Miscellaneous 7-limit temperaments: Difference between revisions

(5 intermediate revisions by the same user not shown)

Line 1:

Below are listed some [[7-limit]] [[rank-3 ~~temperament|rank-3]] [[regular temperament|~~temperament]]s that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 7-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by [[TE logflat badness]]. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:

Below are listed some [[7-limit]] [[rank-3 temperament]]s that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 7-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by [[TE logflat badness]]. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:

* Individual [[temperament families and clans]]

* [[Very low accuracy temperaments]]

Line 44:

[[Badness]] (Sintel): 0.661

== Canopic a.k.a. mirkwai ==

: ''For extensions, see [[Swetismic temperaments #Indra]].''

Canopic, a.k.a. mirkwai, tempers out the [[canopic comma]] in the 7-limit.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 16875/16807

: Mapping generators: ~2, ~3, ~10/7

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9999{{c}}, ~3/2 = 701.7827{{c}}, ~10/7 = 616.0944{{c}}

: [[error map]]: {{val| -0.000 -0.172 -0.493 +0.900 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7827{{c}}, ~10/7 = 616.0945{{c}}

: error map: {{val| 0.000 -0.172 -0.493 +0.900 }}

[[Minimax tuning]]:

* [[7-odd-limit]]

: {{monzo list| 1 0 0 0 | 0 4/7 -4/7 5/7 | 0 -3/7 3/7 5/7 | 0 0 0 1 }}

: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.7

* [[9-odd-limit]]

: {{monzo list| 1 0 0 0 | 0 8/11 -4/11 5/11 | 0 -6/11 3/11 10/11 | 0 0 0 1 }}

: eigenmonzo (unchanged-interval) basis: 2.9/5.7

[[Badness]] (Sintel): 1.51

[[Projection pair]]s: <code>5 84375/16807 7 16875/2401</code> to 2.3.7/5

== Greenwoodmic ==

Line 176:

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 241:

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 468:

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 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 1: / Line 1: @@
 {{Technical data page}}
-Below are listed some [[7-limit]] [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 7-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by [[TE logflat badness]]. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:
+Below are listed some [[7-limit]] [[rank-3 temperament]]s that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 7-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by [[TE logflat badness]]. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:
 * Individual [[temperament families and clans]]
 * [[Very low accuracy temperaments]]
@@ Line 44: / Line 44: @@
 [[Badness]] (Sintel): 0.661
+== Canopic a.k.a. mirkwai ==
+: ''For extensions, see [[Swetismic temperaments #Indra]].''
+Canopic, a.k.a. mirkwai, tempers out the [[canopic comma]] in the 7-limit.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 16875/16807
+{{Mapping|legend=1| 1 0 -5 -4 | 0 1 3 3 | 0 0 5 4 }}
+: Mapping generators: ~2, ~3, ~10/7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9999{{c}}, ~3/2 = 701.7827{{c}}, ~10/7 = 616.0944{{c}}
+: [[error map]]: {{val| -0.000 -0.172 -0.493 +0.900 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7827{{c}}, ~10/7 = 616.0945{{c}}
+: error map: {{val| 0.000 -0.172 -0.493 +0.900 }}
+[[Minimax tuning]]:
+* [[7-odd-limit]]
+: {{monzo list| 1 0 0 0 | 0 4/7 -4/7 5/7 | 0 -3/7 3/7 5/7 | 0 0 0 1 }}
+: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.7
+* [[9-odd-limit]]
+: {{monzo list| 1 0 0 0 | 0 8/11 -4/11 5/11 | 0 -6/11 3/11 10/11 | 0 0 0 1 }}
+: eigenmonzo (unchanged-interval) basis: 2.9/5.7
+{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224 }}
+[[Badness]] (Sintel): 1.51
+[[Projection pair]]s: <code>5 84375/16807 7 16875/2401</code> to 2.3.7/5
 == Greenwoodmic ==
@@ Line 176: / 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 241: / 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 468: / 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 ==