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No-fives subgroup temperaments: Difference between revisions

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== Temperaments with a 2.3.7 gene ==
== Temperaments with a 2.3.7 gene ==
=== Semaphore ===
See [[Semaphoresmic clan #Semaphore]].
=== Bleu ===
Bleu can be described as the {{nowrap| 8d & 9 }} temperament in the no-5 13-limit.
[[Subgroup]]: 2.3.7
[[Comma list]]: 17496/16807
{{Mapping|legend=2| 1 1 2 | 0 5 7 }}
{{Mapping|legend=3| 1 1 0 2 | 0 5 0 7 }}
: mapping generators: ~2, ~54/49
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.3538{{c}}, ~54/49 = 139.848{{c}}
: [[error map]]: {{val| -0.646 -3.736 +8.293 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~54/49 = 139.848{{c}}
: error map: {{val| 0.000 -3.270 +9.333 }}
{{Optimal ET sequence|legend=1| 8d, 9, 17, 43, 60d, 103d }}
[[Badness]] (Sintel): 2.48
==== 2.3.7.11 subgroup ====
Subgroup: 2.3.7.11
Comma list: 99/98, 864/847
Subgroup-val mapping: {{mapping| 1 1 2 3 | 0 5 7 4 }}
Gencom mapping: {{mapping| 1 1 0 2 3 | 0 5 0 7 4 }}
Optimal tunings:
* WE: ~2 = 1198.6613{{c}}, ~12/11 = 139.8489{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 139.7839{{c}}
{{Optimal ET sequence|legend=0| 8d, 9, 17, 43, 60d }}
Badness (Sintel): 0.624
==== 2.3.7.11.13 subgroup ====
Subgroup: 2.3.7.11.13
Comma list: 78/77, 99/98, 144/143
Subgroup-val mapping: {{mapping| 1 1 2 3 3 | 0 5 7 4 6 }}
Gencom mapping: {{mapping| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}
Optimal tunings:
* WE: ~2 = 1198.9768{{c}}, ~13/12 = 139.8704{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8166{{c}}
{{Optimal ET sequence|legend=0| 8d, 9, 17, 43, 60d }}
Badness (Sintel): 0.400
; Music
* ''On a Well Worn Riff'' (2011) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/on-a-well-worn-riff-bleu-17/ blog] | [https://web.archive.org/web/20201127014513/http://micro.soonlabel.com/temperaments/Bleu/20131103_2-11-13-subgroup-Bleu17_a-well-worn-riff.mp3 play] – in Bleu[17]
=== Archy ===
=== Archy ===
See [[Archytas clan #Archy]].  
See [[Archytas clan #Archy]].  
Line 109: Line 47:
Badness (Sintel): 1.28
Badness (Sintel): 1.28


=== Skwares ===
=== Semaphore ===
{{Main| Squares }}
See [[Semaphoresmic clan #Semaphore]].
 
=== Slendric ===
See [[Gamelismic clan #Slendric]].
 
=== Slendroschismic ===
See [[5th-octave temperaments #Slendroschismic]].
 
==== Pentadecoid ====
See [[15th-octave temperaments #Pentadecoid]].


Skwares is the no-5 [[restriction]] of [[squares]].  
=== Navy ===
This temperament is the common [[restriction]] of [[tsaharuk]] and [[quanic]].  


[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7


[[Comma list]]: 19683/19208
[[Comma list]]: 282429536481/281974669312


{{Mapping|legend=2| 1 -1 -3 | 0 4 9 }}
{{Mapping|legend=2| 1 1 0| 0 5 24 }}
 
: mapping generators: ~2, ~243/224
{{Mapping|legend=3| 1 -1 0 -3 | 0 4 0 9 }}
: mapping generators: ~2, ~14/9


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.3703{{c}}, ~14/9 = 774.8736{{c}}
* [[WE]]: ~2 = 1200.0302{{c}}, ~243/224 = 140.3698{{c}}
: [[error map]]: {{val| +0.370 -2.831 +3.925 }}
: [[error map]]: {{val| +0.030 -0.076 +0.050 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 774.6974{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/224 = 140.3681{{c}}
: error map: {{val| 0.000 -3.166 +3.450 }}
: error map: {{val| 0.000 -0.115 +0.008 }}


{{Optimal ET sequence|legend=1| 14, 17, 31, 48, 79 }}
{{Optimal ET sequence|legend=1| 17, 60, 77, 94, 171, 265, 436, 2351, 2787, 3223, 3659, 4095, 7754b }}


[[Badness]] (Sintel): 1.55
[[Badness]] (Sintel): 0.670


==== 2.3.7.11 ====
==== 2.3.7.11 ====
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11


Comma list: 99/98, 243/242
Comma list: 1331/1323, 19712/19683


Subgroup-val mapping: {{mapping| 1 -1 -3 -3 | 0 4 9 10 }}
Subgroup-val mapping: {{mapping| 1 1 0 1 | 0 5 24 21 }}
 
Gencom mapping: {{mapping| 1 -1 0 -3 -3 | 0 4 0 9 10 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.3726{{c}}, ~14/9 = 774.9970{{c}}
* WE: ~2 = 1200.1038{{c}}, ~88/81 = 140.4190{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.8197{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~88/81 = 140.4133{{c}}


{{Optimal ET sequence|legend=0| 14, 17, 31, 48, 79, 127 }}
{{Optimal ET sequence|legend=0| 17, 60e, 77, 94 }}


