| 1 -5 -5 5 2 22 | 0 9 10 -3 2 -25 }}
 
Optimal tunings:
* WE: ~2 = 1199.8272{{c}}, ~5/3 = 878.1538{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.2795{{c}}
 
{{Optimal ET sequence|legend=0| 15f, 41, 97, 138e }}
 
Badness (Sintel): 1.40
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 100/99, 154/153, 196/195, 245/242, 256/255


9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
Mapping: {{mapping| 1 -5 -5 5 2 22 18 | 0 9 10 -3 2 -25 -19 }}
|47/21 10/21 0 -5/21&gt;, |20/7 -2/7 0 1/7&gt;]
Eigenmonzos: 2, 9/7


[[POTE tuning|POTE generator]]: 77.864
Optimal tunings:  
Algebraic generator: [[Algebraic number|smaller root]] of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents.
* WE: ~2 = 1199.5964{{c}}, ~5/3 = 878.0482{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.3444{{c}}


Map: [&lt;1 1 2 3|, &lt;0 9 5 -3|]
{{Optimal ET sequence|legend=0| 15f, 41, 56, 97g }}
Wedgie: &lt;&lt;9 5 -3 -13 -30 -21||
EDOs: 15, 31, 46, 77, 185, 262cd
Badness: 0.0311


==11-limit==  
Badness (Sintel): 1.45
[[Comma|Commas]]: 121/120, 126/125, 176/175
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 100/99, 133/132, 154/153, 190/189, 196/195, 256/255
 
Mapping: {{mapping| 1 -5 -5 5 2 22 18 -6 | 0 9 10 -3 2 -25 -19 14 }}
 
Optimal tunings:
* WE: ~2 = 1199.6638{{c}}, ~5/3 = 878.1109{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.3566{{c}}
 
{{Optimal ET sequence|legend=0| 15f, 41, 56, 97g }}
 
Badness (Sintel): 1.36
 
== Dee leap week ==
{{Main| Dee leap week }}
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 2460375/2458624
 
{{Mapping|legend=1| 1 -5 25 5 | 0 9 -31 -3 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4835{{c}}, ~224/135 = 878.2507{{c}}
: [[error map]]: {{val| +0.484 -0.117 +0.004 -1.160 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~224/135 = 877.8926{{c}}
: error map: {{val| 0.000 -0.921 -0.985 -2.504 }}
 
{{Optimal ET sequence|legend=1| 41, 108, 149, 190 }}
 
[[Badness]] (Sintel): 2.12
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 2460375/2458624
 
Mapping: {{mapping| 1 -5 25 5 -28 | 0 9 -31 -3 43 }}
 
Optimal tunings:
* WE: ~2 = 1200.4874{{c}}, ~224/135 = 878.2543{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~224/135 = 877.8987{{c}}
 
{{Optimal ET sequence|legend=0| 41, 108e, 149, 190 }}
 
Badness (Sintel): 1.35
 
== Unidec ==
{{Main| Unidec }}
 
Unidec tempers out the ragisma, [[4375/4374]], and may be described as the {{nowrap| 26 & 46 }} temperament. It has a [[semi-octave]] [[period]] and a generator of ~[[80/63]], two of which minus a period make slendric's generator; its [[ploidacot]] is therefore diploid gamma-hexacot. In the 11-limit, the generator represents [[14/11]]. [[190edo]] makes for an excellent tuning in both the 7-limit and 11-limit.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 4375/4374
 
{{Mapping|legend=1| 2 -1 -3 7 | 0 6 11 -2 }}
 
[[Optimal tuning]]s:  
* [[WE]]: ~1225/864 = 600.2429{{c}}, ~80/63 = 417.0073{{c}}
: [[error map]]: {{val| +0.486 -0.154 +0.038 -1.140 }}
* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~80/63 = 416.8688{{c}}
: error map: {{val| 0.000 -0.924 -1.090 -2.503 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
[|1 0 0 0 0&gt;, |1 0 0 -9/10 9/10&gt;,
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/26 0 -1/13 1/13 }}
|2 0 0 -1/2 1/2&gt;, |3 0 0 3/10 -3/10&gt;, |3 0 0 -7/10 7/10&gt;]
: {{monzo list| 1 0 0 0 | 47/26 0 6/13 -6/13 | 71/26 0 11/13 -11/13 | 71/26 0 -2/13 2/13 }}
Eigenmonzos: 2, 11/7
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
* [[9-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
: {{Monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 57/28 11/7 0 -11/14 | 20/7 -2/7 0 1/7 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
 
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 190 }}
 
[[Badness]] (Sintel): 0.972
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 4375/4374
 
Mapping: {{mapping| 2 -1 -3 7 9 | 0 6 11 -2 -3 }}
 
Optimal tunings:
* WE: ~99/70 = 600.2497{{c}}, ~14/11 = 417.0085{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~14/11 = 416.8543{{c}}
 
Minimax tuning:
* [[11-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 57/28 11/7 0 -11/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 99/28 -3/7 0 3/14 0 }}]
: unchanged-interval (eigenmonzo) basis: 2.9/7
 
{{Optimal ET sequence|legend=0| 26, 46, 72, 118, 190 }}
 
Badness (Sintel): 0.512
 
==== Ekadash ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 385/384, 441/440, 625/624, 729/728
 
Mapping: {{mapping| 2 -1 -3 7 9 -19 | 0 6 11 -2 -3 38 }}
 
Optimal tunings:
* WE: ~99/70 = 600.2497{{c}}, ~14/11 = 417.0085{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~14/11 = 416.8543{{c}}
 
{{Optimal ET sequence|legend=0| 46f, 72, 118, 190, 262df, 452cdef }}
 
Badness (Sintel): 0.842
 
==== Hendec ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 325/324, 364/363, 385/384
 
Mapping: {{mapping| 2 -1 -3 7 9 6 | 0 6 11 -2 -3 2 }}
 
Optimal tunings:
* WE: ~91/64 = 600.3825{{c}}, ~14/11 = 417.0678{{c}}
* CWE: ~91/64 = 600.0000{{c}}, ~14/11 = 416.8290{{c}}
 
{{Optimal ET sequence|legend=0| 26, 46, 72, 190ff }}
 
Badness (Sintel): 0.732
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 221/220, 273/272, 325/324, 364/363
 
Mapping: {{mapping| 2 -1 -3 7 9 6 4 | 0 6 11 -2 -3 2 6 }}
 
Optimal tunings:
* WE: ~17/12 = 600.3991{{c}}, ~14/11 = 417.0809{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~14/11 = 416.8330{{c}}
 
{{Optimal ET sequence|legend=0| 26, 46, 72, 190ffg }}
 
Badness (Sintel): 0.595
 
== Restles ==
{{See also| Lesser tendoneutralic }}
 
Restles may be described as the {{nowrap| 77 & 87 }} temperament, and has a [[ploidacot]] signature of gamma-dodecacot. It was named by [[Petr Pařízek]] in 2011 for it is some sort of opposite to [[beatles]]<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 153664/151875
 
{{Mapping|legend=1| 1 -2 8 4 | 0 12 -19 -4 }}
: mapping generators: ~2. ~315/256
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0322{{c}}, ~315/256 = 358.5581{{c}}
: [[error map]]: {{val| +0.032 +0.678 +1.340 -2.930 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~315/256 = 358.5484{{c}}
: error map: {{val| 0.000 +0.626 +1.267 -3.019 }}
 
{{Optimal ET sequence|legend=1| 77, 87, 164 }}
 
[[Badness]] (Sintel): 2.73
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 153664/151875
 
Mapping: {{mapping| 1 -2 8 4 -7 | 0 12 -19 -4 35 }}
 
Optimal tunings:
* WE: ~2 = 1200.1110{{c}}, ~27/22 = 358.6045{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~27/22 = 358.5720{{c}}
 
{{Optimal ET sequence|legend=0| 77, 87, 164, 251d }}
 
Badness (Sintel): 1.81
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 385/384, 676/675
 
Mapping: {{mapping| 1 -2 8 4 -7 4 | 0 12 -19 -4 35 -1 }}
 
Optimal tunings:
* WE: ~2 = 1200.0482{{c}}, ~~16/13 = 358.5883{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/13 = 358.5741{{c}}
 
{{Optimal ET sequence|legend=0| 77, 87, 164, 251d }}
 
Badness (Sintel): 1.16
 
== Necromanteion ==
Necromanteion, named by [[Johannes Werpup]] in 2014<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106371.html Yahoo! Tuning Group | ''Temperament ideas: A cuckoo, and two oracles'']</ref> may be described as the {{nowrap| 31 & 51c }} temperament. The generator is a subfifth representing ~[[35/24]], four of which minus two octaves make slendric's generator. Therefore, its [[ploidacot]] is wau-dodecacot.
 
[[Subgroup]]: 2.3.5.7


[[POTE tuning|POTE generator]]: 77.881
[[Comma list]]: 1029/1024, 5103/5000
Algebraic generator: [[Algebraic number|positive root]] of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5.


