60th-octave temperaments: Difference between revisions

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[[60edo]] is a [[highly composite edo]], and some its multiples are notable for their consistency limits, such as [[2460edo]], which is a [[~~The~~ Riemann zeta function ~~and tuning~~ #Zeta edo lists|zeta record edo]].

[[60edo]] is a [[highly composite edo]], and some its multiples are notable for their consistency limits, such as [[2460edo]], which is a [[Riemann zeta function #Zeta edo lists|zeta record edo]].

See [[minutes]] and [[neodymium]].

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== 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.

=== Magnetismic (rank-3) ===

Subgroup: 2.3.29.43

Comma list: 2.3.29.43 {{monzo| -61 60 60 -60 }}

: mapping generators: ~87/86, ~3/2 ~29/16

Optimal tunings:

* WE: ~87/86 = 20.000{{c}}, ~3/2 = 701.954{{c}}, ~29/16 = 1029.570{{c}}

* CWE: ~87/86 = 20.000{{c}}, ~3/2 = 709.954{{c}}, ~29/16 = 1029.570{{c}}

[[Support]]ing [[ET]]s: {{EDOs|600, 660, 720, 780, 1260, 1140, 1920, 2460, 4380}}

Badness (Sintel): 797.107

=== Neodymium magnet ===

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.

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 {{Infobox fractional-octave|60}}
-[[60edo]] is a [[highly composite edo]], and some its multiples are notable for their consistency limits, such as [[2460edo]], which is a [[The Riemann zeta function and tuning #Zeta edo lists|zeta record edo]].
+[[60edo]] is a [[highly composite edo]], and some its multiples are notable for their consistency limits, such as [[2460edo]], which is a [[Riemann zeta function #Zeta edo lists|zeta record edo]].
 See [[minutes]] and [[neodymium]].
@@ Line 6: / Line 6: @@
 == 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.
+=== Magnetismic (rank-3) ===
+Subgroup: 2.3.29.43
+Comma list: 2.3.29.43 {{monzo| -61 60 60 -60 }}
+{{mapping|legend=2| 60 60 240 239 | 0 1 0 1 | 0 0 1 1 }}
+: mapping generators: ~87/86, ~3/2 ~29/16
+Optimal tunings:
+* WE: ~87/86 = 20.000{{c}}, ~3/2 = 701.954{{c}}, ~29/16 = 1029.570{{c}}
+* CWE: ~87/86 = 20.000{{c}}, ~3/2 = 709.954{{c}}, ~29/16 = 1029.570{{c}}
+[[Support]]ing [[ET]]s: {{EDOs|600, 660, 720, 780, 1260, 1140, 1920, 2460, 4380}}
+Badness (Sintel): 797.107
 === Neodymium magnet ===
+{{Main|Landscape microtemperaments#Neodymium}}
 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.