Dicot family: Difference between revisions

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The '''dicot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[25/24]], the classical chromatic semitone. 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)}}.

The '''dicot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[25/24]], the classical chromatic semitone.

== Dicot ==

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.

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]].

~~== Dicot ==~~

[[Subgroup]]: 2.3.5

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* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 351.086{{c}}

: error map: {{val| 0.000 +0.216 -35.228 }}

~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 354.664{{c}}~~

~~: [[error map]]: {{val| 0.000 +7.374 -31.649 }}~~

* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 348.594{{c}}

~~: error map: {{val| 0.000 -4.766 -37.719 }} -->~~

[[Tuning ranges]]:

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=== 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, sharpie adds 28/27, and dichotic adds 64/63, all retaining the same period and generator.

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.

Decimal adds 49/48, sidi adds 245/243, and jamesbond 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.

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.

Temperaments discussed elsewhere are:

* ''[[Geryon]]'' → [[Very low accuracy temperaments #Geryon|Very low accuracy temperaments]]

* ''[[Jamesbond]]'' → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]]

The rest are considered below.

=== 2.3.5.11 subgroup ===

The 2.3.5.11-subgroup extension ~~is related to~~ [[~~#Septimal dicot|septimal dicot~~]], [[~~#Sharpie|sharpie~~]], ~~and [[#Dichotic|dichotic]]~~.

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.

Subgroup: 2.3.5.11

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Gencom mapping: {{mapping| 1 1 2 0 2 | 0 2 1 0 5 }}

~~: gencom: [2 5/4; 25/24 45/44]~~

Optimal tunings:

* WE: ~2 = 1206.750{{c}}, ~6/5 = 348.684{{c}}

* CWE: ~2 = 1200.000{{c}}, ~6/5 = 348.954{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 352.287{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~6/5 = 346.734{{c}} -->

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Gencom mapping: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }}

~~: gencom: [2 5/4; 25/24 40/39 45/44]~~

Optimal tunings:

* WE: ~2 = 1202.433{{c}}, ~6/5 = 351.237{{c}}

* WE: ~2 = 1202.433{{c}}, ~5/4 = 351.237{{c}}

* CWE~~: ~2 = 1200.000{{c}}, ~6/5 = 350.978{{c}}~~

* CWE: ~2 = 1200.000{{c}}, ~5/4 = 350.978{{c}}

~~<!-- * CTE~~: ~2 = 1200.000{{c}}, ~5/4 ~~= 352.420{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~6/5 = 350.~~526~~{{c}} ~~-->~~

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== 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 is a giant block 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.

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.

[[Subgroup]]: 2.3.5.7

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* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.561{{c}}

: error map: {{val| 0.000 -24.834 -47.753 +46.856 }}

~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 342.257{{c}}~~

~~: [[error map]]: {{val| 0.000 -17.441 -44.056 +57.946 }}~~

* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 336.381{{c}}

~~: error map: {{val| 0.000 -29.193 -49.933 +40.316 }} -->~~

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* WE: ~2 = 1203.346{{c}}, ~6/5 = 343.078{{c}}

* CWE: ~2 = 1200.000{{c}}, ~6/5 = 343.260{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 345.596{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~6/5 = 342.125{{c}} -->

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* WE: ~2 = 1205.828{{c}}, ~6/5 = 337.683{{c}}

* CWE: ~2 = 1200.000{{c}}, ~6/5 = 336.909{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 340.417{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~6/5 = 336.051{{c}} -->

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* WE: ~2 = 1202.660{{c}}, ~6/5 = 339.597{{c}}

* CWE: ~2 = 1200.000{{c}}, ~6/5 = 339.104{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 340.835{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~6/5 = 338.846{{c}} -->

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== 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.

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.

