Meantone family: Difference between revisions

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=== Meanpop ===

Meanpop<ref name="meantone & meanpop 2003"/><ref name="meantone & meanpop 2004"/> maps the 11/8 to the double-diminished fifth (C–G𝄫), and tridecimal meanpop maps the 13/8 to the double-augmented fifth (C–G𝄪), tempering out 144/143 like in grosstone. Note also 11/10 is a double-diminished third; 12/11~13/12, double-augmented unison; and 14/13, minor second.

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Badness (Sintel): 1.28

=== Migration ===

See [[Rastmic clan #Migration|Rastmic clan]].

== Flattone ==

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Badness (Sintel): 1.12

=== 13-limit ===

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

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Badness (Sintel): 0.920

=== Ptolemy ===

See [[Rastmic clan #Ptolemy|Rastmic clan]].

== Dominant ==

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Badness (Sintel): 0.864

=== Neutrominant ===

See [[Rastmic clan #Neutrominant|Rastmic clan]].

== Flattertone ==

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Mohajira can be viewed as derived from [[mohaha]] which maps the interval half a [[chromatic semitone|chroma]] flat of the minor seventh to ~7/4 so that 7/4 is mapped to a semidiminished seventh (C–Bdb), although mohajira really makes more sense as an 11-limit temperament. It tempers out 6144/6125, the [[porwell comma]]. It can be described as {{nowrap| 24 & 31 }}; its ploidacot is dicot. [[31edo]] makes for an excellent mohajira tuning, with generator 9\31.

Mohajira can be viewed as derived from [[mohaha]] which maps the interval half a [[chromatic semitone|chroma]] flat of the minor seventh to ~7/4 so that 7/4 is mapped to a semidiminished seventh (C–Bdb), although mohajira really makes more sense as an 11-limit temperament. It tempers out 6144/6125, the [[porwell comma]]. It can be described as {{nowrap| 24 & 31 }}; its ploidacot is dicot. [[31edo]] makes for an excellent mohajira tuning, with generator 9\31. Note that while 24 + 31 = [[55edo]] doesn't apear in the optimal ET sequence, it is a [[patent val]] tuning and recommendable if you prefer a light meantone tempering.

[[Subgroup]]: 2.3.5.7

@@ Line 406: / Line 406: @@
 === Meanpop ===
-{{See also| Meantone vs meanpop }}
+{{See also| Huygens vs meanpop }}
 Meanpop<ref name="meantone & meanpop 2003"/><ref name="meantone & meanpop 2004"/> maps the 11/8 to the double-diminished fifth (C–G𝄫), and tridecimal meanpop maps the 13/8 to the double-augmented fifth (C–G𝄪), tempering out 144/143 like in grosstone. Note also 11/10 is a double-diminished third; 12/11~13/12, double-augmented unison; and 14/13, minor second.
@@ Line 794: / Line 794: @@
 Badness (Sintel): 1.28
+=== Migration ===
+See [[Rastmic clan #Migration|Rastmic clan]].
 == Flattone ==
@@ Line 852: / Line 855: @@
 Badness (Sintel): 1.12
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
@@ Line 870: / Line 873: @@
 Badness (Sintel): 0.920
+=== Ptolemy ===
+See [[Rastmic clan #Ptolemy|Rastmic clan]].
 == Dominant ==
@@ Line 1,012: / Line 1,018: @@
 Badness (Sintel): 0.864
+=== Neutrominant ===
+See [[Rastmic clan #Neutrominant|Rastmic clan]].
 == Flattertone ==
@@ Line 1,231: / Line 1,240: @@
 {{Main| Mohajira }}
-Mohajira can be viewed as derived from [[mohaha]] which maps the interval half a [[chromatic semitone|chroma]] flat of the minor seventh to ~7/4 so that 7/4 is mapped to a semidiminished seventh (C–Bdb), although mohajira really makes more sense as an 11-limit temperament. It tempers out 6144/6125, the [[porwell comma]]. It can be described as {{nowrap| 24 & 31 }}; its ploidacot is dicot. [[31edo]] makes for an excellent mohajira tuning, with generator 9\31.
+Mohajira can be viewed as derived from [[mohaha]] which maps the interval half a [[chromatic semitone|chroma]] flat of the minor seventh to ~7/4 so that 7/4 is mapped to a semidiminished seventh (C–Bdb), although mohajira really makes more sense as an 11-limit temperament. It tempers out 6144/6125, the [[porwell comma]]. It can be described as {{nowrap| 24 & 31 }}; its ploidacot is dicot. [[31edo]] makes for an excellent mohajira tuning, with generator 9\31. Note that while 24 + 31 = [[55edo]] doesn't apear in the optimal ET sequence, it is a [[patent val]] tuning and recommendable if you prefer a light meantone tempering.
 [[Subgroup]]: 2.3.5.7