Badness (Sintel): 0.405
Badness (Sintel): 0.887


===== 2.3.7.11.13 =====
==== 2.3.7.11.13 ====
Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13


Comma list: 78/77, 99/98, 243/242
Comma list: 352/351, 729/728, 1331/1323


Subgroup-val mapping: {{mapping| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}
Subgroup-val mapping: {{mapping| 1 1 0 1 3 | 0 5 24 21 6 }}
 
Gencom mapping: {{mapping| 1 -1 0 -3 -3 -6 | 0 4 0 9 10 15}}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.3264{{c}}, ~14/9 = 775.1081{{c}}
* WE: ~2 = 1199.8640{{c}}, ~13/12 = 140.4206{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 775.4463{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.4292{{c}}


{{Optimal ET sequence|legend=0| 14f, 17, 48f }}
{{Optimal ET sequence|legend=0| 17, 60e, 77, 94 }}


Badness (Sintel): 0.587
Badness (Sintel): 0.520
 
===== Skwairs =====
Subgroup: 2.3.7.11.13
 
Comma list: 99/98, 144/143, 243/242
 
Subgroup-val mapping: {{mapping| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}
 
Gencom mapping: {{mapping| 1 -1 0 -3 -3 5 | 0 4 0 9 10 -2 }}
 
Optimal tunings:
* WE: ~2 = 1198.8812{{c}}, ~14/9 = 775.5748{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 775.1930{{c}}
 
{{Optimal ET sequence|legend=0| 14, 17, 31, 48, 65d, 113df }}
 
Badness (Sintel): 0.538
 
===== Byhearted =====
This temperament is the restriction of [[weasel]] to the 2.3.7.11.19 subgroup.
 
Subgroup: 2.3.7.11.19
 
Comma list: 99/98, 243/242, 363/361
 
Subgroup-val mapping: {{mapping| 2 2 3 4 5 | 0 4 9 10 12 }}
: mapping generators: ~209/147, ~21/19
 
Optimal tunings:
* WE: ~2 = 600.1836{{c}}, ~21/19 = 174.7882{{c}}
* CWE: ~2 = 600.0000{{c}}, ~21/19 = 174.7975{{c}}
 
{{Optimal ET sequence|legend=0| 14, 34dh, 48, 110e }}
 
Badness (Sintel): 0.893
 
=== Harrison ===
Harrison is the no-5 [[restriction]] of [[meantone]]. As such, there is little reason to consider this temperament in practice – since intervals of 5 in meantone are as accurate as intervals of 7, only simpler, they are always available by the time intervals of 7 are generated.


=== Lee ===
[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7


[[Comma list]]: [[59049/57344]]
[[Comma list]]: 177147/175616


{{Mapping|legend=2| 1 0 -13 | 0 1 10 }}
{{Mapping|legend=2| 1 0 -3 | 0 3 11 }}


{{Mapping|legend=3| 1 0 0 -13 | 0 1 0 10 }}
{{Mapping|legend=3| 1 0 0 -3 | 0 3 0 11 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~81/56


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1201.5353{{c}}, ~3/2 = 697.4352{{c}}
* [[WE]]: ~2 = 1200.2962{{c}}, ~81/56 = 633.6812{{c}}
: [[error map]]: {{val| +1.535 -2.984 +0.920 }}
: [[error map]]: {{val| +0.296 -0.912 +0.778 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.7289{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~81/56 = 633.5658{{c}}
: error map: {{val| 0.000 -5.226 -1.537 }}
: error map: {{val| 0.000 -1.258 +0.398 }}


{{Optimal ET sequence|legend=1| 12, 19, 31, 112b, 143b, 174b }}
{{Optimal ET sequence|legend=1| 17, 36, 89, 125, 161, 358, 519b }}


[[Badness]] (Sintel): 2.35
[[Badness]] (Sintel): 0.741


=== Leapfrog ===
=== Buzzard ===
{{See also| Gentle region }}
See [[Buzzardsmic clan #Buzzard]].


Leapfrog is generated by a [[3/2|perfect fifth]] and the [[interval class]] of [[7/1|7]] is found at +15 steps, as a double-augmented fifth (C–G𝄪). For this to work, it entails a fifth about 2–3 cents sharp of just; as a result the major third lands comfortably at a near-just [[14/11]] so that it can be extended to the [[2.3.7.11 subgroup]] via tempering out [[896/891]]. The minor third can then be identified with [[13/11]], tempering out [[352/351]] and [[364/363]], which implies [[169/168]] is tempered out as well in this case. Leapfrog is most naturally treated as such, in which it is very efficient.
=== Hemif ===
 
Hemif is the no-5 [[restriction]] of [[hemififths]], and the add-7 [[extension]] of [[namo]].  
A notable [[patent val|patent-val]] edo tuning not appearing in the [[optimal ET sequence]] is [[80edo]], which is approximately the just-13's tuning (as [[10edo]] is used as a [[consistent circle]] of [[~]][[16/13]]'s therein), with 13/8 still tuned slightly flat so qualifying a reasonable tuning for the 2.3.13 subgroup (as evidenced by appearing in the sequence for [[tetris]]).
 
