Rastmic clan: Difference between revisions

(26 intermediate revisions by 9 users not shown)

Line 1:

The '''rastmic clan''' of temperaments [[tempers out]] 243/242.

The '''rastmic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[rastma]], {{nowrap|243/242 {{=}} {{monzo| -1 5 0 0 -2 }}}}.

== Neutral ==

Neutral can be thought of as the 2.3.11 version of either [[mohajira]] or [[~~maqamic~~]], as well as suhajira and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]].

Neutral is the 2.3.11-[[subgroup]] temperament with a [[generator]] of a neutral third which can be taken to represent {{nowrap|[[11/9]] [[~]] [[27/22]]}}, two of which make up a perfect fifth of [[3/2]]. It can be thought of as the 2.3.11 version of either [[mohajira]] or [[neutrominant]], as well as [[suhajira]] and [[archytas clan #Ringo|ringo]]. Among other things, it is the temperament optimizing the [[neutral tetrad]].

[[Subgroup]]: 2.3.11

Line 14:

Line 15:

: gencom: [2 11/9; 243/242]

: [[gencom]]: [2 11/9; 243/242]

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 350.525

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1\1, ~11/9 = 350.572

* [[POTE]]: ~2 = 1\1, ~11/9 = 350.525

{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 }}

Line 25:

Line 28:

=== Namo ===

Namo adds [[144/143]] to the comma list and finds ~[[16/13]] at the same neutral third. With {{nowrap|11/9 ~ 16/13}}, it requires a slightly flat ~[[27/22]] as the tuning of the neutral third. [[58edo]] is the largest [[patent val]] tuning for it in the [[optimal ET sequence]], with a tuning between that of [[17edo]] and [[41edo]], so that ~11 and ~13 are practically equally sharp, given that [[29edo]] forms a [[consistent circle]] of [[13/11]]'s with a [[closing error]] of 31.2%. It might be recommended as a tuning for this reason, as having the neutral third much sharper to optimize plausibility of ~16/13 implies that the 11 is extremely sharp because 11/9 must be tuned sharp so that 11 must be sharper than 9, which is thus four times as sharp as however sharp of the (3/2)<sup>1/2</sup> neutral third is, while tuning it much flatter means that you increase the error of 16/13, which in 58edo is already as almost 8{{cent}} off and in [[99edo|99ef]] it is only slightly worse. For these reasons, Godtone is not fond of the recommendations by the various [[optimal tuning]]s to tune flat of 58edo, although it is clear that in an optimal tuning nothing much sharper than 58edo should be used, as making 11 more off than 13 would imply damaging 3 and 11/9 more than necessary. Curiously, [[POTE]] recommends a sharper tuning than both [[CTE]] and [[CWE]] here, but still flat of 58edo.

[[Subgroup]]: 2.3.11.13

Line 35:

Line 40:

: gencom: [2 11/9; 144/143 243/242]

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 351.488

[[Optimal tuning]]s:

* [[CTE]]: 2 = 1\1, ~11/9 = 350.746

* [[CWE]]: 2 = 1\1, ~11/9 = 351.270

* [[POTE]]: 2 = 1\1, ~11/9 = 351.488

{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 58, 99ef, 239eefff, 338eeeffff }}

[[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents

== Suhajira ==

Subgroup: 2.3.7.11

[[Subgroup]]: 2.3.7.11

Comma list: 64/63, 243/242

[[Comma list]]: 64/63, 243/242

~~Sval mapping:~~ {{~~mapping~~| 1 1 4 2 | 0 2 -4 5 }}

: sval mapping generators: ~2, ~11/9

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

: gencom: [2 3/2; 64/63 99/98]

: [[gencom]]: [2 11/9; 64/63 243/242]

Optimal tuning (POTE): ~11/9 = 353.958

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1\1, ~11/9 = 353.139

* [[POTE]]: ~2 = 1\1, ~11/9 = 353.958

Line 67:

