5809edo: Difference between revisions

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5809edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]]. Moreover, it is a strong no-23 [[43-limit]] system, consistent to the no-23 45-odd-limit. Its full 43-limit interpretation using the [[patent val]] is also obvious, as [[23/22]], [[23/13]], [[37/23]] and their [[octave complement]]s exhaust the inconsistently mapped intervals in the full 45-odd-limit.

We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler ~~commas~~ it [[tempering out|tempers out]] in the higher limits include [[123201/123200]] in the 13-limit; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the 17-limit; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the 23-limit.

We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler [[comma]]s it [[tempering out|tempers out]] in the higher limits include [[123201/123200]] in the [[13-limit]]; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the [[17-limit]]; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the [[23-limit]].

=== Prime harmonics ===

{{Harmonics in equal|5809|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 5809edo (continued)}}

=== Subsets and supersets ===

Since 5809 factors into primes as 37 × 157, 5809edo contains [[37edo]] and [[157edo]] as subsets.

Since 5809 factors into primes as {{nowrap| 37 × 157 }}, 5809edo contains [[37edo]] and [[157edo]] as subsets.

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 edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]]. Moreover, it is a strong no-23 [[43-limit]] system, consistent to the no-23 45-odd-limit. Its full 43-limit interpretation using the [[patent val]] is also obvious, as [[23/22]], [[23/13]], [[37/23]] and their [[octave complement]]s exhaust the inconsistently mapped intervals in the full 45-odd-limit.
-We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler commas it [[tempering out|tempers out]] in the higher limits include [[123201/123200]] in the 13-limit; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the 17-limit; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the 23-limit.
+We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler [[comma]]s it [[tempering out|tempers out]] in the higher limits include [[123201/123200]] in the [[13-limit]]; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the [[17-limit]]; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the [[23-limit]].
 === Prime harmonics ===
-{{Harmonics in equal|5809|columns=15}}
+{{Harmonics in equal|5809|columns=11}}
+{{Harmonics in equal|5809|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 5809edo (continued)}}
 === Subsets and supersets ===
-Since 5809 factors into primes as 37 × 157, 5809edo contains [[37edo]] and [[157edo]] as subsets.
+Since 5809 factors into primes as {{nowrap| 37 × 157 }}, 5809edo contains [[37edo]] and [[157edo]] as subsets.