Strong extensions for prime 5 include [[leapday]] (29 & 46), [[leapweek]] (46 & 63), and [[leapmonth]] (63 & 80), all of which are more complex than vanilla leapfrog. A low-complexity low-accuracy extension is given by [[supermean]] (5de & 17c), where it is merged with [[meantone]]. [[Srutal]] (46 & 80), usually considered as a strong extension of [[diaschismic]], is a weak extension of leapfrog, and yet another weak extension is [[immune]] (29 & 63), which is in turn a strong extension of 5-limit [[immunity]].  


[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7


[[Comma list]]: 14680064/14348907
[[Comma list]]: 1605632/1594323


{{Mapping|legend=2| 1 0 -21 | 0 1 15 }}
{{Mapping|legend=2| 1 1 -1 | 0 2 13 }}


{{Mapping|legend=3| 1 0 0 -21 | 0 1 0 15 }}
{{Mapping|legend=3| 1 1 0 -1 | 0 2 0 13 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~2187/1792


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.1807{{c}}, ~3/2 = 704.2400{{c}}
* [[WE]]: ~2 = 1199.7303{{c}}, ~2187/1792 = 351.4056{{c}}
: [[error map]]: {{val| -0.819 +1.466 -0.311 }}
: [[error map]]: {{val| -0.270 +0.586 -0.284 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.6600{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~2187/1792 = 351.4569{{c}}
: error map: {{val| 0.000 +2.705 +1.074 }}
: error map: {{val| 0.000 +0.959 +0.114 }}


{{Optimal ET sequence|legend=1| 17, 46, 63, 235b, 298b, 361bd, 424bd, 487bbd }}
{{Optimal ET sequence|legend=1| 17, 41, 58, 99, 239, 338, 437, 775b, 1212bb }}


[[Badness]] (Sintel): 4.33
[[Badness]] (Sintel): 0.901


==== 2.3.7.11 ====
==== 2.3.7.11 ====
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11


Comma list: 896/891, 1331/1323
Comma list: 243/242, 896/891


Subgroup-val mapping: {{mapping| 1 0 -21 -14 | 0 1 15 11 }}
Subgroup-val mapping: {{mapping| 1 1 -1 2 | 0 2 13 5 }}


Gencom mapping: {{mapping| 1 0 0 -21 -14 | 0 1 0 15 11 }}
Gencom mapping: {{mapping| 1 1 0 -1 2 | 0 2 0 13 5 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.2683{{c}}, ~3/2 = 704.3230{{c}}
* WE: ~2 = 1199.2633{{c}}, ~11/9 = 351.3189{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.6926{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4593{{c}}


{{Optimal ET sequence|legend=0| 17, 46, 63 }}
{{Optimal ET sequence|legend=0| 17, 41, 58, 99e }}


Badness (Sintel): 0.629
Badness (Sintel): 0.409


==== 2.3.7.11.13 ====
===== 2.3.7.11.13 =====
Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13


Comma list: 169/168, 352/351, 364/363
Comma list: 144/143, 243/242, 364/363


Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 | 0 1 15 11 8 }}
Sval mapping: {{mapping| 1 1 -1 2 4 | 0 2 13 5 -1 }}


Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 | 0 1 0 15 11 8 }}
Gencom mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 0 13 5 -1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.5654{{c}}, ~3/2 = 704.4898{{c}}
* WE: ~2 = 1198.7603{{c}}, ~11/9 = 351.3275{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.7084{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.6042{{c}}


{{Optimal ET sequence|legend=0| 17, 46, 63 }}
{{Optimal ET sequence|legend=0| 17, 41, 58, 331deeeffff }}


Badness (Sintel): 0.436
Badness (Sintel): 0.358


===== Skidoo =====
===== Heartful =====
Subgroup: 2.3.7.11.13.23
{{See also| Heartland }}


Comma list: 169/168, 208/207, 352/351, 364/363
Related temperaments: [[bunya]].


Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}
Subgroup: 2.3.7.11.19


Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 0 0 -5 | 0 1 0 15 11 8 0 0 6 }}
Comma list: 243/242, 896/891, 1083/1078


Optimal tunings:
Subgroup-val mapping: {{mapping| 1 1 -1 2 0 | 0 4 26 10 29 }}
* WE: ~2 = 1199.6639{{c}}, ~3/2 = 704.5315{{c}}
: mapping generators: ~2, ~21/19
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.7021{{c}}
 
{{Optimal ET sequence|legend=0| 17, 46, 63 }}
 
Badness (Sintel): 0.356
 
====== 2.3.7.11.13.23.29 ======
Subgroup: 2.3.7.11.13.23.29
 
Comma list: 169/168, 208/207, 232/231, 352/351, 364/363
 
Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}
 
Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 -5 0 0 -38 | 0 1 0 15 11 8 0 0 6 27 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.5755{{c}}, ~3/2 = 704.5533{{c}}
* WE: ~2 = 1199.2636{{c}}, ~21/19 = 175.6963{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.7750{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.7665{{c}}


{{Optimal ET sequence|legend=0| 17, 46, 63 }}
{{Optimal ET sequence|legend=0| 34dh, 41, 116e, 157e }}


Badness (Sintel): 0.441
Badness (Sintel): 0.984


; Music
=== Hearts ===
* Suite for Harpsichord in A Locrian, tuning: Eb–G# in [[46edo]] by [[Inthar]] (in progress):
** I. Prelude
** II. Allemande
** III. Courante
** [[:File:Locrian Suite Sarabande.mp3|IV. Sarabande]] ([[:File:Locrian Suite Sarabande Score.pdf|score]], [[:File:Locrian Suite Sarabande 17edo.mp3|17edo version]])
** [[:File:Locrian Suite Menuet.mp3|V. Menuet and Trio]]
** [[:File:Locrian Suite Gavotte.mp3|VI. Gavotte I and II]]
** [[:File:Locrian Suite Gigue.mp3|VII. Gigue]]
 
=== Doublehearted ===
{{See also| Heartland }}
{{See also| Heartland }}


This temperament is the no-5 [[restriction]] of [[octacot]].  
This temperament is the common [[restriction]] of [[monkey]] and [[sesquiquartififths]].  


