15edo: Difference between revisions

== Approximation to JI ==

15edo offers some minor improvements over 12et in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a [[5L 5s]] [[MOS scale]] wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as the [[blackwood]] temperament, named after [[Easley Blackwood Jr.]], who is the first to document its existence. It has also been written on extensively by [[Igliashon Jones]] in the paper [http://www.cityoftheasleep.com/etc/5nEDOs.pdf ''Five is Not an Odd Number'']. For an in-depth treatment of harmony in 15edo based on this temperament (and its 7- and 11-limit extensions), see [[Blacksmith temperament modal harmony (in 15edo)]].

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== Notation ==

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