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 }}.

== Horwell ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 65625/65536

~~[[Mapping]]: [~~{{~~val~~| 1 0 0 16 ~~}}, {{val~~| 0 1 0 -1 ~~}}, {{val~~| 0 0 1 -5 }}]

~~Mapping~~ generators: ~2, ~3, ~5

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

Mapping to lattice: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]

[[Mapping to lattice]]: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]

Lattice basis:

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[[Minimax tuning]]:

* [[7-odd-limit]]

: [{{monzo| 1 0 0 0 ~~}}, {{monzo~~| 16/7 6/7 -5/7 -1/7 ~~}}, {{monzo~~| 16/7 -1/7 2/7 -1/7 ~~}}, {{monzo~~| 16/7 -1/7 -5/7 6/7 }}]

: {{monzo list| 1 0 0 0 | 16/7 6/7 -5/7 -1/7 | 16/7 -1/7 2/7 -1/7 | 16/7 -1/7 -5/7 6/7 }}

: [[Eigenmonzo]]s: 2, 7/~~6, 6/5~~

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.7/3

* [[9-odd-limit]]

: [{{monzo| 1 0 0 0 ~~}}, {{monzo~~| 16/13 12/13 -5/13 -1/13 ~~}}, {{monzo~~| 32/13 -2/13 3/13 -2/13 ~~}}, {{monzo~~| 32/13 -2/13 -10/13 11/13 }}]

: {{monzo list| 1 0 0 0 | 16/13 12/13 -5/13 -1/13 | 32/13 -2/13 3/13 -2/13 | 32/13 -2/13 -10/13 11/13 }}

: [[Eigenmonzo]]s: 2, 9/7~~, 7/5~~

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

{{~~Val list~~|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, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}

[[Badness]]: 0.173 × 10-3

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== Zelda ==

Subgroup: 2.3.5.7.11

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 385/384, 3388/3375

~~[[Mapping]]: [~~{{~~val~~| 1 0 0 16 -9 ~~}}, {{val~~| 0 1 0 -1 2 ~~}}, {{val~~| 0 0 1 -5 4 }}]

{{~~Val list~~|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }}

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

[[Badness]]: 0.642 × 10-3

== Horwellic ==

Subgroup: 2.3.5.7.11

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 3025/3024, 65625/65536

~~[[Mapping]]: [~~{{~~val~~| 1 0 0 16 10 ~~}}, {{val~~| 0 1 0 -1 1 ~~}}, {{val~~| 0 0 2 -10 -7 }}]

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

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

[[Badness]]: 0.505 × 10-3

[[Category:~~Regular temperament theory~~]]

[[Category:Temperament families]]

[[Category:~~Temperament family~~]]

[[Category:Pages with mostly numerical content]]

[[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 }}.
 == Horwell ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 65625/65536
-[[Mapping]]: [{{val| 1 0 0 16 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -5 }}]
+{{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }}
-Mapping generators: ~2, ~3, ~5
+: mapping generators: ~2, ~3, ~5
-Mapping to lattice: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]
+[[Mapping to lattice]]: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]
 Lattice basis:
@@ Line 18: / Line 19: @@
 [[Minimax tuning]]:
 * [[7-odd-limit]]
-: [{{monzo| 1 0 0 0 }}, {{monzo| 16/7 6/7 -5/7 -1/7 }}, {{monzo| 16/7 -1/7 2/7 -1/7 }}, {{monzo| 16/7 -1/7 -5/7 6/7 }}]
+: {{monzo list| 1 0 0 0 | 16/7 6/7 -5/7 -1/7 | 16/7 -1/7 2/7 -1/7 | 16/7 -1/7 -5/7 6/7 }}
-: [[Eigenmonzo]]s: 2, 7/6, 6/5
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.7/3
 * [[9-odd-limit]]
-: [{{monzo| 1 0 0 0 }}, {{monzo| 16/13 12/13 -5/13 -1/13 }}, {{monzo| 32/13 -2/13 3/13 -2/13 }}, {{monzo| 32/13 -2/13 -10/13 11/13 }}]
+: {{monzo list| 1 0 0 0 | 16/13 12/13 -5/13 -1/13 | 32/13 -2/13 3/13 -2/13 | 32/13 -2/13 -10/13 11/13 }}
-: [[Eigenmonzo]]s: 2, 9/7, 7/5
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7
-{{Val list|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, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}
 [[Badness]]: 0.173 × 10<sup>-3</sup>
@@ Line 31: / Line 32: @@
 == Zelda ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 385/384, 3388/3375
-[[Mapping]]: [{{val| 1 0 0 16 -9 }}, {{val| 0 1 0 -1 2 }}, {{val| 0 0 1 -5 4 }}]
+{{Mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }}
-{{Val list|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }}
+{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }}
 [[Badness]]: 0.642 × 10<sup>-3</sup>
 == Horwellic ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 3025/3024, 65625/65536
-[[Mapping]]: [{{val| 1 0 0 16 10 }}, {{val| 0 1 0 -1 1 }}, {{val| 0 0 2 -10 -7 }}]
+{{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }}
-{{Val list|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}
+{{Optimal ET sequence|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}
 [[Badness]]: 0.505 × 10<sup>-3</sup>
-[[Category:Regular temperament theory]]
+[[Category:Temperament families]]
-[[Category:Temperament family]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Horwell family| ]] <!-- main article -->
+[[Category:Horwell| ]] <!-- key article -->
 [[Category:Rank 3]]