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-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments.

[[20edo]] (in isolation) 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. It's worth noting that [[Degrees]] (discussed elsewhere) is a no-31's [[41-limit]] temperament which serves as a well-temperament of [[80edo]] in the corresponding subgroup, as a 60L 20s MOS is sufficient for finding all its primes.

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.

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=== 19-limit ===

Both [[11/7]] and [[19/16]] are reached in eight generator steps.

2000edo and 2460edo are adjacent members of a sequence of tunings with progressively less error in 19-limit. Both [[11/7]] and [[19/16]] are reached in eight generator steps.

Subgroup: 2.3.5.7.11.13.17.19

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[[Category:20edo]]

~~[[Category:Temperament collections]]~~

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-[[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.
+{{Infobox fractional-octave|20}}
+[[20edo]] (in isolation) 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. It's worth noting that [[Degrees]] (discussed elsewhere) is a no-31's [[41-limit]] temperament which serves as a well-temperament of [[80edo]] in the corresponding subgroup, as a 60L 20s MOS is sufficient for finding all its primes.
 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.
@@ Line 100: / Line 101: @@
 === 19-limit ===
-Both [[11/7]] and [[19/16]] are reached in eight generator steps.
+edo and 2460edo are adjacent members of a sequence of tunings with progressively less error in 19-limit. Both [[11/7]] and [[19/16]] are reached in eight generator steps.
 Subgroup: 2.3.5.7.11.13.17.19
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 {{Optimal ET sequence|legend=1|460, 2000, 2460}}
+{{Navbox fractional-octave}}
 [[Category:20edo]]
-[[Category:Temperament collections]]