2460edo: Difference between revisions

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The '''2460''' ~~equal division~~ divides the [[~~Octave|~~octave]] into 2460 equal parts of 0.4878 [[~~cent|~~cent]]s each. It has been used in [[~~Sagittal_notation|~~Sagittal notation]] to define the "olympian level" of JI notation, and has been proposed as the basis for a unit, the [[~~mina|~~mina]], which could be used in place of the ~~[[cent|~~cent]]. It is uniquely [[~~consistent|~~consistent]] through to the [[27-~~limit|27~~-limit]], which is not very remarkable in itself ([[~~388edo|~~388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-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 [[~~Tenney-Euclidean_metrics#Logflat TE badness|~~ TE ~~loglfat~~ badness]] than any smaller edo and less than any until [[16808edo|16808]].

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]].

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.

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.

Since its prime factorization is 2<sup>2</sup> × 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.

Since its prime factorization is 2^2*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|12edo]] is too well-known to need any introduction, [[41edo|41edo]] is an important system, and [[205edo|205edo]] has proponents such as [[Aaron_Andrew_Hunt|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|Mem]]). Aside from these, [[15edo|15edo]], [[20edo|20edo]], [[30edo|30edo]], [[60edo|60edo]], and [[164edo|164edo]] all have drawn some attention. Moreover a cent is exactly 2.05 [[mina|mina]]s, and a mem, 1\205 octaves, is exactly 12 minas.

[[Category:Equal divisions of the octave]]

[[Category:~~mina~~]]

[[Category:Mina]]

[[Category:~~nano~~]]

[[Category:Zeta]]

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-The '''2460''' equal division divides the [[Octave|octave]] into 2460 equal parts of 0.4878 [[cent|cent]]s each. It has been used in [[Sagittal_notation|Sagittal notation]] to define the "olympian level" of JI notation, and has been proposed as the basis for a unit, the [[mina|mina]], which could be used in place of the [[cent|cent]]. It is uniquely [[consistent|consistent]] through to the [[27-limit|27-limit]], which is not very remarkable in itself ([[388edo|388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-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 [[Tenney-Euclidean_metrics#Logflat TE badness| TE loglfat badness]] than any smaller edo and less than any until [[16808edo|16808]].
+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]].
-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.
+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.
+Since its prime factorization is 2<sup>2</sup> × 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.
+{{Primes in edo|2460}}
-Since its prime factorization is 2^2*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|12edo]] is too well-known to need any introduction, [[41edo|41edo]] is an important system, and [[205edo|205edo]] has proponents such as [[Aaron_Andrew_Hunt|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|Mem]]). Aside from these, [[15edo|15edo]], [[20edo|20edo]], [[30edo|30edo]], [[60edo|60edo]], and [[164edo|164edo]] all have drawn some attention. Moreover a cent is exactly 2.05 [[mina|mina]]s, and a mem, 1\205 octaves, is exactly 12 minas.
 [[Category:Equal divisions of the octave]]
-[[Category:mina]]
+[[Category:Mina]]
-[[Category:nano]]
+[[Category:Zeta]]