420edo: Difference between revisions

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420edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning of [[3/1|3]], [[5/1|5]], and [[7/1|7]] as [[140edo]]. The [[13/1|13th]] [[harmonic]] is also present in 140edo, and ultimately derives from [[10edo]]. The [[29/1|29th harmonic]], while having significantly drifted in terms of [[relative interval error]], has retained its step position from [[7edo]]. In addition, in the 29-limit, only 11 and 17 have step correspondences coprime with 420. This means that all other approximations are preserved from smaller edos, thus enabling edo mergers and mashups.

420edo is ~~better~~ at the 2.5.7.11.13.19.23 [[subgroup]], and works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].

420edo is good at the 2.5.7.11.13.19.23 [[subgroup]], and has a great potential as a near-just xenharmonic system. It also works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].

=== Odd harmonics ===

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=== Subsets and supersets ===

420 is a largely composite number, being divisible by {{EDOs| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, and 210 }}. For this reason 420edo is rich in modulation circles.

== Trivia ==

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 edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning of [[3/1|3]], [[5/1|5]], and [[7/1|7]] as [[140edo]]. The [[13/1|13th]] [[harmonic]] is also present in 140edo, and ultimately derives from [[10edo]]. The [[29/1|29th harmonic]], while having significantly drifted in terms of [[relative interval error]], has retained its step position from [[7edo]]. In addition, in the 29-limit, only 11 and 17 have step correspondences coprime with 420. This means that all other approximations are preserved from smaller edos, thus enabling edo mergers and mashups.
-edo is better at the 2.5.7.11.13.19.23 [[subgroup]], and works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].
+edo is good at the 2.5.7.11.13.19.23 [[subgroup]], and has a great potential as a near-just xenharmonic system. It also works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].
 === Odd harmonics ===
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
 is a largely composite number, being divisible by {{EDOs| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, and 210 }}. For this reason 420edo is rich in modulation circles.
 == Trivia ==