Map: [&lt;1 1 2 3 3|, &lt;0 9 5 -3 7|]
{{Mapping|legend=1| 1 -5 -7 5 | 0 12 17 -4 }}
Generators: 2, 21/20
: mapping generators: ~2, ~35/24
[[edo|Edos]]: 15, 31, 46, 77, 262cde, 339cde
Badness: 0.0167


[[Chords of valentine]]
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.2959{{c}}, ~35/24 = 658.3833{{c}}
: [[error map]]: {{val| +0.296 -2.835 +4.130 -0.879 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 658.2313{{c}}
: error map: {{val| 0.000 -3.179 +3.619 -1.751 }}


=Unidec=
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 144c, 175c }}
Comma: 31381059609/31250000000


POTE generator: ~10/9 = 183.047
[[Badness]] (Sintel): 2.98


Map: [&lt;2 5 8|, &lt;0 -6 -11|]
=== 11-limit ===
EDOs: 26, 46, 72, 118, 2524, 2642, 2760, 5002bc
Subgroup: 2.3.5.7.11
Badness: 0.0824


==7-limit==
Comma list: 176/175, 243/242, 1029/1024
[[Comma|Commas]]: 1029/1024, 4375/4374


[[Minimax tuning]]:
Mapping: {{mapping| 1 -5 -7 5 -13 | 0 12 17 -4 30 }}
7-limit: [|1 0 0 0&gt;, |47/26 0 6/13 -6/13&gt;,
 
|71/26 0 11/13 -11/13&gt;, |71/26 0 -2/13 2/13&gt;]
Optimal tunings:
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5
* WE: ~2 = 1200.2862{{c}}, ~22/15 = 658.4276{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.2805{{c}}
 
{{Optimal ET sequence|legend=0| 20ce, 31, 113c, 144c }}
 
Badness (Sintel): 1.77
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 144/143, 176/175, 243/242, 343/338
 
Mapping: {{mapping| 1 -5 -7 5 -13 7 | 0 12 17 -4 30 -6 }}
 
Optimal tunings:
* WE: ~2 = 1199.3663{{c}}, ~22/15 = 658.0465{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.3800{{c}}
 
{{Optimal ET sequence|legend=0| 20ce, 31, 82cf, 113cf }}
 
Badness (Sintel): 1.94
 
== Lagaca ==
Cryptically named by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, lagaca may be described as the {{nowrap| 10 & 118 }} temperament with a [[ploidacot]] signature of diploid wau-enneacot. The name actually refers to the fact that 12 generator steps in this temperament make ~[[7/3]], where "l", "g", "c" are integers alphabetically converted to letters.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 11529602/11390625
 
{{Mapping|legend=1| 2 -4 15 8 | 0 9 -13 -3 }}
: mapping generators: ~3375/2401, ~450/343
 
[[Optimal tuning]]s:
* [[WE]]: ~3375/2401 = 600.1355{{c}}, ~450/343 = 478.0813{{c}}
: [[error map]]: {{val| +0.271 +0.235 +0.662 -1.986 }}
* [[CWE]]: ~3375/2401 = 600.000{{c}}, ~450/343 = 477.9725{{c}}
: error map: {{val| 0.000 -0.202 +0.043 -2.743 }}
 
{{Optimal ET sequence|legend=1| 10, 98, 108, 118 }}
 
[[Badness]] (Sintel): 3.65
 
== Quartemka ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Quartemka]].''
 
Quartemka may be described as the {{nowrap| 26 & 61 }} temperament. Its [[ploidacot]] is 18-sheared 21-cot. It was named by [[Petr Pařízek]] in 2011 for its generator is close to 1/4 of the generator for [[emka]]<ref name="petr's long post"/>.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 1250000/1240029
 
{{Mapping|legend=1| 1 -17 -26 9 | 0 21 32 -7 }}
: mapping generators: ~2, ~50/27
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.5278{{c}}, ~50/27 = 1062.4614{{c}}
: [[error map]]: {{val| +0.528 +0.762 -1.272 -1.305 }}
* [[CWE]]: ~21 = 1200.0000{{c}}, ~50/27 = 1062.0046{{c}}
: error map: {{val| 0.000 +0.142 -2.167 -2.858 }}
 
{{Optimal ET sequence|legend=1| 26, 61, 87, 113, 200 }}
 
[[Badness]] (Sintel): 3.85
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 800000/793881


9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
Mapping: {{mapping| 1 -17 -26 9 7 | 0 21 32 -7 -4 }}
|57/28 11/7 0 -11/14&gt;, |20/7 -2/7 0 1/7&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7


[[POTE tuning|POTE generator]]: ~10/9 = 183.161
Optimal tunings:  
* WE: ~2 = 1200.3051{{c}}, ~50/27 = 1062.2805{{c}}
* CWE: ~21 = 1200.0000{{c}}, ~50/27 = 1062.0147{{c}}


Map: [&lt;2 5 8 5|, &lt;0 -6 -11 2|]
{{Optimal ET sequence|legend=0| 26, 61, 87, 200, 287d }}
Wedgie: &lt;&lt;12 22 -4 7 -40 -71||
EDOs: 26, 46, 72, 118, 190


==11-limit==
Badness (Sintel): 1.89
[[Comma|Commas]]: 385/384, 441/440, 4375/4374


[[Minimax tuning]]:
=== 13-limit ===
[|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;, |57/28 11/7 0 -11/14 0&gt;,
Subgroup: 2.3.5.7.11.13
|20/7 -2/7 0 1/7 0&gt;, |99/28 -3/7 0 3/14 0&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7


[[POTE tuning|POTE generator]]: 183.165
Comma list: 325/324, 364/363, 385/384, 2200/2197


Map: [&lt;2 5 8 5 6|, &lt;0 -6 -11 2 3|]
Mapping: {{mapping| 1 -17 -26 9 7 -14 | 0 21 32 -7 -4 20 }}
EDOs: 26, 46, 72, 118, 190


Optimal tunings:
* WE: ~2 = 1200.2708{{c}}, ~24/13 = 1062.2496{{c}}
* CWE: ~21 = 1200.0000{{c}}, ~24/13 = 1062.0139{{c}}


[[Chords of unidec]]
{{Optimal ET sequence|legend=0| 26, 61, 87, 200 }}


==Ekadash==
Badness (Sintel): 1.17
Commas: 385/384, 441/440, 625/624, 729/728


[[POTE tuning|POTE generator]]: ~10/9 = 183.187
== Tritriple ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritriple]].''


Map: [&lt;2 5 8 5 6 19|, &lt;0 -6 -11 2 3 -38|]
Tritriple may be described as the {{nowrap| 103 & 118 }} temperament. Its [[ploidacot]] is iota-beta-27-cot. It was named by [[Petr Pařízek]] in 2011 for its generator is 1/9 of the generator for [[slendric]], so that 3×3 generators [[octave reduction|octave reduced]] give slendric's generator, and another ×3 give the [[3/2|perfect fifth]]<ref name="petr's long post"/>.  
EDOs: 20cf, 26f, 46f, 72, 118, 190, 262df, 452cdef
Bad: 0.0204


==Hendec==
[[Subgroup]]: 2.3.5.7
Commas: 169/168, 325/324, 364/363, 1716/1715


[[POTE tuning|POTE generator]]: ~10/9 = 183.187
[[Comma list]]: 1029/1024, 1959552/1953125


Map: [&lt;2 5 8 5 6 8|, &lt;0 -6 -11 2 3 -2|]
{{Mapping|legend=1| 1 -11 -7 7 | 0 27 20 -9 }}
EDOs: 26, 46, 72
: mapping generators: ~2, ~864/625
Bad: 0.0177


===17-limit===  
[[Optimal tuning]]s:
Commas: 169/168, 221/220, 273/272, 325/324, 364/363
* [[WE]]: ~2 = 1200.4239{{c}}, ~864/625 = 559.4921{{c}}
: [[error map]]: {{val| +0.424 -0.331 +0.561 -1.287 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~864/625 = 559.3015{{c}}
: error map: {{val| 0.000 -0.815 -0.284 -2.539 }}


[[POTE tuning|POTE generator]]: ~10/9 = 183.196
{{Optimal ET sequence|legend=1| 15, …, 88, 103, 118, 221, 339d }}


Map: [&lt;2 5 8 5 6 8 10|, &lt;0 -6 -11 2 3 -2 -6|]
[[Badness]] (Sintel): 3.00
EDOs: 26, 46, 72


===Music===  
=== 11-limit ===
[[Technical Notes for Newbeams#Track%20notes:-Hypnocloudsmack%202|Hypnocloudsmack 2]] by [[Andrew Heathwaite]]
Subgroup: 2.3.5.7.11


=Hemithirds=
Comma list: 385/384, 441/440, 43923/43750


==7-limit==
Mapping: {{mapping| 1 -11 -7 7 -4 | 0 27 20 -9 16 }}
[[Comma|Commas]]: 1029/1024, 3136/3125


