2460edo: Difference between revisions

The '''2460 equal divisions of the octave''' ('''2460edo''') divides the [[octave]] into 2460 equal parts of 0.4878 [[cent]]s each. It has been used in [[Sagittal notation]] to define the ''olympian level'' of JI notation, and has been proposed as the basis for a unit, the [[mina]], which could be used in place of the cent. It is uniquely [[consistent]] through to the [[27-odd-limit]], which is not very remarkable in itself ([[388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-odd-limit intervals. It is also a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta peak and zeta peak integer edo]] and has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any edo until [[3395edo|3395]], and a lower 23-limit relative error than any until [[8269edo|8269]]. Also it has a lower 23-limit [[TE logflat badness]] than any smaller edo and less than any until [[16808edo|16808]].

Since its prime factorization is 2² × 3 × 5 × 41, 2460 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 410, 492, 615, 820, and 1230. Of these, [[12edo]] is too well-known to need any introduction, [[41edo]] is an important system, and [[205edo]] has proponents such as [[Aaron Andrew Hunt]], who uses it as the default tuning for [http://www.h-pi.com/theory/measurement3.html Hi-pi Instruments] (and as a unit: [[mem]]). Aside from these, [[15edo]], [[20edo]], [[30edo]], [[60edo]], and [[164edo]] all have drawn some attention. Moreover a cent is exactly 2.05 [[mina]]s, and a mem, 1\205, is exactly 12 minas.

[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->