Keemic family: Difference between revisions

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The '''keemic family''' is a family of [[rank-3 temperament]]s which [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864).

The '''keemic family''' is a family of [[rank-3 temperament]]s which [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864). For [[rank-2 temperament]]s, see [[keemic temperaments]].

== Keemic ==

Keemic, also known as ''supermagic'' in earlier materials, has the same lattice structure as [[5-limit]] JI, and [[7/4]] is found by a stack of three [[~]][[6/5]]'s.

~~== Supermagic ==~~

[[Subgroup]]: 2.3.5.7

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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8060{{c}}, ~5/4 = 381.0536{{c}}

: error map: {{val| 0.000 +0.851 -5.260 -3.569 }}

~~~~

[[Minimax tuning]]:

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Scales: [[supermagic15]]

== Undecimal ~~supermagic~~ ==

== Undecimal keemic ==

Keemic is naturally an [[11-limit]] temperament due to the identity 875/864 = ([[100/99]])⋅([[385/384]]). This identifies a stack of two ~6/5's as ~[[16/11]].

[[Subgroup]]: 2.3.5.7.11

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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1922{{c}}, ~5/4 = 381.5339{{c}}

: error map: {{val| 0.000 +2.237 -4.780 -0.851 +3.365 }}

~~~~

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== Supernatural ==

Supernatural uses the same mapping as [[7-limit]] [[magic]] with an independent generator for prime 11.

[[Subgroup]]: 2.3.5.7.11

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* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.4576{{c}}, ~11/8 = 548.8962{{c}}

: error map: {{val| 0.000 +0.333 -5.856 -3.335 -2.422 }}

~~~~

{{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde }} *

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* WE: ~2 = 1201.3389{{c}}, ~5/4 = 380.4641{{c}}, ~11/8 = 547.2772{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1532{{c}}, ~11/8 = 548.2678{{c}}

~~~~

{{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }}

{{Optimal ET sequence|legend=0| 19, 22f, 38df, 41, 60e, 79d, 101cd }}

Badness (Sintel): 1.07

[[Category:Temperament families]]

~~[[Category:Pages with mostly numerical content]]~~

[[Category:Keemic family| ]]

~~[[Category:Supermagic]]~~

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''keemic family''' is a family of [[rank-3 temperament]]s which [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864).
+The '''keemic family''' is a family of [[rank-3 temperament]]s which [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864). For [[rank-2 temperament]]s, see [[keemic temperaments]].
+== Keemic ==
+Keemic, also known as ''supermagic'' in earlier materials, has the same lattice structure as [[5-limit]] JI, and [[7/4]] is found by a stack of three [[~]][[6/5]]'s.
-== Supermagic ==
 [[Subgroup]]: 2.3.5.7
@@ Line 21: / Line 23: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8060{{c}}, ~5/4 = 381.0536{{c}}
 : error map: {{val| 0.000 +0.851 -5.260 -3.569 }}
-<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8733{{c}}, ~5/4 = 380.4684{{c}} -->
 [[Minimax tuning]]:
@@ Line 36: / Line 37: @@
 Scales: [[supermagic15]]
-== Undecimal supermagic ==
+== Undecimal keemic ==
-{{See also| Ptolemismic clan #Supermagic }}
+{{See also| Ptolemismic clan #Keemic }}
+Keemic is naturally an [[11-limit]] temperament due to the identity 875/864 = ([[100/99]])⋅([[385/384]]). This identifies a stack of two ~6/5's as ~[[16/11]].
 [[Subgroup]]: 2.3.5.7.11
@@ Line 50: / Line 53: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1922{{c}}, ~5/4 = 381.5339{{c}}
 : error map: {{val| 0.000 +2.237 -4.780 -0.851 +3.365 }}
-<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1985{{c}}, ~5/4 = 381.5394{{c}} -->
 {{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104 }}
@@ Line 59: / Line 61: @@
 == Supernatural ==
+Supernatural uses the same mapping as [[7-limit]] [[magic]] with an independent generator for prime 11.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 71: / Line 75: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.4576{{c}}, ~11/8 = 548.8962{{c}}
 : error map: {{val| 0.000 +0.333 -5.856 -3.335 -2.422 }}
-<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.3520{{c}}, ~11/8 = 547.5758{{c}} -->
 {{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde }} *
@@ Line 89: / Line 92: @@
 * WE: ~2 = 1201.3389{{c}}, ~5/4 = 380.4641{{c}}, ~11/8 = 547.2772{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1532{{c}}, ~11/8 = 548.2678{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~5/4 = 380.0401{{c}}, ~11/8 = 546.6672{{c}} -->
-{{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }}
+{{Optimal ET sequence|legend=0| 19, 22f, 38df, 41, 60e, 79d, 101cd }}
 Badness (Sintel): 1.07
 [[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Keemic family| ]] <!-- main article -->
-[[Category:Supermagic]]
 [[Category:Rank 3]]