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The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic_semitone|chromatic semitone]]. Its [[monzo]] is |-3 -1 2>, and flipping that yields <<2 1 -3|| for the [[wedgie]]. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are [[7edo]], [[24edo]] using the val <24 38 55| (24c) and [[31edo]] using the val <31 49 71| (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all.
{{Technical data page}}
The '''dicot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[25/24]], the classical chromatic semitone.  


==Seven limit children==
== Dicot ==
The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot, with wedgie <<2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie <<2 1 6 -3 4 11|| adds 28/27, and dichotic with wedgie <<2 1 -4 -3 -12 -12|| ads 64/63, all retaining the same period and generator. Decimal with wedgie <<4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie <<4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie <<0 0 7 0 11 16|| adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.
The head of this family, dicot, is [[generator|generated]] by a classical third (major and minor mean the same thing), and two such thirds give a fifth. In fact, {{nowrap|(5/4)<sup>2</sup> {{=}} (3/2)(25/24)}}. Its [[ploidacot]] is the same as its name, dicot.  


=Dicot=
Possible tunings for dicot are [[7edo]], [[10edo]], [[17edo]], [[24edo]] using the val {{val| 24 38 55 }} (24c), and [[31edo]] using the val {{val| 31 49 71 }} (31c). In a sense, what dicot is all about is using neutral thirds and sixths and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", dicot is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].
Comma: 25/24


POTE generator: ~5/4 = 348.594
[[Subgroup]]: 2.3.5


Map: [&lt;1 1 2|, &lt;0 2 1|]
[[Comma list]]: 25/24


EDOs: [[3edo|3]], [[4edo|4]], [[7edo|7]], [[10edo|10]], [[13edo|13]], [[17edo|17]], [[23edo|23b]], [[24edo|24c]], [[27edo|27c]], [[31edo|31c]]
{{Mapping|legend=1| 1 1 2 | 0 2 1 }}


Badness: 0.0130
: mapping generators: ~2, ~5/4


==7-limit==
[[Optimal tuning]]s:
[[Comma]]s: 15/14, 25/24
* [[WE]]: ~2 = 1206.283{{c}}, ~6/5 = 350.420{{c}}
: [[error map]]: {{val| +6.283 +5.167 -23.328 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 351.086{{c}}
: error map: {{val| 0.000 +0.216 -35.228 }}


[[POTE_tuning|POTE generator]]: ~5/4 = 336.381
[[Tuning ranges]]:
* [[5-odd-limit]] [[diamond monotone]]: ~5/4 = [300.000, 400.000] (1\4 to 1\3)
* 5-odd-limit [[diamond tradeoff]]: ~5/4 = [315.641, 386.314] (full comma to untempered)


Map: [&lt;1 1 2 2|, &lt;0 2 1 3|]
{{Optimal ET sequence|legend=1| 3, 4, 7, 17, 24c, 31c }}


Wedgie: &lt;&lt;2 1 3 -3 -1 4||
[[Badness]] (Sintel): 0.306


EDOs: 3d, 4, 7, [[11edo|11c]], [[18edo|18bc]], [[25edo|25bccd]]
=== Overview to extensions ===
The second comma of the [[normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot adds [[36/35]], flattie adds [[21/20]], sharpie adds [[28/27]], and dichotic adds [[64/63]], all retaining the same period and generator.


Badness: 0.0199
Decimal adds [[49/48]], sidi adds [[245/243]], and jamesbond adds [[16/15]]. Here decimal divides the [[period]] to a [[sqrt(2)|semi-octave]], and sidi uses 14/9 as a generator, with two of them making up the combined 5/2~12/5 neutral tenth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.


==11-limit==
Temperaments discussed elsewhere are:
Commas: 15/14, 22/21, 25/24
* ''[[Geryon]]'' → [[Very low accuracy temperaments #Geryon|Very low accuracy temperaments]]
* ''[[Jamesbond]]'' → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]]


POTE generator: ~5/4 = 342.125
The rest are considered below.  