[[Minimax tuning]]:
Optimal tunings:  
7-limit: [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,
* WE: ~2 = 1200.4953{{c}}, ~242/175 = 559.5243{{c}}
|11/5 -1/10 0 1/10&gt;, |5/2 -1/4 0 1/4&gt;]
* CWE: ~2 = 1200.0000{{c}}, ~242/175 = 559.3016{{c}}
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6


9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
{{Optimal ET sequence|legend=0| 15, …, 88, 103, 118, 221e, 339de }}
|82/35 -4/35 0 2/35&gt;, |20/7 -2/7 0 1/7&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6


==11-limit==
Badness (Sintel): 1.17
[[Comma|Commas]]: 385/384, 441/440, 3136/3125


[[Minimax tuning]]:
== Widefourth ==
[|1 0 0 0 0&gt;, |11/9 0 0 -5/9 5/9&gt;, |64/27 0 0 2/27 -2/27&gt;,
[[Subgroup]]: 2.3.5.7
|79/27 0 0 5/27 -5/27&gt;, |79/27 0 0 -22/27 22/27&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/7


POTE generator: ~28/25 = 193.227
[[Comma list]]: 1029/1024, 48828125/48771072


{{Mapping|legend=1| 1 -17 -5 9 | 0 33 13 -11 }}


Map: [&lt;1 4 2 2 7|, &lt;0 -15 2 5 -22|]
[[Optimal tuning]]s:  
[[edo|Edos]]: [[31edo|31]], [[87edo|87]], [[118edo|118]]
* [[WE]]: ~2 = 1200.4770{{c}}, ~4608/3125 = 676.0584{{c}}
Badness: 0.0190
: [[error map]]: {{val| +0.477 -0.137 +0.061 -1.175 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~4608/3125 = 675.7954{{c}}
: error map: {{val| 0.000 -0.705 -0.973 -2.576 }}


[[Chords of hemithirds]]
{{Optimal ET sequence|legend=1| 16, 71, 87, 103, 190 }}


==13-limit==
[[Badness]] (Sintel): 3.90
Commas: 196/195 352/351 1001/1000 1029/1024


POTE generator: ~28/25 = 193.166
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 4 2 2 7 0|, &lt;0 -15 2 5 -22 23|]
Comma list: 385/384, 441/440, 234375/234256
EDOs: 31, 56, 87, 118, 205d
Badness: 0.0217


=Hemiseven=
Mapping: {{mapping| 1 16 8 -2 17 | 0 -33 -13 11 -31 }}
==7-limit==
Commas: 1029/1024, 19683/19600


POTE generator: ~320/243 = 483.267
Optimal tunings:  
* WE: ~2 = 1200.4852{{c}}, ~1250/847 = 676.0634{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~1250/847 = 675.7966{{c}}


Map: [&lt;1 4 14 2|, &lt;0 -6 -29 2|]
{{Optimal ET sequence|legend=0| 16, 71, 87, 103, 190 }}
Wedgie: &lt;&lt;6 29 -2 32 -20 -86||
EDOs: 5, 72, 77, 149, 221, 514bd, 735bcd
Badness: 0.0566


==11-limit==
Badness (Sintel): 1.35
Commas: 385/384, 441/440, 19683/19600


POTE generator: ~320/243 = 483.276
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 4 14 2 -5|, &lt;0 -6 -29 2 21|]
Comma list: 385/384, 441/440, 625/624, 847/845
EDOs: 72, 77, 149, 221e, 293de
Badness: 0.0285


==13-limit==
Mapping: {{mapping| 1 16 8 -2 17 12 | 0 -33 -13 11 -31 -19 }}
Commas: 351/350, 385/384, 441/440, 676/675


POTE generator: ~320/243 = 483.256
Optimal tunings:  
* WE: ~2 = 1200.4217{{c}}, ~77/52 = 676.0286{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/52 = 675.7967{{c}}


Map: [&lt;1 4 14 2 -5 19|, &lt;0 -6 -29 2 21 -38|]
{{Optimal ET sequence|legend=0| 16, 71, 87, 103, 190 }}
EDOs: 72, 77, 149, 221ef


==17-limit==
Badness (Sintel): 0.894
Commas: 273/272, 351/350, 385/384, 441/440, 676/675


POTE generator: ~320/243 = 483.261
== Other subgroup extensions ==
=== Euslendric (2.3.7.13) ===
Forms of slendric in the most optimal range for the 2.3.7 temperament ({{nowrap| 36 & 77 }}) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to the no-fives no-elevens [[29-limit]] by tempering out [[273/272]], [[343/342]], [[378/377]], [[392/391]], [[513/512]], and [[729/728]], or a comma basis defined in terms of [[S-expression]]s as {S7/S8, S14/S16, S15/S20, S24/S26, S27, S28}. [[113edo]] is an obvious tuning.


Map: [&lt;1 4 14 2 -5 19 21|, &lt;0 -6 -29 2 21 -38 -42|]
Subgroup: 2.3.7.13
EDOs: 72, 77, 149, 221ef


=Tritikleismic=
Comma list: 729/728, 1029/1024
==7-limit==
[[Comma|Commas]]: 1029/1024, 15625/15552


[[Minimax tunings]]:
Subgroup-val mapping: {{mapping| 1 1 3 0 | 0 3 -1 19 }}
7-limit: [|1 0 0 0&gt;, |2 0 6/7 -6/7&gt;,
|8/3 0 5/7 -5/7&gt;, |8/3 0 -2/7 2/7&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5


9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
Gencom mapping: {{mapping| 1 1 0 3 0 0 | 0 3 0 -1 0 19 }}
|46/21 5/7 0 -5/14&gt;, |20/7 -2/7 0 1/7&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7


==11-limit==
Optimal tunings:
[[Comma|Commas]]: 385/384, 441/440, 4000/3993
* WE: ~2 = 1200.5057{{c}}, ~8/7 = 233.7200{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6534{{c}}


[[Minimax tuning]]:
{{Optimal ET sequence|legend=0| 5, 31f, 36, 77, 113, 827bdddff }}
[|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;, |46/21 5/7 0 -5/14 0&gt;,
|20/7 -2/7 0 1/7 0&gt;, |71/21 3/7 0 -3/14 0&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7


Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]
Badness (Sintel): 0.339
[[edo|EDOs]]: [[72edo|72]], [[159edo|159]], [[231edo|231]]


==13-limit==  
==== 2.3.7.13.17 subgroup ====
Commas: 325/324, 364/363, 441/440, 625/624
Subgroup: 2.3.7.13.17


Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]
Comma list: 273/272, 729/728, 833/832
EDOs: 15, 72, 87, 159


==17-limit==
Subgroup-val mapping: {{mapping| 1 1 3 0 0 | 0 3 -1 19 21 }}
Commas: 273/272, 325/324, 364/363, 375/374, 385/384


Map: [&lt;3 0 3 10 8 0 -2|, &lt;0 6 5 -2 3 14 18|]
Gencom mapping: {{mapping| 1 1 0 3 0 0 0 | 0 3 0 -1 0 19 21 }}
EDOs: 15g, 72, 87, 159


=Superkleismic=  
Optimal tunings:
Commas: 1029/1024, 875/864
* WE: ~2 = 1200.5282{{c}}, ~8/7 = 233.6492{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.5776{{c}}


POTE generator: ~6/5 = 321.930
{{Optimal ET sequence|legend=0| 5g, 31fg, 36, 113, 149 }}


Map: [&lt;1 4 5 2|, &lt;0 -9 -10 3|]
Badness (Sintel): 0.332
EDOs: 11, 15, 26, 41
Badness: 0.0479


==11-limit==  
==== 2.3.7.13.17.19 subgroup ====
Commas: 100/99, 245/242, 385/384
Subgroup: 2.3.7.13.17.19


POTE generator: ~6/5 = 321.847
Comma list: 273/272, 343/342, 513/512, 729/728


Map: [&lt;1 4 5 2 4|, &lt;0 -9 -10 3 -2|]
Subgroup-val mapping: {{mapping| 1 1 3 0 0 6 | 0 3 -1 19 21 -9 }}
EDOs: 15, 26, 41, 261
Badness: 0.0257


==13-limit==
Gencom mapping: {{mapping| 1 1 0 3 0 0 0 6 | 0 3 0 -1 0 19 21 -9 }}
Commas: 100/99, 105/104, 245/243, 1188/1183


POTE generator: ~6/5 = 321.994
Optimal tunings:  
* WE: ~2 = 1200.3292{{c}}, ~8/7 = 233.6651{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6106{{c}}


Map: [&lt;1 4 5 2 4 8|, &lt;0 -9 -10 3 -2 -16|]
{{Optimal ET sequence|legend=0| 5g, 36, 77, 113, 262df }}
EDOs: 11, 15, 26, 41
Badness: 0.0215


=Gorgo=
Badness (Sintel): 0.380
Commas: 36/35, 1029/1024


[[POTE tuning|POTE generator]]: 228.334
==== 2.3.7.13.17.19.23 subgroup ====
Subgroup: 2.3.7.13.17.19.23