[[Subgroup]]: 2.3.5.7

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* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 335.391{{c}}

: error map: {{val| 0.000 -31.173 -50.922 -104.217 }}

~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 346.438{{c}}~~

~~: [[error map]]: {{val| 0.000 -9.080 -39.876 -115.264 }}~~

* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 331.916{{c}}

~~: error map: {{val| 0.000 -38.123 -54.398 -100.742 }} -->~~

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* WE: ~2 = 1216.069{{c}}, ~6/5 = 342.052{{c}}

* CWE: ~2 = 1200.000{{c}}, ~6/5 = 338.467{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 343.139{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~6/5 = 337.532{{c}} -->

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* WE: ~2 = 1211.546{{c}}, ~6/5 = 344.304{{c}}

* CWE: ~2 = 1200.000{{c}}, ~6/5 = 341.373{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 343.655{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~6/5 = 341.023{{c}} -->

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== 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.

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.

[[Subgroup]]: 2.3.5.7

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* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 358.495{{c}}

: error map: {{val| 0.000 +15.035 -27.818 -17.854 }}

~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 359.564{{c}}~~

~~: [[error map]]: {{val| 0.000 +17.173 -26.750 -11.442 }}~~

* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 357.938{{c}}

~~: error map: {{val| 0.000 +13.921 -28.376 -21.198 }} -->~~

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* WE: ~2 = 1201.518{{c}}, ~5/4 = 356.557{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/4 = 356.457{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 357.261{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~5/4 = 356.106{{c}} -->

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* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.275{{c}}

: error map: {{val| 0.000 +10.595 -30.039 +6.074 }}

~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.333{{c}}~~

~~: [[error map]]: {{val| 0.000 +10.710 -29.981 +5.844 }}~~

* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.264{{c}}

~~: error map: {{val| 0.000 +10.573 -30.050 +6.119 }} -->~~

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* WE: ~2 = 1199.504{{c}}, ~5/4 = 354.115{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.236{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 354.183{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.262{{c}} -->

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* WE: ~2 = 1199.289{{c}}, ~5/4 = 354.156{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.340{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 354.247{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.365{{c}} -->

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* WE: ~2 = 1203.949{{c}}, ~5/4 = 355.239{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.024{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 353.751{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.073{{c}} -->

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* WE: ~2 = 1202.979{{c}}, ~5/4 = 355.193{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.254{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 353.850{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.313{{c}} -->

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* WE: ~2 = 1197.526{{c}}, ~5/4 = 359.915{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.745{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 361.081{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~5/4 = 360.659{{c}} -->

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* WE: ~2 = 1197.922{{c}}, ~5/4 = 360.021{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.722{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 361.061{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~5/4 = 360.646{{c}} -->

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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

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* [[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 }}

~~<!-- * [[CTE]]: ~7/5 = 600.000{{c}}, ~7/4 = 955.608{{c}} (~8/7 = 244.392{{c}})~~

~~: [[error map]]: {{val| 0.000 +9.260 -30.706 -13.218 }}~~

* [[POTE]]: ~7/5 = 600.000{{c}}, ~7/4 = 948.443{{c}} (~7/6 = 251.557{{c}})

~~: error map: {{val| 0.000 -5.069 -37.871 -20.383 }} -->~~

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* 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}})

~~<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 952.812{{c}} (~8/7 = 247.188{{c}})~~

* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 946.507{{c}} (~7/6 = 253.493{{c}}) -->

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* 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}})

~~<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 954.469{{c}} (~8/7 = 245.531{{c}})~~

* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 947.955{{c}} (~7/6 = 252.045{{c}}) -->

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* 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}})

~~<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 950.940{{c}} (~7/6 = 249.060{{c}})~~

* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 944.934{{c}} (~7/6 = 255.066{{c}}) -->

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* 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}})

~~<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 955.608{{c}} (~8/7 = 244.392{{c}})~~

* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 956.507{{c}} (~8/7 = 243.493{{c}}) -->

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== 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

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* [[CWE]]: ~2 = 1200.000{{c}}, ~14/9 = 773.872{{c}}

