49ed6: Difference between revisions

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== Theory ==

49ed6 is very ~~nearly identical~~ to [[19edo]], but with the [[6/1]] rather than the 2/1 being just. It is extremely close to the [[The Riemann zeta function and tuning|zeta peak]] near 19, thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.

49ed6 is very similar to [[19edo]], but with the [[6/1]] rather than the 2/1 being just. It is extremely close to the [[The Riemann zeta function and tuning|zeta peak]] near 19, 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]]. The fourth is less accurate than in 19edo, and is close in size to a [[flattone]] fourth. Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.

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{{Harmonics in equal|49|6|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 49ed6 (continued)}}

=== Subsets and supersets ===

Since 49 factors into primes as 7<sup>2</sup>, 49ed6 contains [[7ed6]] as its only nontrivial subset ed6.

== Intervals ==

== See also ==

* [[11edf]] – relative edf

* [[19edo]] – relative edo

* [[30edt]] – relative edt

* [[53ed7]] – relative ed7

* [[68ed12]] – relative ed12

* [[93ed30]] – relative ed30

[[Category:19edo]]

[[Category:Godzilla]]

[[Category:Meantone]]

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 == Theory ==
-ed6 is very nearly identical to [[19edo]], but with the [[6/1]] rather than the 2/1 being just. It is extremely close to the [[The Riemann zeta function and tuning|zeta peak]] near 19, thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.
+ed6 is very similar to [[19edo]], but with the [[6/1]] rather than the 2/1 being just. It is extremely close to the [[The Riemann zeta function and tuning|zeta peak]] near 19, 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]]. The fourth is less accurate than in 19edo, and is close in size to a [[flattone]] fourth. Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.
@@ Line 16: / Line 16: @@
 {{Harmonics in equal|49|6|1}}
 {{Harmonics in equal|49|6|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 49ed6 (continued)}}
+=== Subsets and supersets ===
+Since 49 factors into primes as 7<sup>2</sup>, 49ed6 contains [[7ed6]] as its only nontrivial subset ed6.
 == Intervals ==
 {{Interval table}}
+== See also ==
+* [[11edf]] – relative edf
+* [[19edo]] – relative edo
+* [[30edt]] – relative edt
+* [[53ed7]] – relative ed7
+* [[68ed12]] – relative ed12
+* [[93ed30]] – relative ed30
 [[Category:19edo]]
 [[Category:Godzilla]]
 [[Category:Meantone]]