Map: [&lt;1 1 1 3|, &lt;0 3 7 -1|]
Comma list: 273/272, 343/342, 392/391, 513/512, 729/728
Wedgie: &lt;&lt;3 7 -1 4 -10 -22||
EDOs: 5, 16, 21


==11-limit==
Subgroup-val mapping: {{mapping| 1 1 3 0 0 6 9 | 0 3 -1 19 21 -9 -23 }}
Commas: 36/35, 56/55, 1029/1024


POTE generator: ~8/7 = 229.535
Gencom mapping: {{mapping| 1 1 0 3 0 0 0 6 9 | 0 3 0 -1 0 19 21 -9 -23 }}


Map: [&lt;1 1 1 3 5 |, &lt;0 3 7 -1 -8|]
Optimal tunings:  
EDOs: 5, 16e, 21, 47c, 68bce
* WE: ~2 = 1200.3127{{c}}, ~8/7 = 233.6679{{c}}
Badness: 0.0627
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6091{{c}}


==13-limit==
{{Optimal ET sequence|legend=0| 36, 77, 113, 262df }}
Commas: 27/26, 36/35, 56/55, 507/500


POTE generator: ~8/7 = 229.059
Badness (Sintel): 0.474


Map: [&lt;1 1 1 3 5 2|, &lt;0 3 7 -1 -8 9|]
==== 2.3.7.13.17.19.23.29 subgroup ====
EDOs 5, 21, 68bcef
Subgroup: 2.3.7.13.17.19.23.29
Badness: 0.0471


==Music==
Comma list: 273/272, 343/342, 378/377, 392/391, 513/512, 609/608
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3|Gorgo Example]] by [[Herman Miller]]


=Lemba=
Subgroup-val mapping: {{mapping| 1 1 3 0 0 6 9 7 | 0 3 -1 19 21 -9 -23 -11 }}
Commas: 50/49, 525/512


[[POTE tuning|POTE generator]]: 232.089
Gencom mapping: {{mapping| 1 1 0 3 0 0 0 6 9 7 | 0 3 0 -1 0 19 21 -9 -23 -11 }}


Map: [&lt;2 2 5 6|, &lt;3 -1 -1|]
Optimal tunings:  
Wedgie: &lt;&lt;6 -2 -2 -17 -20 1||
* WE: ~2 = 1200.2503{{c}}, ~8/7 = 233.6688{{c}}
EDOs: 10, 16, 26
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6208{{c}}


==Music==
{{Optimal ET sequence|legend=0| 36, 77, 113 }}
By [[Herman Miller]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3|Lemba Galatsia]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3|GPO Lemba]]


=Gidorah=
Badness (Sintel): 0.473
Commas: 21/20, 144/125


POTE generator: ~8/7 = 230.762
=== Baladic (2.3.7.13) ===
Baladic is a 2.3.7.13.17-subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out [[169/168]] ({{S|13}}), which splits [[7/6]] in half ([[13/12]]~[[14/13]]) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]]. 36edo is an excellent baladic tuning.


Map: [&lt;1 1 2 3|, &lt;0 3 2 -1|]
Subgroup: 2.3.7.13
EDOs: 5, 11, 21, 26
Badness: 0.0623


=Clyndro=
Comma list: 169/168, 1029/1024
Commas: 1029/1024, 135/128


POTE generator: ~8/7 = 226.469
Subgroup-val mapping: {{mapping| 2 2 6 7 | 0 3 -1 1 }}


Map: [&lt;1 1 4 3|, &lt;0 3 -9 -1|]
Gencom mapping: {{mapping| 2 2 0 6 0 7 | 0 3 0 -1 0 1 }}
EDOs: 16
: mapping generators: ~91/64, ~8/7


=Necromanteion=  
Optimal tunings:
Commas: 1029/1024, 5103/5000
* WE: ~91/64 = 600.4315{{c}}, ~8/7 = 233.7724{{c}}
* CWE: ~91/64 = 600.0000{{c}}, ~8/7 = 233.7039{{c}}


POTE generator: ~48/35 = 541.779
{{Optimal ET sequence|legend=0| 10, 26, 36, 154f, 190ff, 226ff, 262dfff }}


Map: [&lt;1 7 10 1|, &lt;0 -12 -17 4|]
Badness (Sintel): 0.434
EDOs: 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd
Badness: 0.1177


==11-limit==  
==== 2.3.7.13.17 subgroup ====
Commas: 176/175, 243/242, 1029/1024
Subgroup: 2.3.7.13.17


POTE generator: ~15/11 = 541.729
Comma list: 169/168, 273/272, 289/288


Map: [&lt;1 7 10 1 17|, &lt;0 -12 -17 4 -30|]
Subgroup-val mapping: {{mapping| 2 2 6 7 7 | 0 3 -1 1 3 }}
EDOs: 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde
Badness: 0.0535


==13-limit==
Gencom mapping: {{mapping| 2 2 0 6 0 7 7 | 0 3 0 -1 0 1 3 }}
Commas: 144/143, 176/175, 243/242, 343/338


POTE generator: ~15/11 = 541.606
Optimal tunings:  
* WE: ~17/12 = 600.4436{{c}}, ~8/7 = 233.7883{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~8/7 = 233.7312{{c}}


Map: [&lt;1 7 10 1 17 1|, &lt;0 -12 -17 4 -30 6|]
{{Optimal ET sequence|legend=0| 10, 26, 36, 154f, 190ffg, 226ffg }}
EDOs: 31, 51ce, 82cf, 113cf, 144cf
Badness: 0.0470


=Widefourth=
Badness (Sintel): 0.253
Commas: 1029/1024, 48828125/48771072


POTE generator: ~3125/2304 = 524.210
=== Gigapyth (2.3.7.85) ===
Subgroup: 2.3.7.85


Map: [&lt;1 16 8 -2|, &lt;0 -33 -13 11|]
Comma list: 1029/1024, 7225/7203
Wedgie: &lt;&lt;33 13 -11 -56 -110 -62||
EDOs: 16, 71, 87, 103, 190
Badness: 0.1541


==11-limit==
Subgroup-val mapping: {{mapping| 1 -2 4 7 | 0 6 -2 -1 }}
Commas: 385/384, 441/440, 234375/234256


POTE generator: ~3125/2304 = 524.210
Optimal tunings:  
* WE: ~2 = 1200.8295{{c}}, ~128/85 = 717.2597{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~128/85 = 716.7933{{c}}


Map: [&lt;1 16 8 -2 17|, &lt;0 -33 -13 11 -31|]
{{Optimal ET sequence|legend=0| 5, 42*, 47, 52, 57, 62, 67, 72, 149*, 370d***, 519bdd***** }}
EDOs: 16, 71, 87, 103, 190
Badness: 0.0408