: error map: {{val| 0.000 -6.464 -38.569 -3.973 }}

~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~14/9 = 775.548{{c}}~~

~~: [[error map]]: {{val| 0.000 +0.238 -35.217 +11.108 }}~~

* [[POTE]]: ~2 = 1200.000{{c}}, ~14/9 = 772.792{{c}}

~~: error map: {{val| 0.000 -10.789 -40.731 -13.702 }} -->~~

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* WE: ~2 = 1207.200{{c}}, ~11/7 = 777.363{{c}}

* CWE: ~2 = 1200.000{{c}}, ~11/7 = 773.777{{c}}

~~<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 775.413{{c}}~~

* POTE: ~2 = 1200.000{{c}}, ~11/7 = 772.727{{c}} -->

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''dicot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[25/24]], the classical chromatic semitone. 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)}}.
+The '''dicot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[25/24]], the classical chromatic semitone.
+== Dicot ==
+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.
 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]].
-== Dicot ==
 [[Subgroup]]: 2.3.5
@@ Line 18: / Line 20: @@
 * [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 351.086{{c}}
 : error map: {{val| 0.000 +0.216 -35.228 }}
-<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 354.664{{c}}
-: [[error map]]: {{val| 0.000 +7.374 -31.649 }}
-* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 348.594{{c}}
-: error map: {{val| 0.000 -4.766 -37.719 }} -->
 [[Tuning ranges]]:
@@ Line 32: / Line 30: @@
 === 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, sharpie adds 28/27, and dichotic adds 64/63, all retaining the same period and generator.
+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.
-Decimal adds 49/48, sidi adds 245/243, and jamesbond 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.
+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.
 Temperaments discussed elsewhere are:
 * ''[[Geryon]]'' → [[Very low accuracy temperaments #Geryon|Very low accuracy temperaments]]
+* ''[[Jamesbond]]'' → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]]
 The rest are considered below.
 === 2.3.5.11 subgroup ===
-The 2.3.5.11-subgroup extension is related to [[#Septimal dicot|septimal dicot]], [[#Sharpie|sharpie]], and [[#Dichotic|dichotic]].
+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.
 Subgroup: 2.3.5.11
@@ Line 51: / Line 50: @@
 Gencom mapping: {{mapping| 1 1 2 0 2 | 0 2 1 0 5 }}
-: gencom: [2 5/4; 25/24 45/44]
 Optimal tunings:
 * WE: ~2 = 1206.750{{c}}, ~6/5 = 348.684{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~6/5 = 348.954{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 352.287{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~6/5 = 346.734{{c}} -->
 {{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c }}
@@ Line 72: / Line 67: @@
 Gencom mapping: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }}
-: gencom: [2 5/4; 25/24 40/39 45/44]
 Optimal tunings:
-* WE: ~2 = 1202.433{{c}}, ~6/5 = 351.237{{c}}
+* WE: ~2 = 1202.433{{c}}, ~5/4 = 351.237{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~6/5 = 350.978{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~5/4 = 350.978{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 352.420{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~6/5 = 350.526{{c}} -->
 {{Optimal ET sequence|legend=0| 3e, 7, 17 }}
@@ Line 86: / Line 77: @@
 == 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 is a giant block 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.
+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.
 [[Subgroup]]: 2.3.5.7
@@ Line 99: / Line 90: @@
 * [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.561{{c}}
 : error map: {{val| 0.000 -24.834 -47.753 +46.856 }}
-<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 342.257{{c}}
-: [[error map]]: {{val| 0.000 -17.441 -44.056 +57.946 }}
-* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 336.381{{c}}
-: error map: {{val| 0.000 -29.193 -49.933 +40.316 }} -->
 {{Optimal ET sequence|legend=1| 3d, 4, 7 }}
@@ Line 118: / Line 105: @@
