Miscellaneous 7-limit temperaments: Difference between revisions

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== Uniwiz ==

: ''For extensions, see [[Keenanismic temperaments #Uniwiz]].''

Uniwiz tempers out the [[uniwiz comma]] in the 7-limit, equating the [[9/8|whole tone]] with a stack of four septimal quartertones of [[36/35]], and splits the [[2/1|octave]] in two. This means the quartertone should be sharpened a bit, leading to the natural 11-limit extension where [[385/384]] and [[9801/9800]] are tempered out.

[[Subgroup]]: 2.3.5.7

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== Mirwomo ==

: ''For extensions, see [[Rastmic rank-3 clan #Mirwomo]].''

Mirwomo tempers out the [[mirwomo comma]] in the 7-limit, equating the [[Pythagorean apotome]] with a stack of two septimal quartertones of [[36/35]], and splits the fifth in two. This means the fifth should be flattened a bit and the quartertone should be sharpened, leading to a natural 11-limit extension where [[243/242]] and [[385/384]] are tempered out.

[[Subgroup]]: 2.3.5.7

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[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.8046{{c}}, ~11/9 = 350.3723{{c}}, ~5/4 = 384.1239{{c}}

* [[WE]]: ~2 = 1200.8046{{c}}, ~128/105 = 350.3723{{c}}, ~5/4 = 384.1239{{c}}

: [[error map]]: {{val| +0.805 -0.406 -0.581 -0.848 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.1448{{c}}, ~5/4 = 383.8961{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 350.1448{{c}}, ~5/4 = 383.8961{{c}}

: error map: {{val| 0.000 -1.665 -2.418 -3.157 }}

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== Parahemif ==

: ''For extensions, see [[Rastmic rank-3 clan #Parahemif]].''

Parahemif tempers out the [[parahemif comma]] in the 7-limit, equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out.

[[Subgroup]]: 2.3.5.7

@@ Line 9: / Line 9: @@
 == Uniwiz ==
 : ''For extensions, see [[Keenanismic temperaments #Uniwiz]].''
+Uniwiz tempers out the [[uniwiz comma]] in the 7-limit, equating the [[9/8|whole tone]] with a stack of four septimal quartertones of [[36/35]], and splits the [[2/1|octave]] in two. This means the quartertone should be sharpened a bit, leading to the natural 11-limit extension where [[385/384]] and [[9801/9800]] are tempered out.
 [[Subgroup]]: 2.3.5.7
@@ Line 29: / Line 31: @@
 == Mirwomo ==
 : ''For extensions, see [[Rastmic rank-3 clan #Mirwomo]].''
+Mirwomo tempers out the [[mirwomo comma]] in the 7-limit, equating the [[Pythagorean apotome]] with a stack of two septimal quartertones of [[36/35]], and splits the fifth in two. This means the fifth should be flattened a bit and the quartertone should be sharpened, leading to a natural 11-limit extension where [[243/242]] and [[385/384]] are tempered out.
 [[Subgroup]]: 2.3.5.7
@@ Line 38: / Line 42: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.8046{{c}}, ~11/9 = 350.3723{{c}}, ~5/4 = 384.1239{{c}}
+* [[WE]]: ~2 = 1200.8046{{c}}, ~128/105 = 350.3723{{c}}, ~5/4 = 384.1239{{c}}
 : [[error map]]: {{val| +0.805 -0.406 -0.581 -0.848 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.1448{{c}}, ~5/4 = 383.8961{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 350.1448{{c}}, ~5/4 = 383.8961{{c}}
 : error map: {{val| 0.000 -1.665 -2.418 -3.157 }}
@@ Line 49: / Line 53: @@
 == Parahemif ==
 : ''For extensions, see [[Rastmic rank-3 clan #Parahemif]].''
+Parahemif tempers out the [[parahemif comma]] in the 7-limit, equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out.
 [[Subgroup]]: 2.3.5.7