Line 77:

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

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

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

: gencom: [2 3/2; 64/63 78/77 99/98]

: gencom: [2 11/9; 64/63 78/77 144/143]

Optimal ~~tuning (~~POTE): ~11/9 = 353.775

Optimal tunings:

* CTE: ~2 = 1\1, ~11/9 = 353.219

* POTE: ~2 = 1\1, ~11/9 = 353.775

Optimal ET sequence: {{Optimal ET sequence| 7, 10, 17, 44e, 61de }}

Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]

== Mohaha ==

~~{{See also~~| ~~No-sevens subgroup temperaments~~ #~~Mohaha }}~~

Mohaha can be thought of, intuitively, as "meantone with quartertones"; as is the 3/2 generator subdivided in half, so is the [[~]][[25/24]] chromatic semitone divided into two equal ~[[33/32]] quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10~12/11's, and that maps four 3/2's to 5/1. It has a heptatonic mos with three larger steps and four smaller ones, going [[3L 4s|sLsLsLs]]. Taking septimal meantone mapping of 7 leads to [[#Migration]], flattone mapping of 7 leads to [[#Ptolemy]], and dominant mapping of 7 leads to [[#Neutrominant]], while tempering out [[176/175]] gives [[mohajira]] (shown at [[Meantone family#Mohajira|Meantone family]]).

~~Mohaha is the~~ 2.3.5.11 subgroup temperament with a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 11/9. Mohaha can be thought of, intuitively, as "meantone with quartertones"; as is the 3/2 generator subdivided in half, so is the [[~]][[25/~~24]] chromatic semitone divided into two equal ~[[33~~/32]] quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10~12/11's, and that maps four 3/2's to 5/1. It has a heptatonic mos with three larger steps and four smaller ones, ~~going~~ [[~~4L 3s~~|~~sLsLsLs]]. Taking septimal meantone mapping of 7 leads to [[#Migration]], flattone mapping of 7 leads to [[#Ptolemy]], and dominant mapping of 7 leads to [[#Neutrominant~~]].

=== 2.3.5.11 subgroup ===

The [[S-expression]]-based comma list of this temperament is {[[81/80|S6/S8 = S9]], [[121/120|S11]]}.

[[Subgroup]]: 2.3.5.11

Line 92:

Line 105:

: gencom: [2 11/9; 81/80 121/120]

: [[gencom]]: [2 11/9; 81/80 121/120]

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/9 = 348.8296

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1\1, ~11/9 = 348.8296

* [[POTE]]: ~2 = 1\1, ~11/9 = 348.0938

{{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 69e, 100e, 131bee }}

Line 100:

Line 115:

Scales: [[mohaha7]], [[mohaha10]]

=== Mohoho ===

==== Mohoho ====

Subgroup: 2.3.5.11.13

Line 113:

Line 128:

: gencom: [2 11/9; 66/65 81/80 121/120]

Optimal ~~tuning (~~CTE): ~2 = 1\1, ~11/9 = 348.8794

Optimal tunings:

* CTE: ~2 = 1\1, ~11/9 = 348.8794

* POTE: ~2 = 1\1, ~11/9 = 348.9155

Line 128:

Line 145:

: mapping generators: ~2, ~11/9

Optimal ~~tuning (~~CTE): ~2 = 1\1, ~11/9 = 348.5324

Optimal tunings:

* CTE: ~2 = 1\1, ~11/9 = 348.5324

* POTE: ~2 = 1\1, ~11/9 = 348.182

{{Optimal ET sequence~~|legend=1~~| 7d, 24d, 31, 100de, 131bdee, 162bdee }}

Optimal ET sequence: {{Optimal ET sequence| 7d, 24d, 31, 100de, 131bdee, 162bdee }}

Badness: 0.025516

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 81/80, 121/120, 126/125

Mapping: {{mapping| 1 1 0 -3 2 4 | 0 2 8 20 5 -1 }}

Optimal tunings:

