Breedsmic temperaments: Difference between revisions

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=Tertiaseptal=

Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the ~~140~~&171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[~~171edo|~~171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.

Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 31&171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.

Commas: 2401/2400, 65625/65536

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Map: [<1 3 2 3 7 1|, <0 -22 5 -3 -55 42|]

EDOs: 31, 140e, 171~~, 373ef, 544ef~~

EDOs: 31, 140e, 171

Badness: 0.0369

==17-limit==

Commas: 243/242, 375/374, 441/440, 625/624, 3584/3575

POTE generator: ~68/65 = 77.201

Map: [<1 3 2 3 7 1 1|, <0 -22 5 -3 -55 42 48|]

EDOs: 31, 140e, 171

Badness: 0.0274

==Tertia==

@@ Line 83: / Line 83: @@
 =Tertiaseptal=
-Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo|171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.
+Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 31&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.
 Commas: 2401/2400, 65625/65536
@@ Line 113: / Line 113: @@
 Map: [&lt;1 3 2 3 7 1|, &lt;0 -22 5 -3 -55 42|]
-EDOs: 31, 140e, 171, 373ef, 544ef
+EDOs: 31, 140e, 171
 Badness: 0.0369
+==17-limit==
+Commas: 243/242, 375/374, 441/440, 625/624, 3584/3575
+POTE generator: ~68/65 = 77.201
+Map: [&lt;1 3 2 3 7 1 1|, &lt;0 -22 5 -3 -55 42 48|]
+EDOs: 31, 140e, 171
+Badness: 0.0274
 ==Tertia==