Map: [&lt;1 1 2 2 2|, &lt;0 2 1 3 5|]
=== 2.3.5.11 subgroup ===
The 2.3.5.11-subgroup extension maps [[11/9]]~[[27/22]] to the neutral third. As such, it is related to most of the septimal extensions.


EDOs: 3de, 4e, 7
Subgroup: 2.3.5.11


Badness: 0.0199
Comma list: 25/24, 45/44


==Eudicot==
Subgroup val mapping: {{mapping| 1 1 2 2 | 0 2 1 5 }}
Commas: 15/14, 25/24, 33/32


POTE generator: ~5/4 = 336.051
Gencom mapping: {{mapping| 1 1 2 0 2 | 0 2 1 0 5 }}


Map: [&lt;1 1 2 2 4|, &lt;0 2 1 3 -2|]
Optimal tunings:  
* WE: ~2 = 1206.750{{c}}, ~6/5 = 348.684{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 348.954{{c}}


EDOs: 3d, 4, 7, 11c, 18bc, 25bccd
{{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c }}


Badness: 0.0271
Badness (Sintel): 0.370


===13-limit===
==== 2.3.5.11.13 subgroup ====
Commas: 15/14, 25/24, 33/32, 40/39
Subgroup: 2.3.5.11.13


POTE generator: ~5/4 = 338.846
Comma list: 25/24, 40/39, 45/44


Map: [&lt;1 1 2 2 4 4|, &lt;0 2 1 3 -2 -1|]
Subgroup val mapping: {{mapping| 1 1 2 2 4 | 0 2 1 5 -1 }}


EDOs: 3d, 4, 7, 11c, 18bc, 25bccd
Gencom mapping: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }}


Badness: 0.0238
Optimal tunings:  
* WE: ~2 = 1202.433{{c}}, ~5/4 = 351.237{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 350.978{{c}}


=Flat=
{{Optimal ET sequence|legend=0| 3e, 7, 17 }}
Commas: 21/20, 25/24


POTE generator: ~5/4 = 331.916
Badness (Sintel): 0.536


Map: [&lt;1 1 2 3|, &lt;0 2 1 -1|]
== Septimal dicot ==
Septimal dicot is the extension where [[7/6]] and [[9/7]] are also conflated into 5/4~6/5. Although 5/4~6/5 covers a giant block of pitches already, 7/6 and 9/7 are often considered as thirds too. On that account one could argue for the canonicity of this extension, despite the relatively poor accuracy.


Wedgie: &lt;&lt;2 1 -1 -3 -7 -5||
[[Subgroup]]: 2.3.5.7


EDOs: 3, 4, 7d, 11cd
[[Comma list]]: 15/14, 25/24


Badness: 0.0254
{{Mapping|legend=1| 1 1 2 2 | 0 2 1 3 }}


==11-limit==
[[Optimal tuning]]s:
Commas: 21/20, 25/24, 33/32
* [[WE]]: ~2 = 1205.532{{c}}, ~6/5 = 337.931{{c}}
: [[error map]]: {{val| +5.532 -20.561 -37.319 +56.032 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.561{{c}}
: error map: {{val| 0.000 -24.834 -47.753 +46.856 }}


POTE generator: ~5/4 = 337.532
{{Optimal ET sequence|legend=1| 3d, 4, 7 }}


Map: [&lt;1 1 2 3 4|, &lt;0 2 1 -1 -2|]
[[Badness]] (Sintel): 0.504


EDOs: 3, 4, 7d, 11cd
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0250
Comma list: 15/14, 22/21, 25/24


==13-limit==
Mapping: {{mapping| 1 1 2 2 2 | 0 2 1 3 5 }}
Commas: 14/13, 21/20, 25/24, 33/32


POTE generator: ~5/4 = 341.023
Optimal tunings:  
* WE: ~2 = 1203.346{{c}}, ~6/5 = 343.078{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 343.260{{c}}


Map: [&lt;1 1 2 3 4 4|, &lt;0 2 1 -1 -2 -1|]
{{Optimal ET sequence|legend=0| 3de, 4e, 7 }}


