1984edo: Difference between revisions

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1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[~~3/1|3]], [[5~~/1|5]]~~, [[7/1|7]], [[11/1|11]], and [[17/1|17]] all~~ tuned sharp. ~~Harmonics~~ 9 ~~and~~ 15, ~~though~~, ~~are tuned~~ flat, which results in [[consistency|inconsistencies]], that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and {{nowrap|3145 + 3145 {{=}} 6290}}, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and {{nowrap|3145 + 4607 {{=}} 7752}}, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.

1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with all primes up to [[23/1|23]] tuned sharp. However, harmonics 9, 15, and 21 are more than 50% of a step sharp by patent val, and flat by direct approximation, which results in [[consistency|inconsistencies]]; that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and {{nowrap|3145 + 3145 {{=}} 6290}}, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and {{nowrap|3145 + 4607 {{=}} 7752}}, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.

In the 7-limit the equal temperament [[tempering out|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).

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 {{ED intro}}
-edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[17/1|17]] all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in [[consistency|inconsistencies]], that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and {{nowrap|3145 + 3145 {{=}} 6290}}, ≠&nbsp;6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and {{nowrap|3145 + 4607 {{=}} 7752}}, ≠&nbsp;7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.
+edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with all primes up to [[23/1|23]] tuned sharp. However, harmonics 9, 15, and 21 are more than 50% of a step sharp by patent val, and flat by direct approximation, which results in [[consistency|inconsistencies]]; that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and {{nowrap|3145 + 3145 {{=}} 6290}}, ≠&nbsp;6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and {{nowrap|3145 + 4607 {{=}} 7752}}, ≠&nbsp;7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.
 In the 7-limit the equal temperament [[tempering out|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).