Horwell family: Difference between revisions

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The '''horwell family''' of rank-3 ~~temperaments~~ tempers out the [[horwell comma]]~~, 65625/65536 =~~ {{monzo| -16 1 5 1 }}.

The '''horwell family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[horwell comma]] ({{monzo|legend=1| -16 1 5 1 }}, 65625/65536).

== Horwell ==

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: mapping generators: ~2, ~3, ~5

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: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7

{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, ~~2587cd, 2758cd, 2929cd, 3100cd, 3271ccd~~, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}

{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, …, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}

[[Badness]]: 0.~~173 × 10-3~~

[[Badness]] (Sintel): 0.761

[[Projection pair]]: 7 65536/9375

[[Projection pair]]: <code>7 65536/9375</code>

== Zelda ==

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{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, ~~547de~~ }}

{{Optimal ET sequence|legend=1| 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee }}

[[Badness]]: 0.~~642 × 10-3~~

[[Badness]] (Sintel): 0.771

== Horwellic ==

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{{Optimal ET sequence|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}

{{Optimal ET sequence|legend=1| 25e, 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}

[[Badness]]: 0.~~505 × 10-3~~

[[Badness]] (Sintel): 0.607

[[Category:Temperament families]]

[[Category:Horwell family| ]]

~~[[Category:Horwell| ]] ~~

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''horwell family''' of rank-3 temperaments tempers out the [[horwell comma]], 65625/65536 = {{monzo| -16 1 5 1 }}.
+The '''horwell family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[horwell comma]] ({{monzo|legend=1| -16 1 5 1 }}, 65625/65536).
 == Horwell ==
@@ Line 8: / Line 8: @@
 {{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }}
 : mapping generators: ~2, ~3, ~5
@@ Line 25: / Line 24: @@
 : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7
-{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}
+{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, …, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}
-[[Badness]]: 0.173 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.761
-[[Projection pair]]: 7 65536/9375
+[[Projection pair]]: <code>7 65536/9375</code>
 == Zelda ==
@@ Line 38: / Line 37: @@
 {{Mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }}
-{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }}
+{{Optimal ET sequence|legend=1| 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee }}
-[[Badness]]: 0.642 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.771
 == Horwellic ==
@@ Line 49: / Line 48: @@
 {{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }}
-{{Optimal ET sequence|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}
+{{Optimal ET sequence|legend=1| 25e, 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}
-[[Badness]]: 0.505 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.607
 [[Category:Temperament families]]
 [[Category:Horwell family| ]] <!-- main article -->
-[[Category:Horwell| ]] <!-- key article -->
 [[Category:Rank 3]]