[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7


[[Comma list]]: 5764801/5668704
[[Comma list]]: 34451725707/34359738368


{{Mapping|legend=2| 1 1 2 | 0 8 11 }}
{{Mapping|legend=2| 1 1 5 | 0 4 -15 }}
: mapping generators: ~2, ~343/342
: mapping generators: ~2, ~567/512


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0000{{c}}, ~343/324 = 87.8431{{c}}
* [[WE]]: ~2 = 1200.0845{{c}}, ~567/512 = 175.4449{{c}}
: [[error map]]: {{val| +0.174 +0.964 -2.204 }}
: [[error map]]: {{val| +0.085 -0.091 -0.076 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/324 = 87.8492{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~567/512 = 175.4307{{c}}
: error map: {{val| 0.000 +0.838 -2.485 }}
: error map: {{val| 0.000 -0.232 -0.286 }}


{{Optimal ET sequence|legend=1| 14, 27, 41 }}
{{Optimal ET sequence|legend=1| 7, 27d, 34, 41, 89, 130, 171, 643, 814, 985, 1156 }}


[[Badness]] (Sintel): 2.62
[[Badness]] (Sintel): 0.959


==== 2.3.7.11 ====
==== 2.3.7.11 ====
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11


Comma list: 243/242, 2401/2376
Comma list: 243/242, 65536/65219


Subgroup-val mapping: {{mapping| 1 1 2 2 | 0 8 11 20 }}
Subgroup-val mapping: {{mapping| 1 1 5 2 | 0 4 -15 10 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.4071{{c}}, ~22/21 = 87.6809{{c}}
* WE: ~2 = 1199.8467{{c}}, ~256/231 = 175.3468{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 87.6902{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~256/231 = 175.3691{{c}}


{{Optimal ET sequence|legend=0| 14, 27e, 41, 96d, 137d, 178d }}
{{Optimal ET sequence|legend=0| 7, 34, 41, 89, 130, 349e, 479e }}


Badness (Sintel): 0.815
Badness (Sintel): 0.801


==== 2.3.7.11.19 ====
==== 2.3.7.11.19 ====
Subgroup: 2.3.7.11.19
Subgroup: 2.3.7.11.19


Comma list: 133/132, 243/242, 343/342
Comma list: 243/242, 513/512, 1083/1078


Subgroup-val mapping: {{mapping| 1 1 2 2 3 | 0 8 11 20 17 }}
Subgroup-val mapping: {{mapping| 1 1 5 2 6 | 0 4 -15 10 -12 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.6100{{c}}, ~19/18 = 87.7129{{c}}
* WE: ~2 = 1199.9531{{c}}, ~21/19 = 175.3344{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~19/18 = 87.7285{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.3417{{c}}


{{Optimal ET sequence|legend=0| 14, 27e, 41, 137dh }}
{{Optimal ET sequence|legend=0| 7, 34, 41, 89, 130, 219 }}


Badness (Sintel): 0.560
Badness (Sintel): 0.529


=== Magi ===
=== Magi ===
Line 493: Line 371:
Badness (Sintel): 0.424
Badness (Sintel): 0.424


=== Lee ===
=== Skwares ===
{{Main| Squares }}
 
Skwares is the no-5 [[restriction]] of [[squares]].
 
[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7


[[Comma list]]: 177147/175616
[[Comma list]]: 19683/19208


{{Mapping|legend=2| 1 0 -3 | 0 3 11 }}
{{Mapping|legend=2| 1 -1 -3 | 0 4 9 }}


{{Mapping|legend=3| 1 0 0 -3 | 0 3 0 11 }}
{{Mapping|legend=3| 1 -1 0 -3 | 0 4 0 9 }}
: mapping generators: ~2, ~81/56
: mapping generators: ~2, ~14/9


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.2962{{c}}, ~81/56 = 633.6812{{c}}
* [[WE]]: ~2 = 1200.3703{{c}}, ~14/9 = 774.8736{{c}}
: [[error map]]: {{val| +0.296 -0.912 +0.778 }}
: [[error map]]: {{val| +0.370 -2.831 +3.925 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~81/56 = 633.5658{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 774.6974{{c}}
: error map: {{val| 0.000 -1.258 +0.398 }}
: error map: {{val| 0.000 -3.166 +3.450 }}
 
{{Optimal ET sequence|legend=1| 14, 17, 31, 48, 79 }}
 
[[Badness]] (Sintel): 1.55
 
==== 2.3.7.11 ====
Subgroup: 2.3.7.11
 
Comma list: 99/98, 243/242


{{Optimal ET sequence|legend=1| 17, 36, 89, 125, 161, 358, 519b }}
Subgroup-val mapping: {{mapping| 1 -1 -3 -3 | 0 4 9 10 }}


[[Badness]] (Sintel): 0.741
Gencom mapping: {{mapping| 1 -1 0 -3 -3 | 0 4 0 9 10 }}


=== Buzzard ===
Optimal tunings:
See [[Buzzardsmic clan #Buzzard]].  
* WE: ~2 = 1200.3726{{c}}, ~14/9 = 774.9970{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.8197{{c}}


=== Slendric ===
{{Optimal ET sequence|legend=0| 14, 17, 31, 48, 79, 127 }}
See [[Gamelismic clan #Slendric]].