EDOs: 3, 4, 7d, 11cd
Badness (Sintel): 0.656


Badness: 0.0234
=== Eudicot ===
Subgroup: 2.3.5.7.11


=Sharp=
Comma list: 15/14, 25/24, 33/32
Commas: 25/24, 28/27


[[POTE_tuning|POTE generator]]: ~5/4 = 357.938
Mapping: {{mapping| 1 1 2 2 4 | 0 2 1 3 -2 }}


Map: [&lt;1 1 2 1|, &lt;0 2 1 6|]
Optimal tunings:  
* WE: ~2 = 1205.828{{c}}, ~6/5 = 337.683{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 336.909{{c}}


EDOs: 3d, 7d, [[10edo|10]], 17d, [[57edo|57bccdd]]
{{Optimal ET sequence|legend=0| 3d, 4, 7, 18bc, 25bccd }}


Badness: 0.0289
Badness (Sintel): 0.896


==11-limit==
==== 13-limit ====
Commas: 25/24, 28/27, 35/33
Subgroup: 2.3.5.7.11.13


POTE generator: ~5/4 = 356.106
Comma list: 15/14, 25/24, 33/32, 40/39


Map: [&lt;1 1 2 1 2|, &lt;0 2 1 6 5|]
Mapping: {{mapping| 1 1 2 2 4 4 | 0 2 1 3 -2 -1 }}


EDOs: 3de, 7d, 10, 17d, 27cde
Optimal tunings:  
* WE: ~2 = 1202.660{{c}}, ~6/5 = 339.597{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 339.104{{c}}


Badness: 0.0224
{{Optimal ET sequence|legend=0| 3d, 4, 7 }}


=Decimal=
Badness (Sintel): 0.985
Commas: 25/24, 49/48


[[POTE_tuning|POTE generator]]: ~7/6 = 251.557
== Flattie ==
This temperament used to be known as ''flat''. Unlike septimal dicot where 7/6 is added to the neutral third, here [[8/7]] is added instead.  


Map: [&lt;2 0 3 4|, &lt;0 2 1 1|]
[[Subgroup]]: 2.3.5.7


Wedgie: &lt;&lt;4 2 2 -6 -8 -1||
[[Comma list]]: 21/20, 25/24


EDOs: [[10edo|10]], [[14edo|14c]], [[24edo|24c]], [[38edo|38cd]]
{{Mapping|legend=1| 1 1 2 3 | 0 2 1 -1 }}


Badness: 0.0283
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1220.466{{c}}, ~6/5 = 337.577{{c}}
: [[error map]]: {{val| +20.466 -6.335 -7.804 -45.004 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 335.391{{c}}
: error map: {{val| 0.000 -31.173 -50.922 -104.217 }}


==11-limit==
{{Optimal ET sequence|legend=1| 3, 4, 7d, 11cd, 18bcddd }}
Commas: 25/24, 45/44, 49/48


[[POTE_tuning|POTE generator]]: ~7/6 = 253.493
[[Badness]] (Sintel): 0.642


Map: [&lt;2 0 3 4 -1|, &lt;0 2 1 1 5|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: 10, 14c, 24c, 38cd
Comma list: 21/20, 25/24, 33/32


Badness: 0.0267
Mapping: {{mapping| 1 1 2 3 4 | 0 2 1 -1 -2 }}


==Decimated==
Optimal tunings:
Commas: 25/24, 33/32, 49/48
* WE: ~2 = 1216.069{{c}}, ~6/5 = 342.052{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 338.467{{c}}


[[POTE_tuning|POTE generator]]: ~7/6 = 255.066
{{Optimal ET sequence|legend=0| 3, 4, 7d }}


Map: [&lt;2 0 3 4 10|, &lt;0 2 1 1 -2|]
Badness (Sintel): 0.826


EDOs: 4, 10e, 14c
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.0315
Comma list: 14/13, 21/20, 25/24, 33/32


==Decibel==
Mapping: {{mapping| 1 1 2 3 4 4 | 0 2 1 -1 -2 -1 }}
Commas: 25/24, 35/33, 49/48


POTE generator: ~8/7 = 243.493
Optimal tunings:  
* WE: ~2 = 1211.546{{c}}, ~6/5 = 344.304{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 341.373{{c}}


Map: [&lt;2 0 3 4 7|, &lt;0 2 1 1 0|]
{{Optimal ET sequence|legend=0| 3, 4, 7d }}


EDOs: 4, 6, 10
Badness (Sintel): 0.968


Badness: 0.0324
== Sharpie ==
This temperament used to be known as ''sharp''. This is where you find 7/6 at the major second and [[7/4]] at the major sixth.  


