420edo: Difference between revisions

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Remarkably, approximation to the third harmonic (perfect fifth plus an octave, or tritave) constitutes 666 steps of 420edo. Nice.

Being a highly composite number of steps, 420edo is rich in modulation circles. In addition, of the first 10 prime harmonics, 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, and showing the vibrant and highly composite nature of 420~~. 29th harmonic, while having significantly drifted, has retained its step position from [[7edo]]~~.

Being a highly composite number of steps, 420edo is rich in modulation circles. In addition, of the first 10 prime harmonics, 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, and showing the vibrant and highly composite nature of 420.

420edo can be adapted for use with 2.7.11.13.19.23 subgroup.

In the 7-limit, ~~420edo~~ tempers out ~~the~~ [[~~breedsma~~]] and the [[~~ragisma~~]].

420edo is [[enfactored]] in the 7-limit, with the same tuning of 3, 5, and 7 as [[140edo]]. The 13th harmonic is also present in 140edo, and ultimately derives from [[10edo]]. The 29th harmonic, while having significantly drifted, has retained its step position from [[7edo]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].

=== Prime harmonics ===

@@ Line 7: / Line 7: @@
 Remarkably, approximation to the third harmonic (perfect fifth plus an octave, or tritave) constitutes 666 steps of 420edo. Nice.
-Being a highly composite number of steps, 420edo is rich in modulation circles. In addition, of the first 10 prime harmonics, 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, and showing the vibrant and highly composite nature of 420. 29th harmonic, while having significantly drifted, has retained its step position from [[7edo]].
+Being a highly composite number of steps, 420edo is rich in modulation circles. In addition, of the first 10 prime harmonics, 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, and showing the vibrant and highly composite nature of 420.
 edo can be adapted for use with 2.7.11.13.19.23 subgroup.
-In the 7-limit, 420edo tempers out the [[breedsma]] and the [[ragisma]].
+edo is [[enfactored]] in the 7-limit, with the same tuning of 3, 5, and 7 as [[140edo]]. The 13th harmonic is also present in 140edo, and ultimately derives from [[10edo]]. The 29th harmonic, while having significantly drifted, has retained its step position from [[7edo]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].
 === Prime harmonics ===