789edo: Difference between revisions

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789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.

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=== Odd harmonics ===

~~{{stub}}~~

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 {{EDO intro|789}}
-edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.
+edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.
 [[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.
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 === Odd harmonics ===
 {{Harmonics in equal|789}}
-{{stub}}