31edo: Difference between revisions
| Line 80: | Line 80: | ||
Because of the near-just 5/4 and 7/4 and because the 11th harmonic is almost twice as flat as the 3rd harmonic, 31-et is relatively quite accurate and is [[The Riemann Zeta Function and Tuning#Zeta EDO lists|the 6th zeta integral edo, the 7th zeta gap edo, a zeta peak edo and a zeta peak integer edo]]. (Another way in which 31edo is especially accurate is that it represents a record in [[Pepper ambiguity]] in the 7-, 9- and [[11-odd-limit]], which it is [[consistent]] through.) | Because of the near-just 5/4 and 7/4 and because the 11th harmonic is almost twice as flat as the 3rd harmonic, 31-et is relatively quite accurate and is [[The Riemann Zeta Function and Tuning#Zeta EDO lists|the 6th zeta integral edo, the 7th zeta gap edo, a zeta peak edo and a zeta peak integer edo]]. (Another way in which 31edo is especially accurate is that it represents a record in [[Pepper ambiguity]] in the 7-, 9- and [[11-odd-limit]], which it is [[consistent]] through.) | ||
The fact that 31edo has meantone scales is well-known, but some other | The fact that 31edo has meantone scales is well-known, but some other [[MOS]]es and MOS chains are also useful: | ||
* 31edo's 9\31 neutral third generator generates [[Step ratio|ultrasoft]] [[3L 4s|mosh]] and [[Step ratio|superhard]] [[7L 3s|dicoid]] MOSes. | * 31edo's 9\31 neutral third generator generates [[Step ratio|ultrasoft]] [[3L 4s|mosh]] and [[Step ratio|superhard]] [[7L 3s|dicoid]] MOSes. | ||
* Its 12\31 generator generates a [[Step ratio|semihard]] [[oneirotonic]] scale, similar to the 5L 3s scale in [[13edo]] but with the 9/8, 5/4 and 7/6 better in tune. | * Its 12\31 generator generates a [[Step ratio|semihard]] [[oneirotonic]] scale, similar to the 5L 3s scale in [[13edo]] but with the 9/8, 5/4 and 7/6 better in tune. | ||