49ed6: Difference between revisions

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'''~~49ed6~~''' ~~divides~~ the ~~just~~ 6:1 ~~into 49 equal parts, resulting in a step size of about 63.3053 cents and an octave approximately 3 cents sharp~~. It is a stretched version of [[19edo|19edo]] and extremely close to the [[The_Riemann_Zeta_Function_and_Tuning|zeta peak]], thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave ~~by this much~~ improves the overall tuning accuracy.

'''[[Ed6|Division of the sixth harmonic]] into 49 equal parts''' (49ED6) is very nearly identical to [[19edo|19 EDO]], but with the [[6/1]] rather than the 2/1 being just. It is a stretched version of [[19edo|19edo]] and extremely close to the [[The_Riemann_Zeta_Function_and_Tuning|zeta peak]], thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.

The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of [[31edo|31edo]]. The fourth is less accurate than in 19edo, and is close in size to a [[Flattone|flattone]] fourth.

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Tunings in this range are a promising option for stiff-stringed instruments since they have stretched partials, and the most noticeable partial is the 2nd; thus, a piano tuned to have beatless octaves will actually have them around 1203 cents or so (depending on string length), which coincidentally is very close to what the zeta-optimal stretched version of 19edo has.

==Harmonics==

== Harmonics ==

[[Category:19edo]]

[[Category:~~godzilla~~]]

[[Category:Godzilla]]

[[Category:~~meantone~~]]

[[Category:Meantone]]

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 {{Infobox ET}}
-'''49ed6''' divides the just 6:1 into 49 equal parts, resulting in a step size of about 63.3053 cents and an octave approximately 3 cents sharp. It is a stretched version of [[19edo|19edo]] and extremely close to the [[The_Riemann_Zeta_Function_and_Tuning|zeta peak]], thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave by this much improves the overall tuning accuracy.
+'''[[Ed6|Division of the sixth harmonic]] into 49 equal parts''' (49ED6) is very nearly identical to [[19edo|19 EDO]], but with the [[6/1]] rather than the 2/1 being just. It is a stretched version of [[19edo|19edo]] and extremely close to the [[The_Riemann_Zeta_Function_and_Tuning|zeta peak]], thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.
 The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of [[31edo|31edo]]. The fourth is less accurate than in 19edo, and is close in size to a [[Flattone|flattone]] fourth.
@@ Line 12: / Line 12: @@
 Tunings in this range are a promising option for stiff-stringed instruments since they have stretched partials, and the most noticeable partial is the 2nd; thus, a piano tuned to have beatless octaves will actually have them around 1203 cents or so (depending on string length), which coincidentally is very close to what the zeta-optimal stretched version of 19edo has.
-==Harmonics==
+== Harmonics ==
 {{Harmonics in equal|49|6|1|prec=2|columns=15}}
 [[Category:19edo]]
-[[Category:godzilla]]
+[[Category:Godzilla]]
-[[Category:meantone]]
+[[Category:Meantone]]