Maja family: Difference between revisions
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{{Technical data page}} | |||
The '''maja family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|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. | ||
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{{Mapping|legend=1| 1 8 11 13 | 0 -17 -23 -27 }} | {{Mapping|legend=1| 1 8 11 13 | 0 -17 -23 -27 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~54/35 = 747.145 | |||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~ | |||
{{Optimal ET sequence|legend=1| 8d, 45, 53 }} | {{Optimal ET sequence|legend=1| 8d, 45, 53 }} | ||
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Mapping: {{mapping| 1 8 11 13 11 | 0 -17 -23 -27 -20 }} | Mapping: {{mapping| 1 8 11 13 11 | 0 -17 -23 -27 -20 }} | ||
Optimal tuning (POTE): ~2 = 1\1, ~ | Optimal tuning (POTE): ~2 = 1\1, ~54/35 = 747.100 | ||
{{Optimal ET sequence|legend=1| 8d, 45e, 53 }} | {{Optimal ET sequence|legend=1| 8d, 45e, 53 }} | ||
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{{Mapping|legend=1| 1 8 11 -7 | 0 -17 -23 26 }} | {{Mapping|legend=1| 1 8 11 -7 | 0 -17 -23 26 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.264 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.264 | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Maja family| ]] <!-- main article --> | [[Category:Maja family| ]] <!-- main article --> | ||
[[Category:Maja| ]] <!-- key article --> | [[Category:Maja| ]] <!-- key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Latest revision as of 00:26, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The maja family of rank-2 temperaments tempers out the maja comma, [-3 -23 17⟩ = 762939453125/753145430616.
Maja was named by Petr Pařízek in 2011 for 13/10 is a generator and that M and J are the 13th letter and the 10th letter, respectively[1]. It is unrelated to either the major quality or magic temperament.
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]]
Optimal tuning (POTE): ~2 = 1\1, ~54/35 = 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, ~54/35 = 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]]
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