Orwellismic family: Difference between revisions

(3 intermediate revisions by one other user not shown)

Line 17:

: 7/6 length = 0.7526, 3/2 length = 1.3931

: Angle (7/6, 3/2) = 97.5081

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.4176{{c}}, ~3/2 = 701.8055{{c}}, ~12/7 = 928.9445{{c}}

: [[error map]]: {{val| -0.582 -0.732 +0.520 +2.288 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6429{{c}}, ~12/7 = 929.2316{{c}}

: error map: {{val| 0.000 -0.312 +1.381 +3.585 }}

[[Minimax tuning]]:

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Line 31:

{{Optimal ET sequence|legend=1| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}

[[Badness]] (~~Smith~~): 0.~~187 × 10-3~~

[[Badness]] (Sintel): 0.826

[[Projection pair]]: ~5 = 1728/343 to 2.3.7

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Line 38:

== Guanyin ==

Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]], tempering out [[540/539]], and two sharpened ~[[5/4]]'s make [[11/7]], tempering out [[176/175]].

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Line 53:

: 7/6 length = 0.5167, 3/2 length = 1.3055

: Angle (7/6, 3/2) = 79.0940

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.2336{{c}}, ~3/2 = 702.4159{{c}}, ~12/7 = 929.3128{{c}}

: [[error map]]: {{val| -0.7664 -0.3055 +1.6247 +1.9781 -1.5717 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2876{{c}}, ~12/7 = 929.7608{{c}}

: error map: {{val| 0.0000 +0.3326 +2.9688 +3.7009 -0.2261 }}

[[Minimax tuning]]:

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{{Optimal ET sequence|legend=1| 22, 27e, 31, 53, 58, 80, 111, 280cd }}

[[Badness]] (~~Smith~~): 0.~~411 × 10-3~~

[[Badness]] (Sintel): 0.494

[[Projection pair]]s: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7

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Line 82:

Mapping: {{mapping| 1 0 0 2 -2 3 | 0 1 0 1 1 -2 | 0 0 3 -1 5 5 }}

Optimal tunings:

* WE: ~2 = 1199.2015{{c}}, ~3/2 = 702.4954{{c}}, ~12/7 = 929.2881{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6821{{c}}, ~12/7 = 929.7296{{c}}

{{Optimal ET sequence|legend=0| 22, 27e, 31, 53, 58, 80, 111, 280cdf }}

Badness (~~Smith~~): 0.~~758 × 10-3~~

Badness (Sintel): 0.708

Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7

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Line 101:

Mapping: {{mapping| 1 0 0 2 -2 6 | 0 1 0 1 1 1 | 0 0 3 -1 5 -5 }}

Optimal tunings:

* WE: ~2 = 1198.4320{{c}}, ~3/2 = 702.7802{{c}}, ~12/7 = 929.4834{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5889{{c}}, ~12/7 = 930.5977{{c}}

{{Optimal ET sequence|legend=0| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }}

Badness (~~Smith~~): 0.~~904 × 10-3~~

Badness (Sintel): 0.845

Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7

Line 98:

Line 120:

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.7839{{c}}, ~3/2 = 699.6996{{c}}, ~12/7 = 928.6481{{c}}

: [[error map]]: {{val| +0.784 -1.471 -0.369 +4.577 -4.695 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 699.6270{{c}}, ~12/7 = 928.0978{{c}}

: error map: {{val| 0.000 -2.328 -2.020 +2.703 -7.514 }}

[[Badness]] (~~Smith~~): 0.~~715 × 10-3~~

[[Badness]] (Sintel): 0.859

Scales: [[orwellian chromatic]]

[[Category:Temperament families]]

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

[[Category:Orwellismic family| ]]

[[Category:Rank 3]]

[[Category:Guanyin]]

[[Category:Listen]]