==13-limit==
<nowiki/>* Wart for 85
Commas: 385/384, 441/440, 625/624, 847/845


POTE generator: ~65/48 = 524.209
== References ==


Map: [&lt;1 16 8 -2 17 12|, &lt;0 -33 -13 11 -31 -19|]
[[Category:Temperament clans]]
EDOs: 16, 71, 87, 103, 190
[[Category:Gamelismic clan| ]] <!-- main article -->
Badness: 0.0216</pre></div>
[[Category:Rank 2]]
<h4>Original HTML content:</h4>
[[Category:Listen]]
<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;Gamelismic clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:140:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:140 --&gt;&lt;!-- ws:start:WikiTextTocRule:141: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Full seven limit children"&gt;Full seven limit children&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:141 --&gt;&lt;!-- ws:start:WikiTextTocRule:142: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Miracle"&gt;Miracle&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:142 --&gt;&lt;!-- ws:start:WikiTextTocRule:143: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:143 --&gt;&lt;!-- ws:start:WikiTextTocRule:144: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Revelation"&gt;Revelation&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:144 --&gt;&lt;!-- ws:start:WikiTextTocRule:145: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Miracle-Revelation-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:145 --&gt;&lt;!-- ws:start:WikiTextTocRule:146: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Miraculous"&gt;Miraculous&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:146 --&gt;&lt;!-- ws:start:WikiTextTocRule:147: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Benediction"&gt;Benediction&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:147 --&gt;&lt;!-- ws:start:WikiTextTocRule:148: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Miracle-Benediction-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:148 --&gt;&lt;!-- ws:start:WikiTextTocRule:149: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Manna"&gt;Manna&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:149 --&gt;&lt;!-- ws:start:WikiTextTocRule:150: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Semimiracle"&gt;Semimiracle&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:150 --&gt;&lt;!-- ws:start:WikiTextTocRule:151: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Miracle-Semimiracle-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:151 --&gt;&lt;!-- ws:start:WikiTextTocRule:152: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Hemimiracle"&gt;Hemimiracle&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:152 --&gt;&lt;!-- ws:start:WikiTextTocRule:153: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Miracle-Hemimiracle-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:153 --&gt;&lt;!-- ws:start:WikiTextTocRule:154: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Oracle"&gt;Oracle&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:154 --&gt;&lt;!-- ws:start:WikiTextTocRule:155: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Phicordial"&gt;Phicordial&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:155 --&gt;&lt;!-- ws:start:WikiTextTocRule:156: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Miracle-Phicordial-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:156 --&gt;&lt;!-- ws:start:WikiTextTocRule:157: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Miracle-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:157 --&gt;&lt;!-- ws:start:WikiTextTocRule:158: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemisecordite"&gt;Hemisecordite&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:158 --&gt;&lt;!-- ws:start:WikiTextTocRule:159: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemisecordite-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:159 --&gt;&lt;!-- ws:start:WikiTextTocRule:160: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Rodan"&gt;Rodan&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:160 --&gt;&lt;!-- ws:start:WikiTextTocRule:161: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Rodan-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:161 --&gt;&lt;!-- ws:start:WikiTextTocRule:162: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Rodan-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:162 --&gt;&lt;!-- ws:start:WikiTextTocRule:163: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Rodan-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:163 --&gt;&lt;!-- ws:start:WikiTextTocRule:164: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Rodan-17-limit-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:164 --&gt;&lt;!-- ws:start:WikiTextTocRule:165: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Rodan-Aerodactyl"&gt;Aerodactyl&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:165 --&gt;&lt;!-- ws:start:WikiTextTocRule:166: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Rodan-Aerodino"&gt;Aerodino&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:166 --&gt;&lt;!-- ws:start:WikiTextTocRule:167: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Rodan-Aerodino-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Rodan-Varan"&gt;Varan&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Rodan-Varan-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:169 --&gt;&lt;!-- ws:start:WikiTextTocRule:170: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Valentine"&gt;Valentine&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:170 --&gt;&lt;!-- ws:start:WikiTextTocRule:171: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:171 --&gt;&lt;!-- ws:start:WikiTextTocRule:172: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:172 --&gt;&lt;!-- ws:start:WikiTextTocRule:173: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Unidec"&gt;Unidec&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:173 --&gt;&lt;!-- ws:start:WikiTextTocRule:174: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Unidec-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:174 --&gt;&lt;!-- ws:start:WikiTextTocRule:175: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Unidec-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:175 --&gt;&lt;!-- ws:start:WikiTextTocRule:176: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Unidec-Ekadash"&gt;Ekadash&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:176 --&gt;&lt;!-- ws:start:WikiTextTocRule:177: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Unidec-Hendec"&gt;Hendec&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:177 --&gt;&lt;!-- ws:start:WikiTextTocRule:178: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Unidec-Hendec-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:178 --&gt;&lt;!-- ws:start:WikiTextTocRule:179: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Unidec-Hendec-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:179 --&gt;&lt;!-- ws:start:WikiTextTocRule:180: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemithirds"&gt;Hemithirds&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:180 --&gt;&lt;!-- ws:start:WikiTextTocRule:181: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemithirds-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:181 --&gt;&lt;!-- ws:start:WikiTextTocRule:182: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemithirds-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:182 --&gt;&lt;!-- ws:start:WikiTextTocRule:183: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemithirds-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:183 --&gt;&lt;!-- ws:start:WikiTextTocRule:184: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemiseven"&gt;Hemiseven&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:184 --&gt;&lt;!-- ws:start:WikiTextTocRule:185: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiseven-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:185 --&gt;&lt;!-- ws:start:WikiTextTocRule:186: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiseven-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:186 --&gt;&lt;!-- ws:start:WikiTextTocRule:187: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiseven-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:187 --&gt;&lt;!-- ws:start:WikiTextTocRule:188: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiseven-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:188 --&gt;&lt;!-- ws:start:WikiTextTocRule:189: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Tritikleismic"&gt;Tritikleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:189 --&gt;&lt;!-- ws:start:WikiTextTocRule:190: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritikleismic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:190 --&gt;&lt;!-- ws:start:WikiTextTocRule:191: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritikleismic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:191 --&gt;&lt;!-- ws:start:WikiTextTocRule:192: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritikleismic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:192 --&gt;&lt;!-- ws:start:WikiTextTocRule:193: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritikleismic-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:193 --&gt;&lt;!-- ws:start:WikiTextTocRule:194: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Superkleismic"&gt;Superkleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:194 --&gt;&lt;!-- ws:start:WikiTextTocRule:195: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Superkleismic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:195 --&gt;&lt;!-- ws:start:WikiTextTocRule:196: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Superkleismic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:196 --&gt;&lt;!-- ws:start:WikiTextTocRule:197: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Gorgo"&gt;Gorgo&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:197 --&gt;&lt;!-- ws:start:WikiTextTocRule:198: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Gorgo-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:198 --&gt;&lt;!-- ws:start:WikiTextTocRule:199: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Gorgo-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:199 --&gt;&lt;!-- ws:start:WikiTextTocRule:200: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Gorgo-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:200 --&gt;&lt;!-- ws:start:WikiTextTocRule:201: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Lemba"&gt;Lemba&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:201 --&gt;&lt;!-- ws:start:WikiTextTocRule:202: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Lemba-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:202 --&gt;&lt;!-- ws:start:WikiTextTocRule:203: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Gidorah"&gt;Gidorah&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:203 --&gt;&lt;!-- ws:start:WikiTextTocRule:204: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Clyndro"&gt;Clyndro&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:204 --&gt;&lt;!-- ws:start:WikiTextTocRule:205: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Necromanteion"&gt;Necromanteion&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:205 --&gt;&lt;!-- ws:start:WikiTextTocRule:206: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Necromanteion-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:206 --&gt;&lt;!-- ws:start:WikiTextTocRule:207: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Necromanteion-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:207 --&gt;&lt;!-- ws:start:WikiTextTocRule:208: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Widefourth"&gt;Widefourth&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:208 --&gt;&lt;!-- ws:start:WikiTextTocRule:209: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Widefourth-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:209 --&gt;&lt;!-- ws:start:WikiTextTocRule:210: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Widefourth-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:210 --&gt;&lt;!-- ws:start:WikiTextTocRule:211: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:211 --&gt;The 2.3.7-&lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt; comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3&amp;gt;. For any member of the clan, for the rank three &lt;a class="wiki_link" href="/Gamelismic%20family#Gamelan"&gt;gamelan temperament&lt;/a&gt; itself, and for the rank two 2.3.7 temperament &lt;a class="wiki_link" href="/slendric"&gt;slendric&lt;/a&gt;, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt; is a good tuning for gamelismic itself, though if the full 7-limit is desired, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt; or &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; might be preferred.&lt;br /&gt;
