20th-octave temperaments: Difference between revisions

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-[[20edo]] is not a particularly harmonically interesting EDO, but some of its multiples have high consistency limits (17-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments.
+[[20edo]] is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments.
-In the 17-limit, one step of 20edo is extremely close to 88/85, which serves as a period in two of these temperaments - Soviet Ferris wheel and calcium.
+In the 17-limit, one step of 20edo is extremely close to 88/85, which serves as a period in two of these temperaments – Soviet Ferris wheel and calcium.
-== Degrees ==
+Temperaments discussed elsewhere include
-''Main article: [[Hemimage temperaments#Degrees]]''
+* ''[[Degrees]]'' → [[Hemimage temperaments #Degrees|Hemimage temperaments]]
-In this temperament, one period equals ~28/27, two equals ~15/14, three equals ~10/9, five equals ~25/21, six equals ~16/13, seven equals ~14/11, nine equals ~15/11, and ten equals ~99/70.
+== Soviet Ferris wheel ==
-Subgroup: 2.3.5.7
-[[Comma list]]: 10976/10935, 390625/388962
-[[Mapping]]: [{{val| 20 0 -17 -39 }}, {{val| 0 1 2 3 }}]
-{{Multival|legend=1| 20 40 60 17 39 27 }}
-[[POTE generator]]: ~3/2 = 703.015
-{{Val list|legend=1| 60, 80, 140, 640b, 780b, 920b }}
-[[Badness]]: 0.106471
-===11-limit===
-Subgroup: 2.3.5.7.11
-Comma list: 1331/1323, 1375/1372, 2200/2187
-Mapping: [{{val| 20 0 -17 -39 -26 }}, {{val| 0 1 2 3 3 }}]
-POTE generator: ~3/2 = 703.231
-Optimal GPV sequence: {{Val list| 60e, 80, 140, 360, 500be, 860bde }}
-Badness: 0.046770
-===13-limit===
-Subgroup: 2.3.5.7.11.13
-Comma list: 325/324, 352/351, 1001/1000, 1331/1323
-Mapping: [{{val| 20 0 -17 -39 -26 74 }}, {{val| 0 1 2 3 3 0 }}]
-POTE generator: ~3/2 = 703.080
-Optimal GPV sequence: {{Val list| 60e, 80, 140, 500be, 640be, 780be }}
-Badness: 0.032718
-==Soviet Ferris wheel==
 Defined as the 320 & 460 temperament, and named because it's a period-20 temperament, and there are 20 cabins on a standard ferris wheel found throughout most of Eastern Europe and Central Asia (as in abandoned Pripyat wheel, for example).