Diaschismic rank-3 family: Difference between revisions

(3 intermediate revisions by the same user not shown)

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* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.9585{{c}}, ~7/4 = 971.2952{{c}}

: error map: {{val| 0.000 +3.003 +3.769 +2.469 }}

~~~~

{{Optimal ET sequence|legend=1| 10, 12, 22, 34d, 46, 58, 68, 80, 126, 206cd, 332bccd }}

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[[Badness]] (Sintel): 1.95

== ~~Julius a~~.k.a. ~~varda ==~~

== Varda ==

Varda tempers out 176/175, 896/891 as well as 9801/9800, and is the main extension of rank-3 diaschismic to the 11-limit. Notice the identity {{nowrap| 2048/2025 {{=}} (176/175)⋅(896/891) }}. In the natural 13-limit extension, 351/350, 352/351 and 364/363 are further tempered out, and in the 17-limit, 136/135, 256/255 and 289/288.

[[Subgroup]]: 2.3.5.7.11

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* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.6576{{c}}, ~7/4 = 971.9790{{c}}

: error map: {{val| 0.000 +2.703 +4.371 +3.153 +2.031 }}

~~~~

[[Minimax tuning]]:

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; Scales

* ~~Julius~~[22] [[hobbit]] [[transversal]]:

* Varda[22] [[hobbit]] [[transversal]]:

: 28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2

* ~~Julius~~[24] hobbit transversal

* Varda[24] hobbit transversal

: 28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2

=== ~~Varda~~ ===

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

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[[Badness]] (Sintel): 2.37

~~[[Category:Temperament families]]~~

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

[[Category:Diaschismic rank-3 family| ]]

[[Category:Diaschismic| ]]

[[Category:~~Rank~~ 3]]

[[Category:Temperament families]]

[[Category:Catalogs of rank-3 temperaments]]

@@ Line 16: / Line 16: @@
 * [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.9585{{c}}, ~7/4 = 971.2952{{c}}
 : error map: {{val| 0.000 +3.003 +3.769 +2.469 }}
-<!-- * [[POTE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8982{{c}}, ~7/4 = 972.1330{{c}} -->
 {{Optimal ET sequence|legend=1| 10, 12, 22, 34d, 46, 58, 68, 80, 126, 206cd, 332bccd }}
@@ Line 22: / Line 21: @@
 [[Badness]] (Sintel): 1.95
-== Julius a.k.a. varda ==
+== Varda ==
+Varda tempers out 176/175, 896/891 as well as 9801/9800, and is the main extension of rank-3 diaschismic to the 11-limit. Notice the identity {{nowrap| 2048/2025 {{=}} (176/175)⋅(896/891) }}. In the natural 13-limit extension, 351/350, 352/351 and 364/363 are further tempered out, and in the 17-limit, 136/135, 256/255 and 289/288.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 40: / Line 41: @@
 * [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.6576{{c}}, ~7/4 = 971.9790{{c}}
 : error map: {{val| 0.000 +2.703 +4.371 +3.153 +2.031 }}
-<!-- * [[POTE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8982{{c}}, ~7/4 = 972.1330{{c}} -->
 [[Minimax tuning]]:
@@ Line 52: / Line 52: @@
 ; Scales
-* Julius[22] [[hobbit]] [[transversal]]:
+* Varda[22] [[hobbit]] [[transversal]]:
 : 28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2
-* Julius[24] hobbit transversal
+* Varda[24] hobbit transversal
 : 28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2
-=== Varda ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 198: / Line 198: @@
 [[Badness]] (Sintel): 2.37
-[[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Diaschismic rank-3 family| ]] <!-- main article -->
 [[Category:Diaschismic| ]] <!-- key article -->
-[[Category:Rank 3]]
+[[Category:Temperament families]]
+[[Category:Catalogs of rank-3 temperaments]]