2460edo: Difference between revisions

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As a micro (or nano) temperament, it is a landscape system in the 7-limit, tempering out [[250047/250000]], and in the 11-limit it tempers out [[9801/9800]]. Beyond that, [[10648/10647]] in the 13-limit, 12376/12375 in the 17-limit, 5929/5928 and 6860/6859 in the 19-limit and 8281/8280 in the 23-limit.

2460 is divisible by {{EDOs|2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 410, 492, 615, 820, and 1230}}, and its [[abundancy index]] is 1.868. Of the divisors, [[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]] is notable for use by [[Easley Blackwood Jr]], [[60edo]] is a [[highly composite edo~~]], and [[615edo]] has a step close in size to the [[schisma~~]].

2460 is divisible by {{EDOs|2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 410, 492, 615, 820, and 1230}}, and its [[abundancy index]] is 1.868. Of the divisors, [[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]] is notable for use by [[Easley Blackwood Jr]], [[60edo]] is a [[highly composite edo]].

In light of having a large amount of divisors and precise approximation of just intonation, 2460edo has been proposed as the basis for a unit, the [[mina]], which could be used in place of the cent. Moreover, a cent is exactly 2.05 [[mina]]s, and a mem, 1\205, is exactly 12 minas.

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== Regular temperament properties ==

2460edo has lower 23-limit relative error than any ~~EDO~~ until [[8269edo|8269]]. Also it has a lower 23-limit [[TE logflat badness]] than any smaller edo and less than any until [[16808edo|16808]].

2460edo has lower 23-limit relative error than any edo until [[8269edo|8269]]. Also it has a lower 23-limit [[TE logflat badness]] than any smaller edo and less than any until [[16808edo|16808]].

In addition, it has the lowest relative error in the 19-limit, being only bettered by [[3395edo]].

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 As a micro (or nano) temperament, it is a landscape system in the 7-limit, tempering out [[250047/250000]], and in the 11-limit it tempers out [[9801/9800]]. Beyond that, [[10648/10647]] in the 13-limit, 12376/12375 in the 17-limit, 5929/5928 and 6860/6859 in the 19-limit and 8281/8280 in the 23-limit.
-is divisible by {{EDOs|2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 410, 492, 615, 820, and 1230}}, and its [[abundancy index]] is 1.868. Of the divisors, [[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]] is notable for use by [[Easley Blackwood Jr]], [[60edo]] is a [[highly composite edo]], and [[615edo]] has a step close in size to the [[schisma]].
+is divisible by {{EDOs|2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 410, 492, 615, 820, and 1230}}, and its [[abundancy index]] is 1.868. Of the divisors, [[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]] is notable for use by [[Easley Blackwood Jr]], [[60edo]] is a [[highly composite edo]].
 In light of having a large amount of divisors and precise approximation of just intonation, 2460edo has been proposed as the basis for a unit, the [[mina]], which could be used in place of the cent. Moreover, a cent is exactly 2.05 [[mina]]s, and a mem, 1\205, is exactly 12 minas.
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 == Regular temperament properties ==
-edo has lower 23-limit relative error than any EDO until [[8269edo|8269]]. Also it has a lower 23-limit [[TE logflat badness]] than any smaller edo and less than any until [[16808edo|16808]].
+edo has lower 23-limit relative error than any edo until [[8269edo|8269]]. Also it has a lower 23-limit [[TE logflat badness]] than any smaller edo and less than any until [[16808edo|16808]].
 In addition, it has the lowest relative error in the 19-limit, being only bettered by [[3395edo]].