 * WE: ~2 = 1203.346{{c}}, ~6/5 = 343.078{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~6/5 = 343.260{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 345.596{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~6/5 = 342.125{{c}} -->
 {{Optimal ET sequence|legend=0| 3de, 4e, 7 }}
@@ Line 135: / Line 120: @@
 * WE: ~2 = 1205.828{{c}}, ~6/5 = 337.683{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~6/5 = 336.909{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 340.417{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~6/5 = 336.051{{c}} -->
 {{Optimal ET sequence|legend=0| 3d, 4, 7, 18bc, 25bccd }}
@@ Line 152: / Line 135: @@
 * WE: ~2 = 1202.660{{c}}, ~6/5 = 339.597{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~6/5 = 339.104{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 340.835{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~6/5 = 338.846{{c}} -->
 {{Optimal ET sequence|legend=0| 3d, 4, 7 }}
@@ Line 160: / Line 141: @@
 == 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.
+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.
 [[Subgroup]]: 2.3.5.7
@@ Line 173: / Line 154: @@
 * [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 335.391{{c}}
 : error map: {{val| 0.000 -31.173 -50.922 -104.217 }}
-<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 346.438{{c}}
-: [[error map]]: {{val| 0.000 -9.080 -39.876 -115.264 }}
-* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 331.916{{c}}
-: error map: {{val| 0.000 -38.123 -54.398 -100.742 }} -->
 {{Optimal ET sequence|legend=1| 3, 4, 7d, 11cd, 18bcddd }}
@@ Line 192: / Line 169: @@
 * WE: ~2 = 1216.069{{c}}, ~6/5 = 342.052{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~6/5 = 338.467{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 343.139{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~6/5 = 337.532{{c}} -->
 {{Optimal ET sequence|legend=0| 3, 4, 7d }}
@@ Line 209: / Line 184: @@
 * WE: ~2 = 1211.546{{c}}, ~6/5 = 344.304{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~6/5 = 341.373{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 343.655{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~6/5 = 341.023{{c}} -->
 {{Optimal ET sequence|legend=0| 3, 4, 7d }}
@@ Line 217: / Line 190: @@
 == 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.
+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.
 [[Subgroup]]: 2.3.5.7
@@ Line 230: / Line 203: @@
 * [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 358.495{{c}}
 : error map: {{val| 0.000 +15.035 -27.818 -17.854 }}
-<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 359.564{{c}}
-: [[error map]]: {{val| 0.000 +17.173 -26.750 -11.442 }}
-* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 357.938{{c}}
-: error map: {{val| 0.000 +13.921 -28.376 -21.198 }} -->
 {{Optimal ET sequence|legend=1| 3d, 7d, 10 }}
@@ Line 249: / Line 218: @@
 * WE: ~2 = 1201.518{{c}}, ~5/4 = 356.557{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~5/4 = 356.457{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 357.261{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~5/4 = 356.106{{c}} -->
 {{Optimal ET sequence|legend=0| 3de, 7d, 10, 17d }}
@@ Line 270: / Line 237: @@
 * [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.275{{c}}
 : error map: {{val| 0.000 +10.595 -30.039 +6.074 }}
-<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.333{{c}}
-: [[error map]]: {{val| 0.000 +10.710 -29.981 +5.844 }}
-* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.264{{c}}
-: error map: {{val| 0.000 +10.573 -30.050 +6.119 }} -->
 {{Optimal ET sequence|legend=1| 3, 7, 10, 17, 27c }}
@@ Line 289: / Line 252: @@
 * WE: ~2 = 1199.504{{c}}, ~5/4 = 354.115{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.236{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 354.183{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.262{{c}} -->
 {{Optimal ET sequence|legend=0| 7, 10, 17 }}
@@ Line 306: / Line 267: @@