&lt;br /&gt;
7-limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |5/2 3/4 0 -3/4&amp;gt;,&lt;br /&gt;
|5/2 -1/4 1 -3/4&amp;gt;, |5/2 -1/4 0 1/4&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 7/6, 6/5&lt;br /&gt;
&lt;br /&gt;
9-limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |10/7 6/7 0 -3/7&amp;gt;,&lt;br /&gt;
|10/7 -1/7 1 -3/7&amp;gt;, |20/7 -2/7 0 1/7&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 6/5, 9/7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 8/7 0.5192 5/4 2.3219&lt;br /&gt;
Angle(8/7, 5/4) = 90 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 3 0 -1|, &amp;lt;0 0 1 0|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3|, &amp;lt;0 3 0 -1|, &amp;lt; 0 0 1 0|]&lt;br /&gt;
Generators: 2, 5, 7&lt;br /&gt;
&lt;br /&gt;
No-fives &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 233.688&lt;br /&gt;
EDOs: 5, 36, 77, 190&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Full seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Full seven limit children&lt;/h2&gt;
To the gamelisma itself we need to add the comma which appears next on the modified &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt;, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Miracle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Miracle&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 225/224&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
7-limit: [|1 0 0 0&amp;gt;, |25/13 6/13 -6/13 0&amp;gt;,&lt;br /&gt;
|25/13 -7/13 7/13 0&amp;gt;, |35/13 -2/13 2/13 0&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 6/5&lt;br /&gt;
&lt;br /&gt;
9-limit: [|1 0 0 0&amp;gt;, |25/19 12/19 -6/19 0&amp;gt;,&lt;br /&gt;
|50/19 -14/19 7/19 0&amp;gt;, |55/19 -4/19 2/19 0&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 116.675&lt;br /&gt;
Algebraic generator: Secor59, &lt;a class="wiki_link" href="/Algebraic%20number"&gt;positive root&lt;/a&gt; of 15x^6-8x^4-12&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3|, &amp;lt;0 6 -7 -2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 -7 -2 -25 -20 15||&lt;br /&gt;
EDOs: 10, 21, 31, 41, 72, &lt;a class="wiki_link" href="/175edo"&gt;175&lt;/a&gt;&lt;br /&gt;
Badness: 0.0167&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Miracle-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 225/224, 243/242&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |25/19 12/19 -6/19 0 0&amp;gt;,&lt;br /&gt;
|50/19 -14/19 7/19 0 0&amp;gt;, |55/19 -4/19 2/19 0 0&amp;gt;,&lt;br /&gt;
|53/19 30/19 -15/19 0 0&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 116.633&lt;br /&gt;
Algebraic generator: Secor59&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2|, &amp;lt;0 6 -7 -2 15|]&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: 10, 31, 41, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, 247c, 319bcde, &lt;a class="wiki_link" href="/391edo"&gt;391bcde&lt;/a&gt;, 463bcde&lt;br /&gt;
Badness: 0.0107&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Chords%20of%20miracle"&gt;Chords of miracle&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Miracle-Revelation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Revelation&lt;/h2&gt;
Commas: 99/98, 176/175, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 116.277&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 5|, &amp;lt;0 6 -7 -2 -16|]&lt;br /&gt;
EDOs: 10, 21, 31&lt;br /&gt;
Badness: 0.0329&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Miracle-Revelation-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h3&gt;
Commas: 66/65, 99/98, 105/104, 1001/1000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 116.268&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 5 4|, &amp;lt;0 6 -7 -2 -16 -3|]&lt;br /&gt;
EDOs: 10, 21, 31&lt;br /&gt;
Badness: 0.0295&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Miracle-Miraculous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Miraculous&lt;/h2&gt;
Commas: 105/104, 144/143, 196/195, 275/273&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 116.747&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2 4|, &amp;lt;0 6 -7 -2 15 -3|]&lt;br /&gt;
EDOs: 10, 31, 41, 72f, 113f, 185cf&lt;br /&gt;
Badness: 0.0187&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Miracle-Benediction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Benediction&lt;/h2&gt;
Commas: 225/224, 243/242, 351/350, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 116.574&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2 7|, &amp;lt;0 6 -7 -2 15 -34|]&lt;br /&gt;
EDOs: 31, 72, 103, &lt;a class="wiki_link" href="/175edo"&gt;175f&lt;/a&gt;&lt;br /&gt;
Badness: 0.0157&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Miracle-Benediction-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;17-limit&lt;/h3&gt;
Commas: 225/224, 243/242, 273/272, 351/350, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 116.585&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2 7 7|, &amp;lt;0 6 -7 -2 15 -34 -30|]&lt;br /&gt;
EDOs: 31, 72, 103, &lt;a class="wiki_link" href="/175edo"&gt;175f&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Miracle-Manna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Manna&lt;/h2&gt;
Commas: 225/224, 243/242, 325/324, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 116.739&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2 0|, &amp;lt;0 6 -7 -2 15 38|]&lt;br /&gt;
EDOs: 10f, 31f, 41, 72, 113, 185cf, 257cf&lt;br /&gt;
Badness: 0.0170&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Miracle-Semimiracle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Semimiracle&lt;/h2&gt;
Commas: 169/168, 225/224, 243/242, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 116.624&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 2 6 6 4 7|, &amp;lt;0 6 -7 -2 15 2|]&lt;br /&gt;
EDOs: 10, 62, 72&lt;br /&gt;
Badness: 0.0246&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Miracle-Semimiracle-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;17-limit&lt;/h3&gt;
Commas: 169/168, 221/220, 225/224, 243/242, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 116.628&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 2 6 6 4 7 7|, &amp;lt;0 6 -7 -2 15 2 6|]&lt;br /&gt;
EDOs: 10, 62, 72&lt;br /&gt;
Badness: 0.0161&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Miracle-Hemimiracle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Hemimiracle&lt;/h2&gt;
Commas: 225/224, 245/242, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~33/32 = 58.408&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 4|, &amp;lt;0 12 -14 -4 -11|]&lt;br /&gt;
EDOs: 20, 21, 41, 123c, 144e, 185ce, 226ce&lt;br /&gt;
Badness: 0.0592&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Miracle-Hemimiracle-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h3&gt;
Commas: 105/104, 196/195, 245/242, 512/507&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~33/32 = 58.430&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 4 4|, &amp;lt;0 12 -14 -4 -11 -6|]&lt;br /&gt;
EDOs: 20, 21, 41, 123cf, 144ef, 185cef&lt;br /&gt;
Badness: 0.0432&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Miracle-Oracle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Oracle&lt;/h2&gt;
Commas: 121/120, 225/224, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/8 = 541.668&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 7 -4 1 3|, &amp;lt;0 -12 14 4 1|]&lt;br /&gt;
EDOs: 11, 20, 31, 51, 82e, 113e, 144e&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Miracle-Phicordial"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Phicordial&lt;/h2&gt;
Commas: 225/224, 243/242, 441/440, 2200/2197&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 361.121&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 7 -4 1 17 4|, &amp;lt;0 -18 21 6 -45 -1|]&lt;br /&gt;
EDOs: 10, 103, 113, 216c&lt;br /&gt;
Badness: 0.0332&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Miracle-Phicordial-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;17-limit&lt;/h3&gt;
Commas: 225/224, 243/242, 273/272, 441/440, 2200/2197&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 361.123&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 7 -4 1 17 4 8|, &amp;lt;0 -18 21 6 -45 -1 -13|]&lt;br /&gt;
EDOs: 10, 103, 113, 216c&lt;br /&gt;
Badness: 0.0247&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Miracle-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Music&lt;/h2&gt;
By &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/RachmaninoffPlaysBlackjack" rel="nofollow"&gt;Rachmaninoff Plays Blackjack&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
By &lt;a class="wiki_link" href="/Joseph%20Pehrson"&gt;Joseph Pehrson&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3" rel="nofollow"&gt;Black and Jill&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3" rel="nofollow"&gt;Blacklight&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3" rel="nofollow"&gt;Blackjack&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Hemisecordite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Hemisecordite&lt;/h1&gt;
Commas: 225/224, 243/242, 441/440, 847/845&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/26 = 58.288&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2 2|, &amp;lt;0 12 -14 -4 30 35|]&lt;br /&gt;
EDOs: 41, 62, 103, 247c, 350bcde&lt;br /&gt;
Badness: 0.0256&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Hemisecordite-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;17-limit&lt;/h2&gt;
Commas: 225/224, 243/242, 273/272, 441/440, 847/845&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/26 = 58.261&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2 2 2|, &amp;lt;0 12 -14 -4 30 35 43|]&lt;br /&gt;
EDOs: 41, 62, 103&lt;br /&gt;
Badness: 0.0225&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Rodan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Rodan&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 245/243&lt;br /&gt;
&lt;br /&gt;
7+9 limit minimax tuning: [|1 0 0 0&amp;gt;, |5/3 0 1/6 -1/6&amp;gt;,&lt;br /&gt;
|25/9 0 17/18 -17/18&amp;gt;, |25/9 0 -1/18 1/18&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/5&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 234.417&lt;br /&gt;
Algebraic generator: &lt;a class="wiki_link" href="/Algebraic%20number"&gt;larger root&lt;/a&gt; of 20x^2-36x+15, or (9+√6)/10.&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3|, &amp;lt;0 3 17 -1|]&lt;br /&gt;
EDOs: 41, 87, 128&lt;br /&gt;
