107edo: Difference between revisions

Note the two possible subgroups
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|107}}
{{ED intro}}


== Theory ==
== Theory ==
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=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|107}}
{{Harmonics in equal|107}}
=== Octave stretch ===
107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[AS|1ed175/174]], a [[Octave stretch|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.
There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 622zpi, 623zpi, 624zpi, 625zpi, 626zpi, 627zpi, 628zpi and 629zpi.
The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.


=== Subsets and supersets ===
=== Subsets and supersets ===
107edo is the 28th [[prime edo]]. [[214edo]], which doubles it, provides correction for the approximation to harmonics 3, 5, and 7.  
107edo is the 28th [[prime edo]], following [[103edo]] and before [[109edo]]. [[214edo]], which doubles it, provides correction for the approximation to harmonics 3, 5, and 7.


== Intervals ==
== Intervals ==