=Dichotic=
[[Subgroup]]: 2.3.5.7
Commas: 25/24, 64/63


POTE generator: ~5/4 = 356.264
[[Comma list]]: 25/24, 28/27


Map: [&lt;1 1 2 4|, &lt;0 2 1 -4|]
{{Mapping|legend=1| 1 1 2 1 | 0 2 1 6 }}


Wedgie: &lt;&lt;2 1 -4 -3 -12 -12||
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1202.488{{c}}, ~5/4 = 358.680{{c}}
: [[error map]]: {{val| +2.488 +17.893 -22.658 -14.258 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 358.495{{c}}
: error map: {{val| 0.000 +15.035 -27.818 -17.854 }}


EDOs: 7, 10, 17, 27c, 37c
{{Optimal ET sequence|legend=1| 3d, 7d, 10 }}


Badness: 0.0376
[[Badness]] (Sintel): 0.732


==11-limit==
=== 11-limit ===
Commas: 25/24, 45/44, 64/63
Subgroup: 2.3.5.7.11


POTE generator: ~5/4 = 354.262
Comma list: 25/24, 28/27, 35/33


Map: [&lt;1 1 2 4 2|, &lt;0 2 1 -4 5|]
Mapping: {{mapping| 1 1 2 1 2 | 0 2 1 6 5 }}


EDOs: 7, 10, 17, 27ce, 44ce
Optimal tunings:  
* WE: ~2 = 1201.518{{c}}, ~5/4 = 356.557{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 356.457{{c}}


Badness: 0.0307
{{Optimal ET sequence|legend=0| 3de, 7d, 10, 17d }}


==Dichosis==
Badness (Sintel): 0.739
Commas: 25/24, 35/33, 64/63


POTE generator: ~5/4 = 360.659
== Dichotic ==
In dichotic, 7/4 is found at a stack of two perfect fourths.  


Map: [&lt;1 1 2 4 5|, &lt;0 2 1 -4 -5|]
[[Subgroup]]: 2.3.5.7


EDOs: 3, 10
[[Comma list]]: 25/24, 64/63


Badness: 0.0414
{{Mapping|legend=1| 1 1 2 4 | 0 2 1 -4 }}


=Jamesbond=
[[Optimal tuning]]s:
Commas: 25/24, 81/80
* [[WE]]: ~2 = 1200.802{{c}}, ~5/4 = 356.502{{c}}
: [[error map]]: {{val| +0.802 +11.851 -28.208 +8.374 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.275{{c}}
: error map: {{val| 0.000 +10.595 -30.039 +6.074 }}


[[POTE_tuning|POTE generator]]: ~8/7 = 258.139
{{Optimal ET sequence|legend=1| 3, 7, 10, 17, 27c }}


Map: [&lt;7 11 16 0|, &lt;0 0 0 1|]
[[Badness]] (Sintel): 0.951


EDOs: 7, [[14edo|14c]]
=== 11-limit ===
Subgroup: 2.3.5.7.11


==11-limit==
Comma list: 25/24, 45/44, 64/63
11-limit jamesbond is called "septimal" on the Regular Temperament Finder.


