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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[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 81/80, 176/175, ~~7058~~/6875

[[Comma list]]: 81/80, 176/175, 7056/6875

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[[Subgroup]]: 2.3.5.7.11.13.17

[[Comma list]]: 81/80, 176/175, 189/~~197~~, 196/195, 832/825

[[Comma list]]: 81/80, 176/175, 189/187, 196/195, 832/825

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=== 19-limit ===

[[Subgroup]]: 2.3.5.7.11.13.19

[[Subgroup]]: 2.3.5.7.11.13.17.19

[[Comma list]]: 81/80, 96/95, 176/175, 189/187, 196/195, 832/825

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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 1,126: / Line 1,126: @@
 [[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 81/80, 176/175, 7058/6875
+[[Comma list]]: 81/80, 176/175, 7056/6875
 {{Mapping|legend=1| 1 0 -4 -32 | 0 1 4 22 30}}
@@ Line 1,158: / Line 1,158: @@
 [[Subgroup]]: 2.3.5.7.11.13.17
-[[Comma list]]: 81/80, 176/175, 189/197, 196/195, 832/825
+[[Comma list]]: 81/80, 176/175, 189/187, 196/195, 832/825
 {{Mapping|legend=1| 1 0 -4 -32 -44 12| 0 1 4 22 30 -5}}
@@ Line 1,172: / Line 1,172: @@
 === 19-limit ===
-[[Subgroup]]: 2.3.5.7.11.13.19
+[[Subgroup]]: 2.3.5.7.11.13.17.19
 [[Comma list]]: 81/80, 96/95, 176/175, 189/187, 196/195, 832/825
@@ Line 1,240: / 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