420edo: Difference between revisions
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'''420 equal divisions of the octave''' divides the octave into parts of 2.857 | The '''420 equal divisions of the octave''' divides the [[octave]] into parts of 2.857 [[cent]]s each. | ||
420 is a highly composite number, being divisible by all numbers inclusively from 2 to 7. It's other divisors are {{EDOs|10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, and 210}}. | == Theory == | ||
420 is a highly composite number, being divisible by all numbers inclusively from 2 to 7. It's other divisors are {{EDOs| 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. | 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. 29th harmonic, while having significantly drifted, has retained its step position from [[7edo]]. | ||
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In the 7-limit, 420edo tempers out the [[breedsma]] and the [[ragisma]]. | In the 7-limit, 420edo tempers out the [[breedsma]] and the [[ragisma]]. | ||
=== Prime harmonics === | |||
{{Primes in edo|420|columns=10}} | |||
[[Category:Equal divisions of the octave]] | |||
Revision as of 14:08, 7 October 2021
The 420 equal divisions of the octave divides the octave into parts of 2.857 cents each.
Theory
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.
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.
Prime harmonics
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