=== Hemif ===
Badness (Sintel): 0.405
Hemif is the no-5 [[restriction]] of [[hemififths]], and the add-7 [[extension]] of [[namo]].  


[[Subgroup]]: 2.3.7
===== 2.3.7.11.13 =====
Subgroup: 2.3.7.11.13


[[Comma list]]: 1605632/1594323
Comma list: 78/77, 99/98, 243/242


{{Mapping|legend=2| 1 1 -1 | 0 2 13 }}
Subgroup-val mapping: {{mapping| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}


{{Mapping|legend=3| 1 1 0 -1 | 0 2 0 13 }}
Gencom mapping: {{mapping| 1 -1 0 -3 -3 -6 | 0 4 0 9 10 15}}
: mapping generators: ~2, ~2187/1792


[[Optimal tuning]]s:  
Optimal tunings:  
* [[WE]]: ~2 = 1199.7303{{c}}, ~2187/1792 = 351.4056{{c}}
* WE: ~2 = 1199.3264{{c}}, ~14/9 = 775.1081{{c}}
: [[error map]]: {{val| -0.270 +0.586 -0.284 }}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 775.4463{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~2187/1792 = 351.4569{{c}}
: error map: {{val| 0.000 +0.959 +0.114 }}


{{Optimal ET sequence|legend=1| 17, 41, 58, 99, 239, 338, 437, 775b, 1212bb }}
{{Optimal ET sequence|legend=0| 14f, 17, 48f }}


[[Badness]] (Sintel): 0.901
Badness (Sintel): 0.587


==== 2.3.7.11 ====
===== Skwairs =====
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11.13


Comma list: 243/242, 896/891
Comma list: 99/98, 144/143, 243/242


Subgroup-val mapping: {{mapping| 1 1 -1 2 | 0 2 13 5 }}
Subgroup-val mapping: {{mapping| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}


Gencom mapping: {{mapping| 1 1 0 -1 2 | 0 2 0 13 5 }}
Gencom mapping: {{mapping| 1 -1 0 -3 -3 5 | 0 4 0 9 10 -2 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.2633{{c}}, ~11/9 = 351.3189{{c}}
* WE: ~2 = 1198.8812{{c}}, ~14/9 = 775.5748{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4593{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 775.1930{{c}}


{{Optimal ET sequence|legend=0| 17, 41, 58, 99e }}
{{Optimal ET sequence|legend=0| 14, 17, 31, 48, 65d, 113df }}


Badness (Sintel): 0.409
Badness (Sintel): 0.538


===== 2.3.7.11.13 =====
===== Byhearted =====
Subgroup: 2.3.7.11.13
This temperament is the restriction of [[weasel]] to the 2.3.7.11.19 subgroup.


Comma list: 144/143, 243/242, 364/363
Subgroup: 2.3.7.11.19


Sval mapping: {{mapping| 1 1 -1 2 4 | 0 2 13 5 -1 }}
Comma list: 99/98, 243/242, 363/361


Gencom mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 0 13 5 -1 }}
Subgroup-val mapping: {{mapping| 2 2 3 4 5 | 0 4 9 10 12 }}
: mapping generators: ~209/147, ~21/19


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.7603{{c}}, ~11/9 = 351.3275{{c}}
* WE: ~2 = 600.1836{{c}}, ~21/19 = 174.7882{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.6042{{c}}
* CWE: ~2 = 600.0000{{c}}, ~21/19 = 174.7975{{c}}


{{Optimal ET sequence|legend=0| 17, 41, 58, 331deeeffff }}
{{Optimal ET sequence|legend=0| 14, 34dh, 48, 110e }}


Badness (Sintel): 0.358
Badness (Sintel): 0.893


===== Heartful =====
=== Harrison ===
{{See also| Heartland }}
Harrison is the no-5 [[restriction]] of [[meantone]]. As such, there is little reason to consider this temperament in practice – since intervals of 5 in meantone are as accurate as intervals of 7, only simpler, they are always available by the time intervals of 7 are generated.


Related temperaments: [[bunya]].  
[[Subgroup]]: 2.3.7


Subgroup: 2.3.7.11.19
[[Comma list]]: [[59049/57344]]


Comma list: 243/242, 896/891, 1083/1078
{{Mapping|legend=2| 1 0 -13 | 0 1 10 }}


Subgroup-val mapping: {{mapping| 1 1 -1 2 0 | 0 4 26 10 29 }}
{{Mapping|legend=3| 1 0 0 -13 | 0 1 0 10 }}
: mapping generators: ~2, ~21/19
: mapping generators: ~2, ~3


Optimal tunings:  
[[Optimal tuning]]s:  
* WE: ~2 = 1199.2636{{c}}, ~21/19 = 175.6963{{c}}
* [[WE]]: ~2 = 1201.5353{{c}}, ~3/2 = 697.4352{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.7665{{c}}
: [[error map]]: {{val| +1.535 -2.984 +0.920 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.7289{{c}}
: error map: {{val| 0.000 -5.226 -1.537 }}


{{Optimal ET sequence|legend=0| 34dh, 41, 116e, 157e }}
{{Optimal ET sequence|legend=1| 12, 19, 31, 112b, 143b, 174b }}


Badness (Sintel): 0.984
[[Badness]] (Sintel): 2.35


=== Hearts ===
=== Bleu ===
{{See also| Heartland }}
Bleu can be described as the {{nowrap| 8d & 9 }} temperament in the no-5 13-limit.


