888edo: Difference between revisions

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== ~~Theory~~ ==

888edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], and [[13/1|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation. The equal temperament [[Tempering out|tempers out]] [[4096/4095]], [[6656/6655]], [[9801/9800]], [[10648/10647]], 105644/105625, 151263/151200, and 250047/250000 in the above subgroup.

=== Odd harmonics ===

888edo is excellent in the no-threes 13-limit, and it may possibly have little attention due to its lack of a perfect fifth. The usage of 3/2 is so deeply entrenched into nearly all musical traditions of the world, that temperaments which lack a perfect fifth do not get considered, even if other harmonics are excellently approximated.

~~888edo tempers out 6656/6655, 105644/105625, 4917248/4915625 and 35153041/35152000 in the no-threes 13 limit.~~

~~[[Category:Equal divisions of the octave~~|~~###]] ~~

=== Subsets and supersets ===

Since 888 factors into {{factorization|888}}, 888edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, and 444 }}. 1776edo, which doubles it, provides a good correction for harmonic 3.

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 {{Infobox ET}}
-{{EDO intro|888}}
+{{ED intro}}
-== Theory ==
+edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], and [[13/1|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation. The equal temperament [[Tempering out|tempers out]] [[4096/4095]], [[6656/6655]], [[9801/9800]], [[10648/10647]], 105644/105625, 151263/151200, and 250047/250000 in the above subgroup.
+=== Odd harmonics ===
 {{Harmonics in equal|888}}
-edo is excellent in the no-threes 13-limit, and it may possibly have little attention due to its lack of a perfect fifth. The usage of 3/2 is so deeply entrenched into nearly all musical traditions of the world, that temperaments which lack a perfect fifth do not get considered, even if other harmonics are excellently approximated.
-edo tempers out 6656/6655, 105644/105625, 4917248/4915625 and 35153041/35152000 in the no-threes 13 limit.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Subsets and supersets ===
+Since 888 factors into {{factorization|888}}, 888edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, and 444 }}. 1776edo, which doubles it, provides a good correction for harmonic 3.