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 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 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 integee 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]].

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.

Revision as of 23:13, 4 December 2020 view source Keenan Pepper category edits (talk \| contribs) Bots 555 edits m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot ← Older edit		Revision as of 08:29, 30 March 2021 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits mNo edit summary Tags: Mobile edit Mobile web edit Newer edit →
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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 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 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 integee 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]].

	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.