60th-octave temperaments: Difference between revisions

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Defined as the 2460 & 4320 temperament, starting with the 13-limit. Named "minutes" for period-60, since there's 60 minutes in an hour. In light of 12 being a divisor of 60, minutes tempers out the [[Kirnberger's atom]], and in the limits below 13, it's a contorted atomic temperament.

Subgroup: 2.3.5.7.11.13

[[Subgroup]]: 2.3.5.7.11.13

Comma list: 9801/9800, 250047/250000, 371293/371250, 184549376/184528125

[[Comma list]]: 9801/9800, 250047/250000, 371293/371250, 184549376/184528125

Mapping: [{{val|60 60 385 730 1085 573}}, {{val|0 1 7 -16 -25 -10}}]

[[Mapping]]: [{{val|60 60 385 730 1085 573}}, {{val|0 1 7 -16 -25 -10}}]

Mapping generators: ~2704/2673, ~3/2

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Vals: {{EDOs|540, 1380, 1920, 2460, 3000, 3840, 4380, 4920, 6300, 6840e}}

=== 19-limit ===

Subgroup: 2.3.5.7.11.13.17

Comma list: 9801/9800, 10241/10240, 13377/13376, 5929/5928, 89376/89375, 23409/23408

Mapping: [{{val|60 4 30 132 244 386 391 182}}, {{val|0 5 6 2 -2 -9 -8 4}}

Mapping generators: ~612/605, ~216/175

Optimal tuning (CTE): ~216/175 = 364.387

== Magnetismic microtemperaments ==

All these temperaments temper out the [[magnetisma]], a 2.3.29.43 subgroup comma which when tempered sets the [[87/86]] interval to 1/60th of the octave, and thus all these temperaments have a period that maps to 87/86.

===Neodymium magnet===

Defined just as neodymium in 1920 & 4380, except adds a mapping for 29 and 43 via the fact that [[87/86]] is very close to 1/60th of the octave. ~~Comma which closes a stack of 60 87/86's at the octave, is named [[magnetisma]] by [[Eliora]],~~ and thus the extension is called "neodymium magnet". Defined starting with 2.3.5.29.43 all the way into the 2.3.5.7.11.13.17.19.23.29.43 subgroup, and unlike plain neodymium, addition of .29.43 harmonics saves it from contorsion.

An extension of neodymium. Defined just as neodymium in 1920 & 4380, except adds a mapping for 29 and 43 via the fact that [[87/86]] is very close to 1/60th of the octave. and thus the extension is called "neodymium magnet". Defined starting with 2.3.5.29.43 all the way into the 2.3.5.7.11.13.17.19.23.29.43 subgroup, and unlike plain neodymium, addition of .29.43 harmonics saves it from contorsion.

Subgroup: 2.3.5.29.43

@@ Line 3: / Line 3: @@
 Defined as the 2460 & 4320 temperament, starting with the 13-limit. Named "minutes" for period-60, since there's 60 minutes in an hour. In light of 12 being a divisor of 60, minutes tempers out the [[Kirnberger's atom]], and in the limits below 13, it's a contorted atomic temperament.
-Subgroup: 2.3.5.7.11.13
+[[Subgroup]]: 2.3.5.7.11.13
-Comma list: 9801/9800, 250047/250000, 371293/371250, 184549376/184528125
+[[Comma list]]: 9801/9800, 250047/250000, 371293/371250, 184549376/184528125
-Mapping: [{{val|60 60 385 730 1085 573}}, {{val|0 1 7 -16 -25 -10}}]
+[[Mapping]]: [{{val|60 60 385 730 1085 573}}, {{val|0 1 7 -16 -25 -10}}]
 Mapping generators: ~2704/2673, ~3/2
@@ Line 50: / Line 50: @@
 Vals: {{EDOs|540, 1380, 1920, 2460, 3000, 3840, 4380, 4920, 6300, 6840e}}
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 9801/9800, 10241/10240, 13377/13376, 5929/5928, 89376/89375, 23409/23408
+Mapping: [{{val|60 4 30 132 244 386 391 182}}, {{val|0 5 6 2 -2 -9 -8 4}}
+Mapping generators: ~612/605, ~216/175
+Optimal tuning (CTE): ~216/175 = 364.387
+== Magnetismic microtemperaments ==
+All these temperaments temper out the [[magnetisma]], a 2.3.29.43 subgroup comma which when tempered sets the [[87/86]] interval to 1/60th of the octave, and thus all these temperaments have a period that maps to 87/86.
 ===Neodymium magnet===
-Defined just as neodymium in 1920 & 4380, except adds a mapping for 29 and 43 via the fact that [[87/86]] is very close to 1/60th of the octave. Comma which closes a stack of 60 87/86's at the octave, is named [[magnetisma]] by [[Eliora]], and thus the extension is called "neodymium magnet". Defined starting with 2.3.5.29.43 all the way into the 2.3.5.7.11.13.17.19.23.29.43 subgroup, and unlike plain neodymium, addition of .29.43 harmonics saves it from contorsion.
+An extension of neodymium. Defined just as neodymium in 1920 & 4380, except adds a mapping for 29 and 43 via the fact that [[87/86]] is very close to 1/60th of the octave.  and thus the extension is called "neodymium magnet". Defined starting with 2.3.5.29.43 all the way into the 2.3.5.7.11.13.17.19.23.29.43 subgroup, and unlike plain neodymium, addition of .29.43 harmonics saves it from contorsion.
 Subgroup: 2.3.5.29.43