16808edo: Difference between revisions

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Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]] and 1990656/1990625; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.

It is not as excellent, but certainly usable beyond the 31-limit, as at this level little can be complained about inaccuracy, even though the [[37/1|37th]] [[harmonic]] is about halfway between its steps.

=== Prime harmonics ===

{{Harmonics in equal|16808|prec=5|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 16808edo (continued)}}

=== Subsets and supersets ===

16808 has subset edos 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.

16808 has subset edos 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns. [[33616edo]], which doubles it, corrects its harmonic 37 to near-just quality.

== Intervals ==

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 Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]] and 1990656/1990625; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.
+It is not as excellent, but certainly usable beyond the 31-limit, as at this level little can be complained about inaccuracy, even though the [[37/1|37th]] [[harmonic]] is about halfway between its steps.
 === Prime harmonics ===
-{{Harmonics in equal|16808|prec=5|columns=11}}
+{{Harmonics in equal|16808|prec=5|columns=9}}
+{{Harmonics in equal|16808|prec=5|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 16808edo (continued)}}
 === Subsets and supersets ===
-has subset edos 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.
+has subset edos 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns. [[33616edo]], which doubles it, corrects its harmonic 37 to near-just quality.
 == Intervals ==