205edo: Difference between revisions
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|205}} | {{Harmonics in equal|205}} | ||
=== Structural properties === | |||
205edo contains a very accurate approximation of the [[2.3.5.11 subgroup]], inheriting the perfect fifth from 41edo. The patent val mappings of primes 7 and 13 can then be found by mapping [[7/5]] to the Pythagorean diminished fifth, and [[13/11]] at the Pythagorean minor third, thus tempering out [[5120/5103]] and [[352/351]], as well as [[847/845]] and [[2080/2079]]. In fact, it is the last edo tempering out 5120/5103 to map both [[7/5]] and [[1024/729]] consistently. It also supports the [[counterpyth]] mapping of prime 19. | |||
Its step size represents several important intervals, such as the septimal kleisma [[225/224]], and the keenanisma [[385/384]]. Notably, the mappings of primes 5, 7, 11, 13, and 19 all differ from their nearest 41edo step by 1 step of 205edo, so 205edo can be considered as 41edo with fine-tuning, similarly to how [[217edo]] can be considered as 31edo with fine-tuning. The intervals [[11/10]], [[12/11]], [[13/12]], [[14/13]], and [[15/14]] are mapped equidistant, corresponding to [[121/120]], [[144/143]], [[169/168]], and [[196/195]] all being mapped to 2 steps. The mappings of 17 and 19 are accurate, with 15/14, [[16/15]], [[17/16]], [[18/17]], [[19/18]], and [[20/19]] all spaced apart from each other by one step. Overall, despite the sharpness of its 7 and 13, 205edo does fairly well in a range of prime limits. | |||
=== Temperament generators and Tonal Plexus === | === Temperament generators and Tonal Plexus === | ||