* CTE: ~2 = 1\1, ~11/9 = 348.5444

* POTE: ~2 = 1\1, ~11/9 = 348.490

Optimal ET sequence: {{Optimal ET sequence| 7d, 24d, 31 }}

Badness: 0.028071

=== Ptolemy ===

{{Redirect|Ptolemy|the Ancient Greek polymath|Wikipedia: Ptolemy}}

Subgroup: 2.3.5.7.11

Line 143:

Line 179:

: mapping generators: ~2, ~11/9

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~11/9 = 346.922

Optimal tunings:

* CTE: ~2 = 1\1, ~11/9 = 346.905

* POTE: ~2 = 1\1, ~11/9 = 346.922

Optimal ET sequence: {{Optimal ET sequence| 7, 31dd, 38d, 45e, 83bcddee }}

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

Comma list: 65/64, 81/80, 105/104, 121/120

Mapping: {{mapping| 1 1 0 8 2 6 | 0 2 8 -18 5 -8 }}

Optimal tunings:

* CTE: ~2 = 1\1, ~11/9 = 346.754

* POTE: ~2 = 1\1, ~11/9 = 346.910

{{Optimal ET sequence~~|legend=1~~| 7, ~~31dd~~, ~~38d~~, ~~45e~~, ~~83bcddee~~ }}

Optimal ET sequence: {{Optimal ET sequence| 7, 31ddf, 38df, 45ef, 83bcddeeff }}

== Neutrominant ==

Badness: 0.034316

=== Neutrominant ===

<span style="display: block; text-align: right;">[[:de:maqamisch|Deutsch]]</span>

Line 161:

Line 214:

: mapping generators: ~2, ~11/9

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~11/9 = 350.934

Optimal tunings:

* CTE: ~2 = 1\1, ~11/9 = 349.865

* POTE: ~2 = 1\1, ~11/9 = 350.934

Optimal ET sequence: {{Optimal ET sequence| 7, 17c, 24d, 41cd }}

Badness: 0.040240

=== 13-limit ===

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

Line 174:

Line 229:

Mapping: {{mapping| 1 1 0 4 2 4 | 0 2 8 -4 5 -1 }}

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~11/9 = 350.816

Optimal tunings:

* CTE: ~2 = 1\1, ~11/9 = 349.904

* POTE: ~2 = 1\1, ~11/9 = 350.816

Optimal ET sequence: {{Optimal ET sequence| 7, 17c, 24d, 41cd }}

Badness: 0.027214

== Semisema ==

In addition to dividing the perfect fifth into two equal parts of {{nowrap|11/9 ~ 27/22}}, semisema, being an extension of [[semaphore]], also divides the perfect fourth into two equal parts of {{nowrap|7/6 ~ 8/7}}.

Subgroup: 2.3.7.11

Comma list: 49/48, 243/242

: sval mapping generators: ~77/54, ~11/9

: [[gencom]]: [77/54 11/9; 49/48 243/242]

Optimal tunings:

* CTE: ~77/54 = 1\2, ~11/9 = 351.181

* POTE: ~77/54 = 1\2, ~11/9 = 348.728

Optimal ET Sequence: {{Optimal ET sequence|10, 14, 24, 62dd}}

[[Category:Temperament clans]]

[[Category:Pages with mostly numerical content]]

[[Category:Rastmic clan| ]]

