888edo: Difference between revisions

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888edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps~~, but 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.

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 ===

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=== Subsets and supersets ===

Since 888 factors into ~~2<sup>3</sup> × 3 × 37~~, 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.

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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 {{EDO intro|888}}
-edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps, but 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.
+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 ===
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 === Subsets and supersets ===
-Since 888 factors into 2<sup>3</sup> × 3 × 37, 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.
+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.