Commas: 25/24, 33/32, 45/44
Mapping: {{mapping| 1 1 2 4 2 | 0 2 1 -4 5 }}


POTE generator: ~8/7 = 258.910
Optimal tunings:  
* WE: ~2 = 1199.504{{c}}, ~5/4 = 354.115{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.236{{c}}


Map: [&lt;7 11 16 0 24|, &lt;0 0 0 1 0|]
{{Optimal ET sequence|legend=0| 7, 10, 17 }}


EDOs: 7, 14c
Badness (Sintel): 1.01


Badness: 0.0235
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==13-limit==
Comma list: 25/24, 40/39, 45/44, 64/63
Commas: 25/24 27/26 33/32 45/44


POTE generator: ~8/7 = 250.764
Mapping: {{mapping| 1 1 2 4 2 4 | 0 2 1 -4 5 -1 }}


Map: [&lt;7 11 16 0 24 26|, &lt;0 0 0 1 0 0|]
Optimal tunings:  
* WE: ~2 = 1199.289{{c}}, ~5/4 = 354.156{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.340{{c}}


EDOs: 7, 14c
{{Optimal ET sequence|legend=0| 7, 10, 17, 27ce, 44cce }}


Badness: 0.0230
Badness (Sintel): 0.896


==Septimal==
=== Dichotomic ===
Commas: 25/24, 33/32, 45/44, 65/63
Subgroup: 2.3.5.7.11


POTE generator: ~8/7 = 247.447
Comma list: 22/21, 25/24, 33/32


Map: [&lt;7 11 16 0 24 6|, &lt;0 0 0 1 0 1|]
Mapping: {{mapping| 1 1 2 4 4 | 0 2 1 -4 -2 }}


EDOs: 7, 14cf
Optimal tunings:  
* WE: ~2 = 1203.949{{c}}, ~5/4 = 355.239{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.024{{c}}


Badness: 0.0226
{{Optimal ET sequence|legend=0| 3, 7, 10e }}


=Sidi=
Badness (Sintel): 1.05
Commas: 25/24, 245/243


[[POTE_tuning|POTE generator]]: ~9/7 = 427.208
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]
Comma list: 22/21, 25/24, 33/32, 40/39


EDOs: [[14edo|14c]], [[45edo|45c]], &lt;59 93 135 165|
Mapping: {{mapping| 1 1 2 4 4 4 | 0 2 1 -4 -2 -1 }}


Badness: 0.0566
Optimal tunings:  
* WE: ~2 = 1202.979{{c}}, ~5/4 = 355.193{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.254{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 3, 7, 10e }}
Commas: 25/24, 45/44, 99/98


POTE generator: ~9/7 = 427.273
Badness (Sintel): 0.940


Map: [&lt;1 3 3 6 7|, &lt;0 -4 -2 -9 -10|]
=== Dichosis ===
Subgroup: 2.3.5.7.11


EDOs: 14c, 17, 45ce, 59bccde
Comma list: 25/24, 35/33, 64/63


Badness: 0.0330
Mapping: {{mapping| 1 1 2 4 5 | 0 2 1 -4 -5 }}


=Quad=
Optimal tunings:
Commas: 9/8, 25/24
* WE: ~2 = 1197.526{{c}}, ~5/4 = 359.915{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.745{{c}}


POTE generator: ~5/4 = 324.482
{{Optimal ET sequence|legend=0| 3, 7e, 10 }}


Map: [&lt;4 6 9 0|, &lt;0 0 0 1|]
Badness (Sintel): 1.37


Wedgie: &lt;&lt;0 0 4 0 6 9||
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


EDOs: 4, 12bcd
Comma list: 25/24, 35/33, 40/39, 64/63


Badness: 0.0460
Mapping: {{mapping| 1 1 2 4 5 4 | 0 2 1 -4 -5 -1 }}


[[Category:Theory]]
Optimal tunings:
[[Category:Temperament family]]
* WE: ~2 = 1197.922{{c}}, ~5/4 = 360.021{{c}}
[[Category:Dicot]]
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.722{{c}}
 
{{Optimal ET sequence|legend=0| 3, 7e, 10 }}
 
Badness (Sintel): 1.15
 
== Decimal ==
{{Main| Decimal }}
{{See also| Jubilismic clan }}
 
Decimal tempers out 49/48 and [[50/49]], and has a semi-octave period for 7/5~10/7 and a hemitwelfth generator for 7/4~12/7. Its ploidacot is diploid dicot. [[10edo]] makes for a good tuning, from which it derives its name. [[14edo]] in the 14c val and [[24edo]] in the 24c val are also among the possibilities.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 25/24, 49/48
 
