Hemimean family: Difference between revisions
Don't know why it doesn't start with order 1 edos ("order 1" means 225/224 and 126/125 are one step each) |
m Cleanup; recategory |
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The '''hemimean family''' of temperaments are rank-3 temperaments tempering out [[3136/3125]]. | |||
The hemimean | |||
[[ | The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with [[Spectrum of a temperament|spectrum]] 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7. | ||
= Hemimean = | |||
[[Comma]]: 3136/3125, hemimean | |||
7 and 9 limit minimax | 7 and 9 limit minimax | ||
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[|1 0 0 0>, |0 1 0 0>, |6/5 0 0 2/5>, |0 0 0 1>] | [|1 0 0 0>, |0 1 0 0>, |6/5 0 0 2/5>, |0 0 0 1>] | ||
[[Eigenmonzo | [[Eigenmonzo]]s: 2, 7/6, 4/3 | ||
Lattice basis: 28/25 length 0.5055 3/2 length 1.5849 | Lattice basis: 28/25 length 0.5055 3/2 length 1.5849 | ||
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Map: [<1 0 0 -3|, <0 1 0 0|, <0 0 2 5|] | Map: [<1 0 0 -3|, <0 1 0 0|, <0 0 2 5|] | ||
[[ | [[Generator]]s: 2, 3, 56/25 | ||
[[EDO|Edos]]: {{EDOs|68, 80, 87, 99, 217, 229, 328, 347, 446, 545c, 675c}} | [[EDO|Edos]]: {{EDOs|68, 80, 87, 99, 217, 229, 328, 347, 446, 545c, 675c}} | ||
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Badness: 0.000160 | Badness: 0.000160 | ||
[[ | [[Projection pair]]s: 5 3136/625 7 68841472/9765625 to 2.3.25/7 | ||
=Belobog= | = Belobog = | ||
[[Comma | [[Comma]]s: 441/440, 3136/3125 | ||
11 limit minimax | 11 limit minimax | ||
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|24/11 -4/11 -13/11 2/11 13/11>] | |24/11 -4/11 -13/11 2/11 13/11>] | ||
[[Eigenmonzo | [[Eigenmonzo]]s: 2, 11/10, 9/7 | ||
Lattice basis: 28/25 0.3829 16/15 1.1705 | Lattice basis: 28/25 0.3829 16/15 1.1705 | ||
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Map: [<1 0 0 -3 -9|, <0 1 0 0 2|, [0 0 2 5 8|] | Map: [<1 0 0 -3 -9|, <0 1 0 0 2|, [0 0 2 5 8|] | ||
[[ | [[Generator]]s: 2, 3, 56/25 | ||
[[EDO|Edos]]: 12, 31, 87, 118, 130, 217, [[248edo|248]], [[378edo|378]], [[626edo|626]], [[961edo|961cd]] | [[EDO|Edos]]: 12, 31, 87, 118, 130, 217, [[248edo|248]], [[378edo|378]], [[626edo|626]], [[961edo|961cd]] | ||
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Projection pairs: 5 3136/625 7 68841472/9765625 11 1700108992512/152587890625 to 2.3.25/7 | Projection pairs: 5 3136/625 7 68841472/9765625 11 1700108992512/152587890625 to 2.3.25/7 | ||
Scales: [[ | Scales: [[belobog31]] | ||
==13-limit== | == 13-limit == | ||
Commas: 441/440, 1001/1000, 3136/3125 | Commas: 441/440, 1001/1000, 3136/3125 | ||
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Badness: 0.00111 | Badness: 0.00111 | ||
==Bellowblog== | == Bellowblog == | ||
Commas: 196/195, 352/351, 625/624 | Commas: 196/195, 352/351, 625/624 | ||
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Badness: 0.00126 | Badness: 0.00126 | ||
=Siebog= | = Siebog = | ||
[[Comma | [[Comma]]s: 540/539, 3136/3125 | ||
11 limit minimax | 11 limit minimax | ||
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|1 3/2 1/2 0 -1/2>, |8/5 3/5 -4/5 0 4/5>] | |1 3/2 1/2 0 -1/2>, |8/5 3/5 -4/5 0 4/5>] | ||
[[Eigenmonzo | [[Eigenmonzo]]s: 2, 11/10, 4/3 | ||
Map: [<1 0 0 -3 8|, <0 1 0 0 3|, <0 0 2 5 -8|] | Map: [<1 0 0 -3 8|, <0 1 0 0 3|, <0 0 2 5 -8|] | ||
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Badness: 0.000870 | Badness: 0.000870 | ||
=Triglav= | = Triglav = | ||
Commas: 3136/3125 | Commas: 3025/3024, 3136/3125 | ||
Map: [<1 0 2 2 1|, <0 1 2 5 2|, <0 0 -4 -10 -1|] | Map: [<1 0 2 2 1|, <0 1 2 5 2|, <0 0 -4 -10 -1|] | ||
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[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Hemimean]] | [[Category:Hemimean]] | ||
[[Category:Rank 3]] | |||