[[Category:Rastmic| ]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
-The '''rastmic clan''' of temperaments [[tempers out]] 243/242.
+{{Technical data page}}
+The '''rastmic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[rastma]], {{nowrap|243/242 {{=}} {{monzo| -1 5 0 0 -2 }}}}.
 == Neutral ==
-Neutral can be thought of as the 2.3.11 version of either [[mohajira]] or [[maqamic]], as well as suhajira and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]].
+Neutral is the 2.3.11-[[subgroup]] temperament with a [[generator]] of a neutral third which can be taken to represent {{nowrap|[[11/9]] [[~]] [[27/22]]}}, two of which make up a perfect fifth of [[3/2]]. It can be thought of as the 2.3.11 version of either [[mohajira]] or [[neutrominant]], as well as [[suhajira]] and [[archytas clan #Ringo|ringo]]. Among other things, it is the temperament optimizing the [[neutral tetrad]].
 [[Subgroup]]: 2.3.11
@@ Line 14: / Line 15: @@
 {{Mapping|legend=3| 1 1 0 0 2 | 0 2 0 0 5 }}
-: gencom: [2 11/9; 243/242]
+: [[gencom]]: [2 11/9; 243/242]
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 350.525
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~11/9 = 350.572
+* [[POTE]]: ~2 = 1\1, ~11/9 = 350.525
 {{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 }}
@@ Line 25: / Line 28: @@
 === Namo ===
+Namo adds [[144/143]] to the comma list and finds ~[[16/13]] at the same neutral third. With {{nowrap|11/9 ~ 16/13}}, it requires a slightly flat ~[[27/22]] as the tuning of the neutral third. [[58edo]] is the largest [[patent val]] tuning for it in the [[optimal ET sequence]], with a tuning between that of [[17edo]] and [[41edo]], so that ~11 and ~13 are practically equally sharp, given that [[29edo]] forms a [[consistent circle]] of [[13/11]]'s with a [[closing error]] of 31.2%. It might be recommended as a tuning for this reason, as having the neutral third much sharper to optimize plausibility of ~16/13 implies that the 11 is extremely sharp because 11/9 must be tuned sharp so that 11 must be sharper than 9, which is thus four times as sharp as however sharp of the (3/2)<sup>1/2</sup> neutral third is, while tuning it much flatter means that you increase the error of 16/13, which in 58edo is already as almost 8{{cent}} off and in [[99edo|99ef]] it is only slightly worse. For these reasons, Godtone is not fond of the recommendations by the various [[optimal tuning]]s to tune flat of 58edo, although it is clear that in an optimal tuning nothing much sharper than 58edo should be used, as making 11 more off than 13 would imply damaging 3 and 11/9 more than necessary. Curiously, [[POTE]] recommends a sharper tuning than both [[CTE]] and [[CWE]] here, but still flat of 58edo.
 [[Subgroup]]: 2.3.11.13
@@ Line 35: / Line 40: @@
 : gencom: [2 11/9; 144/143 243/242]
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 351.488
+[[Optimal tuning]]s:
+* [[CTE]]: 2 = 1\1, ~11/9 = 350.746
+* [[CWE]]: 2 = 1\1, ~11/9 = 351.270
+* [[POTE]]: 2 = 1\1, ~11/9 = 351.488
-{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41 }}
+{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 58, 99ef, 239eefff, 338eeeffff }}
 [[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents
 == Suhajira ==
-Subgroup: 2.3.7.11
+[[Subgroup]]: 2.3.7.11
-Comma list: 64/63, 243/242
+[[Comma list]]: 64/63, 243/242
