Miscellaneous 7-limit temperaments: Difference between revisions

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: ''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.

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 [[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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== Decovulture ==

: ''For extensions, see [[Olympic clan #Baffin]].''

Decovulture tempers out the [[decovulture comma]] and splits the [[3/1|3rd harmonic]] into two semitwelfths, separated from ~[[7/4]] and ~[[12/7]] each by a [[diaschisma]].

[[Subgroup]]: 2.3.5.7

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[[Badness]] (Sintel): 13.3

== Cloudy ==

Cloudy tempers out the [[cloudy comma]], a.k.a. the 5-7-comma, equating the octave with a stack of five [[8/7]]'s.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 16807/16384

: Mapping generators: ~8/7, ~3, ~5

[[Optimal tuning]]s:

* [[WE]]: ~8/7 = 240.3136{{c}}, ~3/2 = 700.3807{{c}}, ~5/4 = 383.1686{{c}}

: [[error map]]: {{val| +1.568 -0.007 -0.010 -4.436 }}

* [[CWE]]: ~8/7 = 240.0000{{c}}, ~3/2 = 700.2940{{c}}, ~5/4 = 383.8804{{c}}

: error map: {{val| 0.000 -1.661 -2.433 -8.826 }}

{{Optimal ET sequence|legend=1| 5, 10, 15, 35, 40, 45, 50, 60, 110d, 170cdd, 175dd, 235cddd }}

[[Badness]] (Sintel): 13.9

== Linus ==

@@ Line 208: / Line 208: @@
 : ''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.
+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 [[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 273: / Line 273: @@
 == Decovulture ==
 : ''For extensions, see [[Olympic clan #Baffin]].''
+Decovulture tempers out the [[decovulture comma]] and splits the [[3/1|3rd harmonic]] into two semitwelfths, separated from ~[[7/4]] and ~[[12/7]] each by a [[diaschisma]].
 [[Subgroup]]: 2.3.5.7
@@ Line 500: / Line 502: @@
 [[Badness]] (Sintel): 13.3
+== Cloudy ==
+Cloudy tempers out the [[cloudy comma]], a.k.a. the 5-7-comma, equating the octave with a stack of five [[8/7]]'s.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 16807/16384
+{{Mapping|legend=1| 5 0 0 14 | 0 1 0 0 | 0 0 1 0 }}
+: Mapping generators: ~8/7, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~8/7 = 240.3136{{c}}, ~3/2 = 700.3807{{c}}, ~5/4 = 383.1686{{c}}
+: [[error map]]: {{val| +1.568 -0.007 -0.010 -4.436 }}
+* [[CWE]]: ~8/7 = 240.0000{{c}}, ~3/2 = 700.2940{{c}}, ~5/4 = 383.8804{{c}}
+: error map: {{val| 0.000 -1.661 -2.433 -8.826 }}
+{{Optimal ET sequence|legend=1| 5, 10, 15, 35, 40, 45, 50, 60, 110d, 170cdd, 175dd, 235cddd }}
+[[Badness]] (Sintel): 13.9
 == Linus ==