This temperament is the common [[restriction]] of [[monkey]] and [[sesquiquartififths]].  
[[Subgroup]]: 2.3.7


[[Subgroup]]: 2.3.7
[[Comma list]]: 17496/16807


[[Comma list]]: 34451725707/34359738368
{{Mapping|legend=2| 1 1 2 | 0 5 7 }}


{{Mapping|legend=2| 1 1 5 | 0 4 -15 }}
{{Mapping|legend=3| 1 1 0 2 | 0 5 0 7 }}
: mapping generators: ~2, ~567/512
: mapping generators: ~2, ~54/49


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0845{{c}}, ~567/512 = 175.4449{{c}}
* [[WE]]: ~2 = 1199.3538{{c}}, ~54/49 = 139.848{{c}}
: [[error map]]: {{val| +0.085 -0.091 -0.076 }}
: [[error map]]: {{val| -0.646 -3.736 +8.293 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~567/512 = 175.4307{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~54/49 = 139.848{{c}}
: error map: {{val| 0.000 -0.232 -0.286 }}
: error map: {{val| 0.000 -3.270 +9.333 }}


{{Optimal ET sequence|legend=1| 7, 27d, 34, 41, 89, 130, 171, 643, 814, 985, 1156 }}
{{Optimal ET sequence|legend=1| 8d, 9, 17, 43, 60d, 103d }}


[[Badness]] (Sintel): 0.959
[[Badness]] (Sintel): 2.48


==== 2.3.7.11 ====
==== 2.3.7.11 subgroup ====
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11


Comma list: 243/242, 65536/65219
Comma list: 99/98, 864/847
 
Subgroup-val mapping: {{mapping| 1 1 2 3 | 0 5 7 4 }}


Subgroup-val mapping: {{mapping| 1 1 5 2 | 0 4 -15 10 }}
Gencom mapping: {{mapping| 1 1 0 2 3 | 0 5 0 7 4 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.8467{{c}}, ~256/231 = 175.3468{{c}}
* WE: ~2 = 1198.6613{{c}}, ~12/11 = 139.8489{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~256/231 = 175.3691{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 139.7839{{c}}
 
{{Optimal ET sequence|legend=0| 8d, 9, 17, 43, 60d }}


{{Optimal ET sequence|legend=0| 7, 34, 41, 89, 130, 349e, 479e }}
Badness (Sintel): 0.624


Badness (Sintel): 0.801
==== 2.3.7.11.13 subgroup ====
Subgroup: 2.3.7.11.13


==== 2.3.7.11.19 ====
Comma list: 78/77, 99/98, 144/143
Subgroup: 2.3.7.11.19


Comma list: 243/242, 513/512, 1083/1078
Subgroup-val mapping: {{mapping| 1 1 2 3 3 | 0 5 7 4 6 }}


Subgroup-val mapping: {{mapping| 1 1 5 2 6 | 0 4 -15 10 -12 }}
Gencom mapping: {{mapping| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9531{{c}}, ~21/19 = 175.3344{{c}}
* WE: ~2 = 1198.9768{{c}}, ~13/12 = 139.8704{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.3417{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8166{{c}}
 
{{Optimal ET sequence|legend=0| 8d, 9, 17, 43, 60d }}
 
Badness (Sintel): 0.400


{{Optimal ET sequence|legend=0| 7, 34, 41, 89, 130, 219 }}
; Music
* ''On a Well Worn Riff'' (2011) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/on-a-well-worn-riff-bleu-17/ blog] | [https://web.archive.org/web/20201127014513/http://micro.soonlabel.com/temperaments/Bleu/20131103_2-11-13-subgroup-Bleu17_a-well-worn-riff.mp3 play] – in Bleu[17]


Badness (Sintel): 0.529
=== Doublehearted ===
{{See also| Heartland }}


=== Navy ===
This temperament is the no-5 [[restriction]] of [[octacot]].  
This temperament is the common [[restriction]] of [[tsaharuk]] and [[quanic]].  


[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7


[[Comma list]]: 282429536481/281974669312
[[Comma list]]: 5764801/5668704


{{Mapping|legend=2| 1 1 0| 0 5 24 }}
{{Mapping|legend=2| 1 1 2 | 0 8 11 }}
: mapping generators: ~2, ~243/224
: mapping generators: ~2, ~343/342


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0302{{c}}, ~243/224 = 140.3698{{c}}
* [[WE]]: ~2 = 1200.0000{{c}}, ~343/324 = 87.8431{{c}}
: [[error map]]: {{val| +0.030 -0.076 +0.050 }}
: [[error map]]: {{val| +0.174 +0.964 -2.204 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/224 = 140.3681{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/324 = 87.8492{{c}}
: error map: {{val| 0.000 -0.115 +0.008 }}
: error map: {{val| 0.000 +0.838 -2.485 }}


{{Optimal ET sequence|legend=1| 17, 60, 77, 94, 171, 265, 436, 2351, 2787, 3223, 3659, 4095, 7754b }}
{{Optimal ET sequence|legend=1| 14, 27, 41 }}


