16808edo: Difference between revisions

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Among the enormous list of 31-limit [[comma]]s it [[tempering out|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)}}

{{Harmonics in equal|16808|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 16808edo (continued)}}

=== Subsets and supersets ===

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 Among the enormous list of 31-limit [[comma]]s it [[tempering out|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}}
+{{Harmonics in equal|16808|columns=11}}
-{{Harmonics in equal|16808|prec=5|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 16808edo (continued)}}
+{{Harmonics in equal|16808|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 16808edo (continued)}}
 === Subsets and supersets ===