124ed8: Difference between revisions

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124 equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of <math>8^{~~\frac~~{1}{~~124~~}}~~</math>, or the 124th root of 8.~~

== ~~Context~~ ==

== Theory ==

124ed8 is an alternative version of [[143ed11]], ~~the best~~ 5.7~~.8.9~~.11.13.17.23 equal step tuning ~~in the world~~. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal ~~[[143ed11]] 5.7.8.9.11.13.17.23~~ tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.

124ed8 is an alternative version of [[143ed11]], which is a strong 8.9.5.7.11.13.17.23 subgroup equal step tuning. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal tuning for the subgroup. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.

== Intervals and approximation to JI ==

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! 124ed8 degree

! Cents

! Ratios in the 5.7~~.8.9~~.11.13.17.23 subgroup

! Ratios in the 8.9.5.7.11.13.17.23 subgroup

! Error (abs, [[Cent|¢]])

! Error (rel, [[Relative cent|%]])

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-equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of <math>8^{\frac{1}{124}}</math>, or the 124th root of 8.
+{{Infobox ET}}
+{{ED intro}}
-== Context ==
+== Theory ==
-ed8 is an alternative version of [[143ed11]], the best 5.7.8.9.11.13.17.23 equal step tuning in the world. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal [[143ed11]] 5.7.8.9.11.13.17.23 tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.
+ed8 is an alternative version of [[143ed11]], which is a strong 8.9.5.7.11.13.17.23 subgroup equal step tuning. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal tuning for the subgroup. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.
+{{Harmonics in equal|124|8|columns=11}}
+{{Harmonics in equal|124|8|columns=11|start=12}}
 == Intervals and approximation to JI ==
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 ! 124ed8<br>degree
 ! Cents
-! Ratios in the<br>5.7.8.9.11.13.17.23<br>subgroup
+! Ratios in the<br>8.9.5.7.11.13.17.23<br>subgroup
 ! Error (abs, [[Cent|¢]])
 ! Error (rel, [[Relative cent|%]])