@@ Line 17: / Line 17: @@
 : 7/6 length = 0.7526, 3/2 length = 1.3931
 : Angle (7/6, 3/2) = 97.5081
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.4176{{c}}, ~3/2 = 701.8055{{c}}, ~12/7 = 928.9445{{c}}
+: [[error map]]: {{val| -0.582 -0.732 +0.520 +2.288 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6429{{c}}, ~12/7 = 929.2316{{c}}
+: error map: {{val| 0.000 -0.312 +1.381 +3.585 }}
 [[Minimax tuning]]:
@@ Line 25: / Line 31: @@
 {{Optimal ET sequence|legend=1| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }}
-[[Badness]] (Smith): 0.187 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.826
 [[Projection pair]]: ~5 = 1728/343 to 2.3.7
@@ Line 32: / Line 38: @@
 == Guanyin ==
+{{See also|Subgroup temperaments#Guanyintet}}
 Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]], tempering out [[540/539]], and two sharpened ~[[5/4]]'s make [[11/7]], tempering out [[176/175]].
@@ Line 45: / Line 53: @@
 : 7/6 length = 0.5167, 3/2 length = 1.3055
 : Angle (7/6, 3/2) = 79.0940
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.2336{{c}}, ~3/2 = 702.4159{{c}}, ~12/7 = 929.3128{{c}}
+: [[error map]]: {{val| -0.7664 -0.3055 +1.6247 +1.9781 -1.5717 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2876{{c}}, ~12/7 = 929.7608{{c}}
+: error map: {{val| 0.0000 +0.3326 +2.9688 +3.7009 -0.2261 }}
 [[Minimax tuning]]:
@@ Line 53: / Line 67: @@
 {{Optimal ET sequence|legend=1| 22, 27e, 31, 53, 58, 80, 111, 280cd }}
-[[Badness]] (Smith): 0.411 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.494
 [[Projection pair]]s: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7
@@ Line 68: / Line 82: @@
 Mapping: {{mapping| 1 0 0 2 -2 3 | 0 1 0 1 1 -2 | 0 0 3 -1 5 5 }}
+Optimal tunings:
+* WE: ~2 = 1199.2015{{c}}, ~3/2 = 702.4954{{c}}, ~12/7 = 929.2881{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6821{{c}}, ~12/7 = 929.7296{{c}}
 {{Optimal ET sequence|legend=0| 22, 27e, 31, 53, 58, 80, 111, 280cdf }}
-Badness (Smith): 0.758 × 10<sup>-3</sup>
+Badness (Sintel): 0.708
 Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7
@@ Line 83: / Line 101: @@
 Mapping: {{mapping| 1 0 0 2 -2 6 | 0 1 0 1 1 1 | 0 0 3 -1 5 -5 }}
+Optimal tunings:
+* WE: ~2 = 1198.4320{{c}}, ~3/2 = 702.7802{{c}}, ~12/7 = 929.4834{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5889{{c}}, ~12/7 = 930.5977{{c}}
 {{Optimal ET sequence|legend=0| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }}
-Badness (Smith): 0.904 × 10<sup>-3</sup>
+Badness (Sintel): 0.845
 Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7
@@ Line 98: / Line 120: @@
 {{Mapping|legend=1| 1 0 0 2 5 | 0 1 0 1 0 | 0 0 3 -1 -2 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.7839{{c}}, ~3/2 = 699.6996{{c}}, ~12/7 = 928.6481{{c}}
+: [[error map]]: {{val| +0.784 -1.471 -0.369 +4.577 -4.695 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 699.6270{{c}}, ~12/7 = 928.0978{{c}}
+: error map: {{val| 0.000 -2.328 -2.020 +2.703 -7.514 }}
 {{Optimal ET sequence|legend=1| 4, 5, 9, 17, 22, 31, 53, 84e }}
-[[Badness]] (Smith): 0.715 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.859
 Scales: [[orwellian chromatic]]
 [[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Orwellismic family| ]] <!-- main article -->
 [[Category:Rank 3]]
 [[Category:Guanyin]]
 [[Category:Listen]]