-Sval mapping: {{mapping| 1 1 4 2 | 0 2 -4 5 }}
+{{Mapping|legend=2| 1 1 4 2 | 0 2 -4 5 }}
 : sval mapping generators: ~2, ~11/9
-Gencom mapping: {{mapping| 1 1 0 4 2 | 0 1 0 -4 5 }}
+{{Mapping|legend=3| 1 1 0 4 2 | 0 2 0 -4 5 }}
-: gencom: [2 3/2; 64/63 99/98]
+: [[gencom]]: [2 11/9; 64/63 243/242]
-Optimal tuning (POTE): ~11/9 = 353.958
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~11/9 = 353.139
+* [[POTE]]: ~2 = 1\1, ~11/9 = 353.958
 {{Optimal ET sequence|legend=1| 7, 10, 17, 44e, 61de }}
@@ Line 67: / Line 77: @@
 Sval mapping: {{mapping| 1 1 4 2 4 | 0 2 -4 5 -1 }}
-Gencom mapping: {{mapping| 1 1 0 4 2 4 | 0 1 0 -4 5 -1 }}
+Gencom mapping: {{mapping| 1 1 0 4 2 4 | 0 2 0 -4 5 -1 }}
-: gencom: [2 3/2; 64/63 78/77 99/98]
+: gencom: [2 11/9; 64/63 78/77 144/143]
-Optimal tuning (POTE): ~11/9 = 353.775
+Optimal tunings:
+* CTE: ~2 = 1\1, ~11/9 = 353.219
+* POTE: ~2 = 1\1, ~11/9 = 353.775
-{{Optimal ET sequence|legend=1| 7, 10, 17, 44e, 61de }}
+Optimal ET sequence: {{Optimal ET sequence| 7, 10, 17, 44e, 61de }}
 Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]
 == Mohaha ==
-{{See also| No-sevens subgroup temperaments #Mohaha }}
+Mohaha can be thought of, intuitively, as "meantone with quartertones"; as is the 3/2 generator subdivided in half, so is the [[~]][[25/24]] chromatic semitone divided into two equal ~[[33/32]] quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10~12/11's, and that maps four 3/2's to 5/1. It has a heptatonic mos with three larger steps and four smaller ones, going [[3L 4s|sLsLsLs]]. Taking septimal meantone mapping of 7 leads to [[#Migration]], flattone mapping of 7 leads to [[#Ptolemy]], and dominant mapping of 7 leads to [[#Neutrominant]], while tempering out [[176/175]] gives [[mohajira]] (shown at [[Meantone family#Mohajira|Meantone family]]).
-Mohaha is the 2.3.5.11 subgroup temperament with a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 11/9. Mohaha can be thought of, intuitively, as "meantone with quartertones"; as is the 3/2 generator subdivided in half, so is the [[~]][[25/24]] chromatic semitone divided into two equal ~[[33/32]] quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10~12/11's, and that maps four 3/2's to 5/1. It has a heptatonic mos with three larger steps and four smaller ones, going [[4L 3s|sLsLsLs]]. Taking septimal meantone mapping of 7 leads to [[#Migration]], flattone mapping of 7 leads to [[#Ptolemy]], and dominant mapping of 7 leads to [[#Neutrominant]].
+=== 2.3.5.11 subgroup ===
+The [[S-expression]]-based comma list of this temperament is {[[81/80|S6/S8 = S9]], [[121/120|S11]]}.
 [[Subgroup]]: 2.3.5.11
@@ Line 92: / Line 105: @@
 {{Mapping|legend=3| 1 1 0 0 2 | 0 2 8 0 5 }}
-: gencom: [2 11/9; 81/80 121/120]
+: [[gencom]]: [2 11/9; 81/80 121/120]
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/9 = 348.8296
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~11/9 = 348.8296
+* [[POTE]]: ~2 = 1\1, ~11/9 = 348.0938
 {{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 69e, 100e, 131bee }}
@@ Line 100: / Line 115: @@
 Scales: [[mohaha7]], [[mohaha10]]
-=== Mohoho ===
+==== Mohoho ====
 Subgroup: 2.3.5.11.13
@@ Line 113: / Line 128: @@
 : gencom: [2 11/9; 66/65 81/80 121/120]
-Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.8794
+Optimal tunings:
