1984edo: Difference between revisions

(5 intermediate revisions by 3 users not shown)

Line 1:

1984edo is consistent in the [[7-odd-limit]] and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. ~~Though, the harmonics~~ 9 and 15 are tuned flat ~~and~~ in ~~consistent mapping they~~ are ~~one step off~~ their direct ~~mapping~~. ~~In higher limit~~, ~~1984edo approximates well~~ the 2.9.19.31.33 subgroup.

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.

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

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

=== Odd harmonics ===

=== Subsets and supersets ===

Since 1984 factors into {{factorization|1984}}, 1984edo has subset edos {{EDOs| 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, and 992 }}.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1984}}
+{{ED intro}}
-edo is consistent in the [[7-odd-limit]] and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and in consistent mapping they are one step off their direct mapping. In higher limit, 1984edo approximates well the 2.9.19.31.33 subgroup.
+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.
+In the 7-limit the equal temperament [[tempering out|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).
-In the 7-limit it tempers out the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).
 === Odd harmonics ===
-{{harmonics in equal|1984}}
+{{Harmonics in equal|1984}}
+=== Subsets and supersets ===
+Since 1984 factors into {{factorization|1984}}, 1984edo has subset edos {{EDOs| 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, and 992 }}.