[[Badness]] (Sintel): 0.670
[[Badness]] (Sintel): 2.62


==== 2.3.7.11 ====
==== 2.3.7.11 ====
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11


Comma list: 1331/1323, 19712/19683
Comma list: 243/242, 2401/2376


Subgroup-val mapping: {{mapping| 1 1 0 1 | 0 5 24 21 }}
Subgroup-val mapping: {{mapping| 1 1 2 2 | 0 8 11 20 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.1038{{c}}, ~88/81 = 140.4190{{c}}
* WE: ~2 = 1200.4071{{c}}, ~22/21 = 87.6809{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~88/81 = 140.4133{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 87.6902{{c}}


{{Optimal ET sequence|legend=0| 17, 60e, 77, 94 }}
{{Optimal ET sequence|legend=0| 14, 27e, 41, 96d, 137d, 178d }}


Badness (Sintel): 0.887
Badness (Sintel): 0.815


==== 2.3.7.11.13 ====
==== 2.3.7.11.19 ====
Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.19


Comma list: 352/351, 729/728, 1331/1323
Comma list: 133/132, 243/242, 343/342


Subgroup-val mapping: {{mapping| 1 1 0 1 3 | 0 5 24 21 6 }}
Subgroup-val mapping: {{mapping| 1 1 2 2 3 | 0 8 11 20 17 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.8640{{c}}, ~13/12 = 140.4206{{c}}
* WE: ~2 = 1200.6100{{c}}, ~19/18 = 87.7129{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.4292{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~19/18 = 87.7285{{c}}
 
{{Optimal ET sequence|legend=0| 14, 27e, 41, 137dh }}
 
Badness (Sintel): 0.560
 
=== Purpleheart ===
{{See also| Whitewood }}
 
[[Subgroup]]: 2.3.7
 
[[Comma list]]: 2187/2048
 
{{Mapping|legend=2| 7 11 0 | 0 0 1 }}
: mapping generators: ~9/8, ~7
 
[[Optimal tuning]]s:
* [[WE]]: ~9/8 = 172.1541{{c}}, ~7/4 = 958.5433{{c}} (~64/63 = 74.3805{{c}})
: [[error map]]: {{val| +5.079 -8.260 -0.124 }}
* [[CWE]]: ~9/8 = 171.4286{{c}}, ~7/4 = 959.2372{{c}} (~64/63 = 69.3373{{c}})
: error map: {{val| 0.000 -16.241 -9.589 }}


{{Optimal ET sequence|legend=0| 17, 60e, 77, 94 }}
{{Optimal ET sequence|legend=1| 7, 14, 35, 49bd }}


Badness (Sintel): 0.520
[[Badness]] (Sintel): 3.00


=== Chrysanthemum ===
=== Chrysanthemum ===
Line 732: Line 652:
Badness (Sintel): 0.324
Badness (Sintel): 0.324


=== Slendroschismic ===
=== Leapfrog ===
See [[5th-octave temperaments #Slendroschismic]].  
{{See also| Gentle region }}
 
Leapfrog is generated by a [[3/2|perfect fifth]] and the [[interval class]] of [[7/1|7]] is found at +15 steps, as a double-augmented fifth (C–G𝄪). For this to work, it entails a fifth about 2–3 cents sharp of just; as a result the major third lands comfortably at a near-just [[14/11]] so that it can be extended to the [[2.3.7.11 subgroup]] via tempering out [[896/891]]. The minor third can then be identified with [[13/11]], tempering out [[352/351]] and [[364/363]], which implies [[169/168]] is tempered out as well in this case. Leapfrog is most naturally treated as such, in which it is very efficient.
 
A notable [[patent val|patent-val]] edo tuning not appearing in the [[optimal ET sequence]] is [[80edo]], which is approximately the just-13's tuning (as [[10edo]] is used as a [[consistent circle]] of [[~]][[16/13]]'s therein), with 13/8 still tuned slightly flat so qualifying a reasonable tuning for the 2.3.13 subgroup (as evidenced by appearing in the sequence for [[tetris]]).
 
Strong extensions for prime 5 include [[leapday]] (29 & 46), [[leapweek]] (46 & 63), and [[leapmonth]] (63 & 80), all of which are more complex than vanilla leapfrog. A low-complexity low-accuracy extension is given by [[supermean]] (5de & 17c), where it is merged with [[meantone]]. [[Srutal]] (46 & 80), usually considered as a strong extension of [[diaschismic]], is a weak extension of leapfrog, and yet another weak extension is [[immune]] (29 & 63), which is in turn a strong extension of 5-limit [[immunity]].
 
[[Subgroup]]: 2.3.7
 
[[Comma list]]: 14680064/14348907
 
{{Mapping|legend=2| 1 0 -21 | 0 1 15 }}
 
{{Mapping|legend=3| 1 0 0 -21 | 0 1 0 15 }}
: mapping generators: ~2, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.1807{{c}}, ~3/2 = 704.2400{{c}}
: [[error map]]: {{val| -0.819 +1.466 -0.311 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.6600{{c}}
: error map: {{val| 0.000 +2.705 +1.074 }}
 