+* CTE: ~2 = 1\1, ~11/9 = 348.8794
+* POTE: ~2 = 1\1, ~11/9 = 348.9155
 {{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 55 }}
@@ Line 128: / Line 145: @@
 : mapping generators: ~2, ~11/9
-Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5324
+Optimal tunings:
+* CTE: ~2 = 1\1, ~11/9 = 348.5324
+* POTE: ~2 = 1\1, ~11/9 = 348.182
-{{Optimal ET sequence|legend=1| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
+Optimal ET sequence: {{Optimal ET sequence| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
 Badness: 0.025516
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 66/65, 81/80, 121/120, 126/125
+Mapping: {{mapping| 1 1 0 -3 2 4 | 0 2 8 20 5 -1 }}
+Optimal tunings:
+* CTE: ~2 = 1\1, ~11/9 = 348.5444
+* POTE: ~2 = 1\1, ~11/9 = 348.490
+Optimal ET sequence: {{Optimal ET sequence| 7d, 24d, 31 }}
+Badness: 0.028071
 === Ptolemy ===
+{{Redirect|Ptolemy|the Ancient Greek polymath|Wikipedia: Ptolemy}}
 Subgroup: 2.3.5.7.11
@@ Line 143: / Line 179: @@
 : mapping generators: ~2, ~11/9
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 346.922
+Optimal tunings:
+* CTE: ~2 = 1\1, ~11/9 = 346.905
+* POTE: ~2 = 1\1, ~11/9 = 346.922
+Optimal ET sequence: {{Optimal ET sequence| 7, 31dd, 38d, 45e, 83bcddee }}
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 65/64, 81/80, 105/104, 121/120
+Mapping: {{mapping| 1 1 0 8 2 6 | 0 2 8 -18 5 -8 }}
+Optimal tunings:
+* CTE: ~2 = 1\1, ~11/9 = 346.754
+* POTE: ~2 = 1\1, ~11/9 = 346.910
-{{Optimal ET sequence|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}
+Optimal ET sequence: {{Optimal ET sequence| 7, 31ddf, 38df, 45ef, 83bcddeeff }}
-== Neutrominant ==
+Badness: 0.034316
+=== Neutrominant ===
 <span style="display: block; text-align: right;">[[:de:maqamisch|Deutsch]]</span>
 {{Main| Neutrominant }}
@@ Line 161: / Line 214: @@
 : mapping generators: ~2, ~11/9
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.934
+Optimal tunings:
+* CTE: ~2 = 1\1, ~11/9 = 349.865
+* POTE: ~2 = 1\1, ~11/9 = 350.934
-{{Optimal ET sequence|legend=1| 7, 17c, 24d, 41cd }}
+Optimal ET sequence: {{Optimal ET sequence| 7, 17c, 24d, 41cd }}
 Badness: 0.040240
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
@@ Line 174: / Line 229: @@
 Mapping: {{mapping| 1 1 0 4 2 4 | 0 2 8 -4 5 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.816
+Optimal tunings:
+* CTE: ~2 = 1\1, ~11/9 = 349.904
+* POTE: ~2 = 1\1, ~11/9 = 350.816
-{{Optimal ET sequence|legend=1| 7, 17c, 24d, 41cd }}
+Optimal ET sequence: {{Optimal ET sequence| 7, 17c, 24d, 41cd }}
 Badness: 0.027214
+== Semisema ==
+In addition to dividing the perfect fifth into two equal parts of {{nowrap|11/9 ~ 27/22}}, semisema, being an extension of [[semaphore]], also divides the perfect fourth into two equal parts of {{nowrap|7/6 ~ 8/7}}.
+Subgroup: 2.3.7.11
+Comma list: 49/48, 243/242
+{{Mapping|2 2 5 4|0 2 1 5|legend=2}}
+: sval mapping generators: ~77/54, ~11/9
+{{Mapping|2 2 0 5 4|0 2 0 1 5|legend=3}}
+: [[gencom]]: [77/54 11/9; 49/48 243/242]
+Optimal tunings:
+* CTE: ~77/54 = 1\2, ~11/9 = 351.181
+* POTE: ~77/54 = 1\2, ~11/9 = 348.728
+Optimal ET Sequence: {{Optimal ET sequence|10, 14, 24, 62dd}}
 [[Category:Temperament clans]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Rastmic clan| ]] <!-- main article -->
 [[Category:Rastmic| ]] <!-- key article -->
 [[Category:Rank 2]]