Badness: 0.0371&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Rodan-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 441/440, 245/243, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;: [|1 0 0 0 0&amp;gt;, |31/19 6/19 0 0 -3/19&amp;gt;,&lt;br /&gt;
|49/19 34/19 0 0 -17/19&amp;gt;, |53/19 -2/19 0 0 1/19&amp;gt;,&lt;br /&gt;
|62/19 -26/19 0 0 13/19&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/9&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 234.459&lt;br /&gt;
Algebraic generator: &lt;a class="wiki_link" href="/Algebraic%20number"&gt;positive root&lt;/a&gt; of x^2+16x-31, or √95-8.&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3 6|, &amp;lt;0 3 17 -1 -13|]&lt;br /&gt;
EDOs: 41, 87, 389d&lt;br /&gt;
Badness: 0.0231&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Chords%20of%20rodan"&gt;Chords of rodan&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Rodan-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
Commas: 196/195, 245/243, 352/351, 364/363&lt;br /&gt;
&lt;br /&gt;
13 and 15 limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |23/14 3/14 0 0 0 -3/28&amp;gt;,&lt;br /&gt;
|37/14 17/14 0 0 0 -17/28&amp;gt;, |39/14 -1/14 0 0 0 1/28&amp;gt;,&lt;br /&gt;
|45/14 -13/14 0 0 0 13/28&amp;gt;, |23/7 -11/7 0 0 0 11/14&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 13/9&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 234.482&lt;br /&gt;
Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly.&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3 6 8|, &amp;lt;0 3 17 -1 -13 -22|]&lt;br /&gt;
Generators: 2, 8/7&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 41, 46, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;&lt;br /&gt;
Badness: 0.0184&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Rodan-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;17-limit&lt;/h2&gt;
Commas: 154/153, 196/195, 245/243, 273/272, 364/363&lt;br /&gt;
&lt;br /&gt;
Eigenmonzos: 2, 18/17&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~8/7 = 234.524&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3 6 8 8|, &amp;lt;0 3 17 -1 -13 -22 -20|]&lt;br /&gt;
Edos: 41, 46, 87, 220dg, 307dg&lt;br /&gt;
Badness: 0.0167&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc23"&gt;&lt;a name="Rodan-17-limit-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Music&lt;/h3&gt;
By &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Pianodactyl" rel="nofollow"&gt;Pianodactyl&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/Pianodactyl/pianodactyl.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Rodan-Aerodactyl"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Aerodactyl&lt;/h2&gt;
Commas: 91/90, 245/243, 385/384, 441/440&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~8/7 = 234.639&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3 6 -1|, &amp;lt;0 3 17 -1 -13 24|&lt;br /&gt;
EDOs: 41f, 46, 51c&lt;br /&gt;
Badness: 0.0340&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Rodan-Aerodino"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Aerodino&lt;/h2&gt;
Commas: 176/175, 245/243, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 234.728&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3 -3|, &amp;lt;0 3 17 -1 33|&lt;br /&gt;
EDOS: 46&lt;br /&gt;
Badness: 0.0543&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc26"&gt;&lt;a name="Rodan-Aerodino-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h3&gt;
Commas: 91/90, 176/175, 245/243, 847/845&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 234.782&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3 -3 -1|, &amp;lt;0 3 17 -1 33 24|&lt;br /&gt;
EDOs: 46&lt;br /&gt;
Badness: 0.0358&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Rodan-Varan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Varan&lt;/h2&gt;
Commas: 100/99, 245/243, 2835/2816&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 234.145&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3 -2|, &amp;lt;0 3 17 -1 28|&lt;br /&gt;
EDOs: 41, 46e&lt;br /&gt;
Badness: 0.0449&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc28"&gt;&lt;a name="Rodan-Varan-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h3&gt;
Commas: 100/99, 105/104, 245/243, 352/351&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 234.089&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 3 -2 0|, &amp;lt;0 3 17 -1 28 19|&lt;br /&gt;
EDOs: 41&lt;br /&gt;
Badness: 0.0323&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Valentine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Valentine&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Valentine-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;7-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 126/125&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
7-limit: [|1 0 0 0&amp;gt;, |5/2 3/4 0 -3/4&amp;gt;,&lt;br /&gt;
|17/6 5/12 0 -5/12&amp;gt;, [5/2 -1/4 0 1/4&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 7/6&lt;br /&gt;
&lt;br /&gt;
9-limit: [|1 0 0 0&amp;gt;, |10/7 6/7 0 -3/7&amp;gt;,&lt;br /&gt;
|47/21 10/21 0 -5/21&amp;gt;, |20/7 -2/7 0 1/7&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 77.864&lt;br /&gt;
Algebraic generator: &lt;a class="wiki_link" href="/Algebraic%20number"&gt;smaller root&lt;/a&gt; of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents.&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 3|, &amp;lt;0 9 5 -3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;9 5 -3 -13 -30 -21||&lt;br /&gt;
EDOs: 15, 31, 46, 77, 185, 262cd&lt;br /&gt;
Badness: 0.0311&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Valentine-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;11-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 121/120, 126/125, 176/175&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |1 0 0 -9/10 9/10&amp;gt;,&lt;br /&gt;
|2 0 0 -1/2 1/2&amp;gt;, |3 0 0 3/10 -3/10&amp;gt;, |3 0 0 -7/10 7/10&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 11/7&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 77.881&lt;br /&gt;
Algebraic generator: &lt;a class="wiki_link" href="/Algebraic%20number"&gt;positive root&lt;/a&gt; of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5.&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 3 3|, &amp;lt;0 9 5 -3 7|]&lt;br /&gt;
Generators: 2, 21/20&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 15, 31, 46, 77, 262cde, 339cde&lt;br /&gt;
Badness: 0.0167&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Chords%20of%20valentine"&gt;Chords of valentine&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="Unidec"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Unidec&lt;/h1&gt;
Comma: 31381059609/31250000000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 183.047&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 5 8|, &amp;lt;0 -6 -11|]&lt;br /&gt;
EDOs: 26, 46, 72, 118, 2524, 2642, 2760, 5002bc&lt;br /&gt;
Badness: 0.0824&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Unidec-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;7-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 4375/4374&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
7-limit: [|1 0 0 0&amp;gt;, |47/26 0 6/13 -6/13&amp;gt;,&lt;br /&gt;
|71/26 0 11/13 -11/13&amp;gt;, |71/26 0 -2/13 2/13&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/5&lt;br /&gt;
&lt;br /&gt;
9-limit: [|1 0 0 0&amp;gt;, |10/7 6/7 0 -3/7&amp;gt;,&lt;br /&gt;
|57/28 11/7 0 -11/14&amp;gt;, |20/7 -2/7 0 1/7&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 183.161&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 5 8 5|, &amp;lt;0 -6 -11 2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;12 22 -4 7 -40 -71||&lt;br /&gt;
EDOs: 26, 46, 72, 118, 190&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Unidec-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;11-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 441/440, 4375/4374&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |10/7 6/7 0 -3/7 0&amp;gt;, |57/28 11/7 0 -11/14 0&amp;gt;,&lt;br /&gt;
|20/7 -2/7 0 1/7 0&amp;gt;, |99/28 -3/7 0 3/14 0&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 183.165&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 5 8 5 6|, &amp;lt;0 -6 -11 2 3|]&lt;br /&gt;
EDOs: 26, 46, 72, 118, 190&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Chords%20of%20unidec"&gt;Chords of unidec&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="Unidec-Ekadash"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Ekadash&lt;/h2&gt;
Commas: 385/384, 441/440, 625/624, 729/728&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 183.187&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 5 8 5 6 19|, &amp;lt;0 -6 -11 2 3 -38|]&lt;br /&gt;
EDOs: 20cf, 26f, 46f, 72, 118, 190, 262df, 452cdef&lt;br /&gt;
Bad: 0.0204&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Unidec-Hendec"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;Hendec&lt;/h2&gt;
Commas: 169/168, 325/324, 364/363, 1716/1715&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 183.187&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 5 8 5 6 8|, &amp;lt;0 -6 -11 2 3 -2|]&lt;br /&gt;
EDOs: 26, 46, 72&lt;br /&gt;
Bad: 0.0177&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc37"&gt;&lt;a name="Unidec-Hendec-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;17-limit&lt;/h3&gt;
Commas: 169/168, 221/220, 273/272, 325/324, 364/363&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 183.196&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 5 8 5 6 8 10|, &amp;lt;0 -6 -11 2 3 -2 -6|]&lt;br /&gt;
EDOs: 26, 46, 72&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc38"&gt;&lt;a name="Unidec-Hendec-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;Music&lt;/h3&gt;
&lt;a class="wiki_link" href="/Technical%20Notes%20for%20Newbeams#Track%20notes:-Hypnocloudsmack%202"&gt;Hypnocloudsmack 2&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc39"&gt;&lt;a name="Hemithirds"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;Hemithirds&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Hemithirds-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;7-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 3136/3125&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
7-limit: [|1 0 0 0&amp;gt;, |5/2 3/4 0 -3/4&amp;gt;,&lt;br /&gt;
|11/5 -1/10 0 1/10&amp;gt;, |5/2 -1/4 0 1/4&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/6&lt;br /&gt;
&lt;br /&gt;
9-limit: [|1 0 0 0&amp;gt;, |10/7 6/7 0 -3/7&amp;gt;,&lt;br /&gt;
|82/35 -4/35 0 2/35&amp;gt;, |20/7 -2/7 0 1/7&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/6&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Hemithirds-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;11-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 441/440, 3136/3125&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |11/9 0 0 -5/9 5/9&amp;gt;, |64/27 0 0 2/27 -2/27&amp;gt;,&lt;br /&gt;
|79/27 0 0 5/27 -5/27&amp;gt;, |79/27 0 0 -22/27 22/27&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/7&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~28/25 = 193.227&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 2 2 7|, &amp;lt;0 -15 2 5 -22|]&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;&lt;br /&gt;
Badness: 0.0190&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Chords%20of%20hemithirds"&gt;Chords of hemithirds&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc42"&gt;&lt;a name="Hemithirds-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;13-limit&lt;/h2&gt;
Commas: 196/195 352/351 1001/1000 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~28/25 = 193.166&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 2 2 7 0|, &amp;lt;0 -15 2 5 -22 23|]&lt;br /&gt;
