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__FORCETOC__
{{Technical data page}}
=Maja=
The '''maja family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] the [[maja comma]], {{monzo| -3 -23 17 }} = 762939453125/753145430616.
Comma: 762939453125/753145430616


POTE generator: ~125/81 = 747.198
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]].  


Map: [&lt;1 8 11|, &lt;0 -17 -23|]
== Maja ==
[[Subgroup]]: 2.3.5


EDOs: 45, 53, 432, 485, 538, 591, 644, 697, 750
[[Comma list]]: 762939453125/753145430616


Badness: 0.3610
{{Mapping|legend=1| 1 8 11 | 0 -17 -23 }}


==7-limit==
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.198
Commas: 2430/2401, 3125/3087


POTE generator: ~125/81 = 747.145
{{Optimal ET sequence|legend=1| 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c }}


Map: [&lt;1 8 11 13|, &lt;0 -17 -23 -27|]
[[Badness]]: 0.361013


EDOs: 45, 53, 469cd
== Septimal maja ==
[[Subgroup]]: 2.3.5.7


Badness: 0.0894
[[Comma list]]: 2430/2401, 3125/3087


==11-limit==
{{Mapping|legend=1| 1 8 11 13 | 0 -17 -23 -27 }}
Commas: 99/98, 121/120, 3125/3087


POTE generator: ~125/81 = 747.100
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~54/35 = 747.145


Map: [&lt;1 8 11 13 11|, &lt;0 -17 -23 -27 -20|]
{{Optimal ET sequence|legend=1| 8d, 45, 53 }}


EDOs: 45e, 53
[[Badness]]: 0.089454


Badness: 0.0500
=== 11-limit ===
Subgroup: 2.3.5.7.11


==13-limit==
Comma list: 99/98, 121/120, 3125/3087
Commas: 176/175, 275/273, 325/324, 540/539


POTE generator: ~125/81 = 747.095
Mapping: {{mapping| 1 8 11 13 11 | 0 -17 -23 -27 -20 }}


Map: [&lt;1 8 11 13 11 12|, &lt;0 -17 -23 -27 -20 -22|]
Optimal tuning (POTE): ~2 = 1\1, ~54/35 = 747.100


EDOs: 45ef, 53
{{Optimal ET sequence|legend=1| 8d, 45e, 53 }}


Badness: 0.0275
Badness: 0.049991


=Majo=
=== 13-limit ===
Commas: 6144/6125, 1250000/1240029
Subgroup: 2.3.5.7.11.13


POTE generator: ~125/81 = 747.264
Comma list: 99/98, 121/120, 169/168, 275/273


Map: [&lt;1 8 11 -7|, &lt;0 -17 -23 26|]
Mapping: {{mapping| 1 8 11 13 11 12 | 0 -17 -23 -27 -20 -22 }}


Wedgie: &lt;&lt;17 23 -26 -3 -89 -125||
Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.095


EDOs: 53, 167, 220
{{Optimal ET sequence|legend=1| 8d, 45ef, 53 }}


Badness: 0.1405
Badness: 0.027532
 
== Majo ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 6144/6125, 1250000/1240029
 
{{Mapping|legend=1| 1 8 11 -7 | 0 -17 -23 26 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.264
 
{{Optimal ET sequence|legend=1| 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: {{mapping| 1 8 11 -7 31 | 0 -17 -23 26 -73 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.287
 
{{Optimal ET sequence|legend=1| 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: {{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|legend=1| 53, 114e, 167, 220, 387bd }}
 
Badness: 0.043128
 
== Notes ==
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Maja family| ]] <!-- main article -->
[[Category:Maja| ]] <!-- key article -->
[[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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