Maja family: Difference between revisions

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The '''maja family''' tempers out the maja comma, {{monzo|-3 -23 17}} = 762939453125/753145430616.
{{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.
 
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<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. It is unrelated to either the [[interval quality|major quality]] or [[magic|magic temperament]].  


== Maja ==
== Maja ==
Line 6: Line 9:
[[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


{{Val list|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 }}


[[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 }}


[[POTE generator]]: ~125/81 = 747.145
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~54/35 = 747.145


{{Val list|legend=1| 8d, 45, 53 }}
{{Optimal ET sequence|legend=1| 8d, 45, 53 }}


[[Badness]]: 0.089454
[[Badness]]: 0.089454
Line 34: Line 35:
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, ~54/35 = 747.100


Optimal GPV sequence: {{Val list| 8d, 45e, 53 }}
{{Optimal ET sequence|legend=1| 8d, 45e, 53 }}


Badness: 0.049991
Badness: 0.049991
Line 47: Line 48:
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 GPV sequence: {{Val list| 8d, 45ef, 53 }}
{{Optimal ET sequence|legend=1| 8d, 45ef, 53 }}


Badness: 0.027532
Badness: 0.027532


== 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}}


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


{{Val list|legend=1| 53, 167, 220, 493bd, 713bdd }}
{{Optimal ET sequence|legend=1| 53, 167, 220, 493bd, 713bdd }}


[[Badness]]: 0.140489
[[Badness]]: 0.140489
Line 75: Line 74:
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 GPV sequence: {{Val list| 53, 114e, 167, 220, 387bd }}
{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}


Badness: 0.081931
Badness: 0.081931
Line 88: Line 87:
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 GPV sequence: {{Val list| 53, 114e, 167, 220, 387bd }}
{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}


Badness: 0.043128
Badness: 0.043128
== Notes ==


[[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: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

Notes

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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