{{Optimal ET sequence|legend=1| 17, 46, 63, 235b, 298b, 361bd, 424bd, 487bbd }}
 
[[Badness]] (Sintel): 4.33
 
==== 2.3.7.11 ====
Subgroup: 2.3.7.11
 
Comma list: 896/891, 1331/1323
 
Subgroup-val mapping: {{mapping| 1 0 -21 -14 | 0 1 15 11 }}
 
Gencom mapping: {{mapping| 1 0 0 -21 -14 | 0 1 0 15 11 }}
 
Optimal tunings:
* WE: ~2 = 1199.2683{{c}}, ~3/2 = 704.3230{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.6926{{c}}
 
{{Optimal ET sequence|legend=0| 17, 46, 63 }}
 
Badness (Sintel): 0.629
 
==== 2.3.7.11.13 ====
Subgroup: 2.3.7.11.13
 
Comma list: 169/168, 352/351, 364/363
 
Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 | 0 1 15 11 8 }}
 
Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 | 0 1 0 15 11 8 }}
 
Optimal tunings:
* WE: ~2 = 1199.5654{{c}}, ~3/2 = 704.4898{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.7084{{c}}
 
{{Optimal ET sequence|legend=0| 17, 46, 63 }}
 
Badness (Sintel): 0.436
 
===== Skidoo =====
Subgroup: 2.3.7.11.13.23
 
Comma list: 169/168, 208/207, 352/351, 364/363
 
Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}
 
Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 0 0 -5 | 0 1 0 15 11 8 0 0 6 }}
 
Optimal tunings:
* WE: ~2 = 1199.6639{{c}}, ~3/2 = 704.5315{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.7021{{c}}
 
{{Optimal ET sequence|legend=0| 17, 46, 63 }}
 
Badness (Sintel): 0.356
 
====== 2.3.7.11.13.23.29 ======
Subgroup: 2.3.7.11.13.23.29
 
Comma list: 169/168, 208/207, 232/231, 352/351, 364/363
 
Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}
 
Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 -5 0 0 -38 | 0 1 0 15 11 8 0 0 6 27 }}
 
Optimal tunings:
* WE: ~2 = 1199.5755{{c}}, ~3/2 = 704.5533{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.7750{{c}}
 
{{Optimal ET sequence|legend=0| 17, 46, 63 }}
 
Badness (Sintel): 0.441
 
; Music
* Suite for Harpsichord in A Locrian, tuning: Eb–G# in [[46edo]] by [[Inthar]] (in progress):
** I. Prelude
** II. Allemande
** III. Courante
** [[:File:Locrian Suite Sarabande.mp3|IV. Sarabande]] ([[:File:Locrian Suite Sarabande Score.pdf|score]], [[:File:Locrian Suite Sarabande 17edo.mp3|17edo version]])
** [[:File:Locrian Suite Menuet.mp3|V. Menuet and Trio]]
** [[:File:Locrian Suite Gavotte.mp3|VI. Gavotte I and II]]
** [[:File:Locrian Suite Gigue.mp3|VII. Gigue]]
 
=== Superslendric ===
In superslendric, eight [[8/7]]'s are equated to [[3/1]]. This relates it to [[8edt]].
 
[[Subgroup]]: 2.3.7
 
[[Comma list]]: 17294403/16777216
 
{{Mapping|legend=2| 1 0 3 | 0 8 -1 }}
: mapping generators: ~2, ~8/7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.1628{{c}}, ~8/7 = 237.7287{{c}}
: [[error map]]: {{val| +1.163 -0.125 -3.066 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 237.5664{{c}}
: error map: {{val| 0.000 -1.424 -6.392 }}
 
{{Optimal ET sequence|legend=1| 5, …, 66b, 71b, 76, 81, 86, 91, 96d }}


==== Pentadecoid ====
[[Badness]] (Sintel): 6.15
See [[15th-octave temperaments #Pentadecoid]].  


=== Hectosaros leap week ===
=== Hectosaros leap week ===
Line 802: Line 842:


Badness (Sintel): 7.46
Badness (Sintel): 7.46
=== Purpleheart ===
{{See also| Whitewood }}
[[Subgroup]]: 2.3.7
[[Comma list]]: 2187/2048
{{Mapping|legend=2| 7 11 0 | 0 0 1 }}
: mapping generators: ~9/8, ~7
[[Optimal tuning]]s:
* [[WE]]: ~9/8 = 172.1541{{c}}, ~7/4 = 958.5433{{c}} (~64/63 = 74.3805{{c}})
: [[error map]]: {{val| +5.079 -8.260 -0.124 }}
* [[CWE]]: ~9/8 = 171.4286{{c}}, ~7/4 = 959.2372{{c}} (~64/63 = 69.3373{{c}})
: error map: {{val| 0.000 -16.241 -9.589 }}
{{Optimal ET sequence|legend=1| 7, 14, 35, 49bd }}
[[Badness]] (Sintel): 3.00
=== Superslendric ===
In superslendric, eight [[8/7]]'s are equated to [[3/1]]. This relates it to [[8edt]].
[[Subgroup]]: 2.3.7
[[Comma list]]: 17294403/16777216
{{Mapping|legend=2| 1 0 3 | 0 8 -1 }}
: mapping generators: ~2, ~8/7
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.1628{{c}}, ~8/7 = 237.7287{{c}}
: [[error map]]: {{val| +1.163 -0.125 -3.066 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 237.5664{{c}}
: error map: {{val| 0.000 -1.424 -6.392 }}
{{Optimal ET sequence|legend=1| 5, …, 66b, 71b, 76, 81, 86, 91, 96d }}
[[Badness]] (Sintel): 6.15


=== Heartland (rank 3) ===
=== Heartland (rank 3) ===
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