420edo: Difference between revisions
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== Theory == | == Theory == | ||
420 is a largely 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 }}. | 420 is a largely 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 | Remarkably, approximation to the third harmonic, which it derives from 70edo, constitutes 666 steps of 420edo. Nice. | ||
Being a | === Largely composite number theory === | ||
Being a largely composite number of steps, 420edo is rich in modulation circles. 420edo is [[enfactoring|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 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 | === Regular temperament theory === | ||
420edo can be adapted for use with 2.5.7.11.13.19.23 subgroup, and it works satisfactorily with the 29-limit as a whole, although due to over 25% error on some harmonics, it's inconsistent. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]]. | |||
=== Harmonics === | |||
{{Harmonics in equal|420}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||