 * WE: ~2 = 1199.289{{c}}, ~5/4 = 354.156{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.340{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 354.247{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.365{{c}} -->
 {{Optimal ET sequence|legend=0| 7, 10, 17, 27ce, 44cce }}
@@ Line 323: / Line 282: @@
 * WE: ~2 = 1203.949{{c}}, ~5/4 = 355.239{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.024{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 353.751{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.073{{c}} -->
 {{Optimal ET sequence|legend=0| 3, 7, 10e }}
@@ Line 340: / Line 297: @@
 * WE: ~2 = 1202.979{{c}}, ~5/4 = 355.193{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.254{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 353.850{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.313{{c}} -->
 {{Optimal ET sequence|legend=0| 3, 7, 10e }}
@@ Line 357: / Line 312: @@
 * WE: ~2 = 1197.526{{c}}, ~5/4 = 359.915{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.745{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 361.081{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~5/4 = 360.659{{c}} -->
 {{Optimal ET sequence|legend=0| 3, 7e, 10 }}
@@ Line 374: / Line 327: @@
 * WE: ~2 = 1197.922{{c}}, ~5/4 = 360.021{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.722{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 361.061{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~5/4 = 360.646{{c}} -->
 {{Optimal ET sequence|legend=0| 3, 7e, 10 }}
@@ Line 384: / Line 335: @@
 {{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
@@ Line 398: / Line 351: @@
 * [[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 }}
-<!-- * [[CTE]]: ~7/5 = 600.000{{c}}, ~7/4 = 955.608{{c}} (~8/7 = 244.392{{c}})
-: [[error map]]: {{val| 0.000 +9.260 -30.706 -13.218 }}
-* [[POTE]]: ~7/5 = 600.000{{c}}, ~7/4 = 948.443{{c}} (~7/6 = 251.557{{c}})
-: error map: {{val| 0.000 -5.069 -37.871 -20.383 }} -->
 {{Optimal ET sequence|legend=1| 4, 10, 14c, 24c, 38ccd }}
@@ Line 417: / Line 366: @@
 * 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}})
-<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 952.812{{c}} (~8/7 = 247.188{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 946.507{{c}} (~7/6 = 253.493{{c}}) -->
 {{Optimal ET sequence|legend=0| 4e, 10, 14c, 24c }}
@@ Line 434: / Line 381: @@
 * 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}})
-<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 954.469{{c}} (~8/7 = 245.531{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 947.955{{c}} (~7/6 = 252.045{{c}}) -->
 {{Optimal ET sequence|legend=0| 4ef, 10, 14cf, 24cf }}
@@ Line 451: / Line 396: @@
 * 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}})
-<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 950.940{{c}} (~7/6 = 249.060{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 944.934{{c}} (~7/6 = 255.066{{c}}) -->
 {{Optimal ET sequence|legend=0| 4, 10e, 14c }}
@@ Line 468: / Line 411: @@
 * 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}})
-<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 955.608{{c}} (~8/7 = 244.392{{c}})
-* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 956.507{{c}} (~8/7 = 243.493{{c}}) -->
 {{Optimal ET sequence|legend=0| 4, 6, 10 }}
@@ Line 476: / Line 417: @@
 == 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
@@ Line 489: / Line 432: @@
 * [[CWE]]: ~2 = 1200.000{{c}}, ~14/9 = 773.872{{c}}
 : error map: {{val| 0.000 -6.464 -38.569 -3.973 }}
-<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~14/9 = 775.548{{c}}
-: [[error map]]: {{val| 0.000 +0.238 -35.217 +11.108 }}
-* [[POTE]]: ~2 = 1200.000{{c}}, ~14/9 = 772.792{{c}}
-: error map: {{val| 0.000 -10.789 -40.731 -13.702 }} -->
 {{Optimal ET sequence|legend=1| 3d, …, 11cd, 14c }}
@@ Line 508: / Line 447: @@
 * WE: ~2 = 1207.200{{c}}, ~11/7 = 777.363{{c}}
 * CWE: ~2 = 1200.000{{c}}, ~11/7 = 773.777{{c}}
-<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 775.413{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~11/7 = 772.727{{c}} -->
 {{Optimal ET sequence|legend=0| 3de, …, 11cdee, 14c }}