420edo: Difference between revisions
Created page with "'''420 equal divisions of the octave''' divides the octave into parts of 2.857 cents each. 420 is a highly composite number, being divisible by all numbers inclusively from..." |
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==Theory== | ==Theory== | ||
{{Primes in edo|420|columns=10}} | {{Primes in edo|420|columns=10}} | ||
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 | 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]]. | ||
420edo can be adapted for use with 2.7.11.13.19.23 subgroup. | 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]]. | In the 7-limit, 420edo tempers out the [[breedsma]] and the [[ragisma]]. | ||
Revision as of 10:31, 7 October 2021
420 equal divisions of the octave divides the octave into parts of 2.857 cents each.
420 is a highly composite number, being divisible by all numbers inclusively from 2 to 7. It's other divisors are 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, and 210.
Remarkably, approximation to the third harmonic (perfect fifth plus an octave, or tritave) constitutes 666 steps of 420edo. Nice.
Theory
Script error: No such module "primes_in_edo". 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.
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.