Maja family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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The '''maja family''' tempers out the maja comma, {{monzo|-3 -23 17}} = 762939453125/753145430616.
The '''maja family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] the [[maja comma]], {{monzo| -3 -23 17 }} = 762939453125/753145430616.


== Maja ==
== Maja ==
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[[Comma list]]: 762939453125/753145430616
[[Comma list]]: 762939453125/753145430616


[[POTE generator]]: ~125/81 = 747.198
{{Mapping|legend=1| 1 8 11 | 0 -17 -23 }}


[[Mapping]]: [{{val|1 8 11}}, {{val|0 -17 -23}}]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.198


{{Optimal ET sequence|legend=1| 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c }}
{{Optimal ET sequence|legend=1| 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c }}
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[[Badness]]: 0.361013
[[Badness]]: 0.361013


=== 7-limit ===
== Septimal maja ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 2430/2401, 3125/3087  
[[Comma list]]: 2430/2401, 3125/3087  


[[Mapping]]: [{{val|1 8 11 13}}, {{val|0 -17 -23 -27}}]
{{Mapping|legend=1| 1 8 11 13 | 0 -17 -23 -27 }}


{{Multival|legend=1| 17 23 27 -3 -5 -2 }}
{{Multival|legend=1| 17 23 27 -3 -5 -2 }}


[[POTE generator]]: ~125/81 = 747.145
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.145


{{Optimal ET sequence|legend=1| 8d, 45, 53 }}
{{Optimal ET sequence|legend=1| 8d, 45, 53 }}
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Comma list: 99/98, 121/120, 3125/3087
Comma list: 99/98, 121/120, 3125/3087


Mapping: [{{val|1 8 11 13 11}}, {{val|0 -17 -23 -27 -20}}]
Mapping: {{mapping| 1 8 11 13 11 | 0 -17 -23 -27 -20 }}


POTE generator: ~77/50 = 747.100
Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.100


{{Optimal ET sequence|legend=1| 8d, 45e, 53 }}
{{Optimal ET sequence|legend=1| 8d, 45e, 53 }}
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Comma list: 99/98, 121/120, 169/168, 275/273
Comma list: 99/98, 121/120, 169/168, 275/273


Mapping: [{{val|1 8 11 13 11 12}}, {{val|0 -17 -23 -27 -20 -22}}]
Mapping: {{mapping| 1 8 11 13 11 12 | 0 -17 -23 -27 -20 -22 }}


POTE generator: ~20/13 = 747.095
Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.095


{{Optimal ET sequence|legend=1| 8d, 45ef, 53 }}
{{Optimal ET sequence|legend=1| 8d, 45ef, 53 }}
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== Majo ==
== Majo ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 6144/6125, 1250000/1240029
[[Comma list]]: 6144/6125, 1250000/1240029


[[Mapping]]: [{{val|1 8 11 -7}}, {{val|0 -17 -23 26}}]
{{Mapping|legend=1| 1 8 11 -7 | 0 -17 -23 26 }}


{{Multival|legend=1|17 23 -26 -3 -89 -125}}
{{Multival|legend=1| 17 23 -26 -3 -89 -125 }}


[[POTE generator]]: ~125/81 = 747.264
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.264


{{Optimal ET sequence|legend=1| 53, 167, 220, 493bd, 713bdd }}
{{Optimal ET sequence|legend=1| 53, 167, 220, 493bd, 713bdd }}
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Comma list: 2200/2187, 3388/3375, 6144/6125
Comma list: 2200/2187, 3388/3375, 6144/6125


Mapping: [{{val|1 8 11 -7 31}}, {{val|0 -17 -23 26 -73}}]
Mapping: {{mapping| 1 8 11 -7 31 | 0 -17 -23 26 -73 }}


POTE generator: ~77/50 = 747.287
Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.287


{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
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Comma list: 325/324, 352/351, 1001/1000, 2704/2695
Comma list: 325/324, 352/351, 1001/1000, 2704/2695


Mapping: [{{val|1 8 11 -7 31 12}}, {{val|0 -17 -23 26 -73 -22}}]
Mapping: {{mapping| 1 8 11 -7 31 12 | 0 -17 -23 26 -73 -22 }}


POTE generator: ~20/13 = 747.286
Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.286


{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Maja family| ]] <!-- main article -->
[[Category:Maja family| ]] <!-- main article -->
[[Category:Maja| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 05:29, 22 September 2023

The maja family of rank-2 temperaments tempers out the maja comma, [-3 -23 17⟩ = 762939453125/753145430616.

Maja

Subgroup: 2.3.5

Comma list: 762939453125/753145430616

Mapping: [⟨1 8 11], ⟨0 -17 -23]]

Optimal tuning (POTE): ~2 = 1\1, ~125/81 = 747.198

Optimal ET sequence: 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c

Badness: 0.361013

Septimal maja

Subgroup: 2.3.5.7

Comma list: 2430/2401, 3125/3087

Mapping: [⟨1 8 11 13], ⟨0 -17 -23 -27]]

Wedgie: ⟨⟨ 17 23 27 -3 -5 -2 ]]

Optimal tuning (POTE): ~2 = 1\1, ~125/81 = 747.145

Optimal ET sequence: 8d, 45, 53

Badness: 0.089454

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 121/120, 3125/3087

Mapping: [⟨1 8 11 13 11], ⟨0 -17 -23 -27 -20]]

Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.100

Optimal ET sequence: 8d, 45e, 53

Badness: 0.049991

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 121/120, 169/168, 275/273

Mapping: [⟨1 8 11 13 11 12], ⟨0 -17 -23 -27 -20 -22]]

Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.095

Optimal ET sequence: 8d, 45ef, 53

Badness: 0.027532

Majo

Subgroup: 2.3.5.7

Comma list: 6144/6125, 1250000/1240029

Mapping: [⟨1 8 11 -7], ⟨0 -17 -23 26]]

Wedgie: ⟨⟨ 17 23 -26 -3 -89 -125 ]]

Optimal tuning (POTE): ~2 = 1\1, ~125/81 = 747.264

Optimal ET sequence: 53, 167, 220, 493bd, 713bdd

Badness: 0.140489

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2200/2187, 3388/3375, 6144/6125

Mapping: [⟨1 8 11 -7 31], ⟨0 -17 -23 26 -73]]

Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.287

Optimal ET sequence: 53, 114e, 167, 220, 387bd

Badness: 0.081931

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 1001/1000, 2704/2695

Mapping: [⟨1 8 11 -7 31 12], ⟨0 -17 -23 26 -73 -22]]

Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.286

Optimal ET sequence: 53, 114e, 167, 220, 387bd

Badness: 0.043128

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