EDOs: 31, 56, 87, 118, 205d&lt;br /&gt;
Badness: 0.0217&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Hemiseven"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Hemiseven&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc44"&gt;&lt;a name="Hemiseven-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;7-limit&lt;/h2&gt;
Commas: 1029/1024, 19683/19600&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~320/243 = 483.267&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 14 2|, &amp;lt;0 -6 -29 2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 29 -2 32 -20 -86||&lt;br /&gt;
EDOs: 5, 72, 77, 149, 221, 514bd, 735bcd&lt;br /&gt;
Badness: 0.0566&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Hemiseven-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;11-limit&lt;/h2&gt;
Commas: 385/384, 441/440, 19683/19600&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~320/243 = 483.276&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 14 2 -5|, &amp;lt;0 -6 -29 2 21|]&lt;br /&gt;
EDOs: 72, 77, 149, 221e, 293de&lt;br /&gt;
Badness: 0.0285&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc46"&gt;&lt;a name="Hemiseven-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;13-limit&lt;/h2&gt;
Commas: 351/350, 385/384, 441/440, 676/675&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~320/243 = 483.256&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 14 2 -5 19|, &amp;lt;0 -6 -29 2 21 -38|]&lt;br /&gt;
EDOs: 72, 77, 149, 221ef&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Hemiseven-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;17-limit&lt;/h2&gt;
Commas: 273/272, 351/350, 385/384, 441/440, 676/675&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~320/243 = 483.261&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 14 2 -5 19 21|, &amp;lt;0 -6 -29 2 21 -38 -42|]&lt;br /&gt;
EDOs: 72, 77, 149, 221ef&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc48"&gt;&lt;a name="Tritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;Tritikleismic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc49"&gt;&lt;a name="Tritikleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;7-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 15625/15552&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tunings"&gt;Minimax tunings&lt;/a&gt;:&lt;br /&gt;
7-limit: [|1 0 0 0&amp;gt;, |2 0 6/7 -6/7&amp;gt;,&lt;br /&gt;
|8/3 0 5/7 -5/7&amp;gt;, |8/3 0 -2/7 2/7&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/5&lt;br /&gt;
&lt;br /&gt;
9-limit: [|1 0 0 0&amp;gt;, |10/7 6/7 0 -3/7&amp;gt;,&lt;br /&gt;
|46/21 5/7 0 -5/14&amp;gt;, |20/7 -2/7 0 1/7&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Tritikleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;11-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 441/440, 4000/3993&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |10/7 6/7 0 -3/7 0&amp;gt;, |46/21 5/7 0 -5/14 0&amp;gt;,&lt;br /&gt;
|20/7 -2/7 0 1/7 0&amp;gt;, |71/21 3/7 0 -3/14 0&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 3 10 8|, &amp;lt;0 6 5 -2 3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/231edo"&gt;231&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Tritikleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;13-limit&lt;/h2&gt;
Commas: 325/324, 364/363, 441/440, 625/624&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 3 10 8 0|, &amp;lt;0 6 5 -2 3 14|]&lt;br /&gt;
EDOs: 15, 72, 87, 159&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc52"&gt;&lt;a name="Tritikleismic-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;17-limit&lt;/h2&gt;
Commas: 273/272, 325/324, 364/363, 375/374, 385/384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 3 10 8 0 -2|, &amp;lt;0 6 5 -2 3 14 18|]&lt;br /&gt;
EDOs: 15g, 72, 87, 159&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc53"&gt;&lt;a name="Superkleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;Superkleismic&lt;/h1&gt;
Commas: 1029/1024, 875/864&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 321.930&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 5 2|, &amp;lt;0 -9 -10 3|]&lt;br /&gt;
EDOs: 11, 15, 26, 41&lt;br /&gt;
Badness: 0.0479&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc54"&gt;&lt;a name="Superkleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;11-limit&lt;/h2&gt;
Commas: 100/99, 245/242, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 321.847&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 5 2 4|, &amp;lt;0 -9 -10 3 -2|]&lt;br /&gt;
EDOs: 15, 26, 41, 261&lt;br /&gt;
Badness: 0.0257&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc55"&gt;&lt;a name="Superkleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;13-limit&lt;/h2&gt;
Commas: 100/99, 105/104, 245/243, 1188/1183&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 321.994&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 5 2 4 8|, &amp;lt;0 -9 -10 3 -2 -16|]&lt;br /&gt;
EDOs: 11, 15, 26, 41&lt;br /&gt;
Badness: 0.0215&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc56"&gt;&lt;a name="Gorgo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;Gorgo&lt;/h1&gt;
Commas: 36/35, 1029/1024&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 228.334&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 3|, &amp;lt;0 3 7 -1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 7 -1 4 -10 -22||&lt;br /&gt;
EDOs: 5, 16, 21&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:114:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc57"&gt;&lt;a name="Gorgo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:114 --&gt;11-limit&lt;/h2&gt;
Commas: 36/35, 56/55, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 229.535&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 3 5 |, &amp;lt;0 3 7 -1 -8|]&lt;br /&gt;
EDOs: 5, 16e, 21, 47c, 68bce&lt;br /&gt;
Badness: 0.0627&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:116:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc58"&gt;&lt;a name="Gorgo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:116 --&gt;13-limit&lt;/h2&gt;
Commas: 27/26, 36/35, 56/55, 507/500&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 229.059&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 3 5 2|, &amp;lt;0 3 7 -1 -8 9|]&lt;br /&gt;
EDOs 5, 21, 68bcef&lt;br /&gt;
Badness: 0.0471&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:118:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc59"&gt;&lt;a name="Gorgo-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:118 --&gt;Music&lt;/h2&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3" rel="nofollow"&gt;Gorgo Example&lt;/a&gt; by &lt;a class="wiki_link" href="/Herman%20Miller"&gt;Herman Miller&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:120:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc60"&gt;&lt;a name="Lemba"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:120 --&gt;Lemba&lt;/h1&gt;
Commas: 50/49, 525/512&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 232.089&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 2 5 6|, &amp;lt;3 -1 -1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 -2 -2 -17 -20 1||&lt;br /&gt;
EDOs: 10, 16, 26&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:122:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc61"&gt;&lt;a name="Lemba-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:122 --&gt;Music&lt;/h2&gt;
By &lt;a class="wiki_link" href="/Herman%20Miller"&gt;Herman Miller&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3" rel="nofollow"&gt;Lemba Galatsia&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3" rel="nofollow"&gt;GPO Lemba&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:124:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc62"&gt;&lt;a name="Gidorah"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:124 --&gt;Gidorah&lt;/h1&gt;
Commas: 21/20, 144/125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 230.762&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 3|, &amp;lt;0 3 2 -1|]&lt;br /&gt;
EDOs: 5, 11, 21, 26&lt;br /&gt;
Badness: 0.0623&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:126:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc63"&gt;&lt;a name="Clyndro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:126 --&gt;Clyndro&lt;/h1&gt;
Commas: 1029/1024, 135/128&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 226.469&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 4 3|, &amp;lt;0 3 -9 -1|]&lt;br /&gt;
EDOs: 16&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:128:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc64"&gt;&lt;a name="Necromanteion"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:128 --&gt;Necromanteion&lt;/h1&gt;
Commas: 1029/1024, 5103/5000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~48/35 = 541.779&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 7 10 1|, &amp;lt;0 -12 -17 4|]&lt;br /&gt;
EDOs: 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd&lt;br /&gt;
Badness: 0.1177&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:130:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc65"&gt;&lt;a name="Necromanteion-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:130 --&gt;11-limit&lt;/h2&gt;
Commas: 176/175, 243/242, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/11 = 541.729&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 7 10 1 17|, &amp;lt;0 -12 -17 4 -30|]&lt;br /&gt;
EDOs: 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde&lt;br /&gt;
Badness: 0.0535&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:132:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc66"&gt;&lt;a name="Necromanteion-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:132 --&gt;13-limit&lt;/h2&gt;
Commas: 144/143, 176/175, 243/242, 343/338&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/11 = 541.606&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 7 10 1 17 1|, &amp;lt;0 -12 -17 4 -30 6|]&lt;br /&gt;
EDOs: 31, 51ce, 82cf, 113cf, 144cf&lt;br /&gt;
Badness: 0.0470&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:134:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc67"&gt;&lt;a name="Widefourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:134 --&gt;Widefourth&lt;/h1&gt;
Commas: 1029/1024, 48828125/48771072&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3125/2304 = 524.210&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 16 8 -2|, &amp;lt;0 -33 -13 11|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;33 13 -11 -56 -110 -62||&lt;br /&gt;
EDOs: 16, 71, 87, 103, 190&lt;br /&gt;
Badness: 0.1541&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:136:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc68"&gt;&lt;a name="Widefourth-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:136 --&gt;11-limit&lt;/h2&gt;
Commas: 385/384, 441/440, 234375/234256&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3125/2304 = 524.210&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 16 8 -2 17|, &amp;lt;0 -33 -13 11 -31|]&lt;br /&gt;
EDOs: 16, 71, 87, 103, 190&lt;br /&gt;
Badness: 0.0408&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:138:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc69"&gt;&lt;a name="Widefourth-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:138 --&gt;13-limit&lt;/h2&gt;
Commas: 385/384, 441/440, 625/624, 847/845&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~65/48 = 524.209&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 16 8 -2 17 12|, &amp;lt;0 -33 -13 11 -31 -19|]&lt;br /&gt;
EDOs: 16, 71, 87, 103, 190&lt;br /&gt;
Badness: 0.0216&lt;/body&gt;&lt;/html&gt;</pre></div>
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