{{Mapping|legend=1| 2 0 3 4 | 0 2 1 1 }}
 
: mapping generators: ~7/5, ~7/4
 
[[Optimal tuning]]s:
* [[WE]]: ~7/5 = 603.286{{c}}, ~7/4 = 953.637{{c}} (~7/6 = 252.935{{c}})
: [[error map]]: {{val| +6.571 +5.318 -22.821 -2.047 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~7/4 = 950.957{{c}} (~7/6 = 249.043{{c}})
: error map: {{val| 0.000 -0.041 -35.357 -17.869 }}
 
{{Optimal ET sequence|legend=1| 4, 10, 14c, 24c, 38ccd }}
 
[[Badness]] (Sintel): 0.717
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 45/44, 49/48
 
Mapping: {{mapping| 2 0 3 4 -1 | 0 2 1 1 5 }}
 
Optimal tunings:
* WE: ~7/5 = 603.558{{c}}, ~7/4 = 952.121{{c}} (~7/6 = 254.996{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 948.610{{c}} (~7/6 = 251.390{{c}})
 
{{Optimal ET sequence|legend=0| 4e, 10, 14c, 24c }}
 
Badness (Sintel): 0.883
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 25/24, 45/44, 49/48, 91/90
 
Mapping: {{mapping| 2 0 3 4 -1 1| 0 2 1 1 5 4}}
 
Optimal tunings:
* WE: ~7/5 = 603.612{{c}}, ~7/4 = 953.663{{c}} (~7/6 = 253.562{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 950.116{{c}} (~7/6 = 249.884{{c}})
 
{{Optimal ET sequence|legend=0| 4ef, 10, 14cf, 24cf }}
 
Badness (Sintel): 0.881
 
=== Decimated ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 33/32, 49/48
 
Mapping: {{mapping| 2 0 3 4 10 | 0 2 1 1 -2 }}
 
Optimal tunings:
* WE: ~7/5 = 604.535{{c}}, ~7/4 = 952.076{{c}} (~7/6 = 256.994{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 946.108{{c}} (~7/6 = 253.892{{c}})
 
{{Optimal ET sequence|legend=0| 4, 10e, 14c }}
 
Badness (Sintel): 1.04
 
=== Decibel ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 35/33, 49/48
 
Mapping: {{mapping| 2 0 3 4 7 | 0 2 1 1 0 }}
 
Optimal tunings:
* WE: ~7/5 = 599.404{{c}}, ~7/4 = 955.557{{c}} (~8/7 = 243.251{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 956.169{{c}} (~8/7 = 243.831{{c}})
 
{{Optimal ET sequence|legend=0| 4, 6, 10 }}
 
Badness (Sintel): 1.07
 
== Sidi ==
Sidi tempers out 245/243, and splits 5/2~12/5 in two. Its ploidacot is beta-tetracot. This relates it to [[squares]], to which it can be used as a simpler alternative. 14edo in the 14c val can be used as a tuning, in which case it is identical to squares, however.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 25/24, 245/243
 
{{Mapping|legend=1| 1 -1 1 -3 | 0 4 2 9 }}
 
: mapping generators: ~2, ~14/9
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1207.178{{c}}, ~14/9 = 777.414{{c}}
: [[error map]]: {{val| +7.178 +0.523 -24.308 +6.367 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~14/9 = 773.872{{c}}
: error map: {{val| 0.000 -6.464 -38.569 -3.973 }}
 
{{Optimal ET sequence|legend=1| 3d, …, 11cd, 14c }}
 
[[Badness]] (Sintel): 1.43
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 45/44, 99/98
 
Mapping: {{mapping| 1 -1 1 -3 -3 | 0 4 2 9 10 }}
 
Optimal tunings:
* WE: ~2 = 1207.200{{c}}, ~11/7 = 777.363{{c}}
* CWE: ~2 = 1200.000{{c}}, ~11/7 = 773.777{{c}}
 
{{Optimal ET sequence|legend=0| 3de, …, 11cdee, 14c }}
 
Badness (Sintel): 1.09
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Dicot family| ]] <!-- main article -->
[[Category:Dicot| ]] <!-- key article -->
[[Category:Rank 2]]
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