Penultimate Amazing
Join Date: Jul 2006
Posts: 13,001
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Originally Posted by calebprime
...
The honor roll:
77,87,94,99,
130,135,159,164,166,171,183
200,207,224,253,270,
306,311,323,378
A slightly more inclusive honor roll:
65, 70, 75, 77, 82, 87, 89, 94, 99, (109 extreme!), 111, 118, 128, 130, 135, 142, 147, 159, 164, 166, 171, 183, 200, 207, 224, 253, 270, 282, 289, 306, 311, 323, 335, 359, 373, 378
These are the equal divisions of the octave (EDOs) that have a 3/2 approximation fairly close to 702, with some other good feature, with the requirement that the higher the EDO, the more accurate it be, below 400.
441EDO may be very accurate, but the number is above my arbitrary cutoff of 400.
Here's a breakdown of the EDOs by how large the 3/2 is. This 3/2 approximation was entered into LMSO, and it found successively larger EDOs that approximated that number with increasing accuracy.
Almost all of the usual suspects show up in this list, except perhaps 19. My bias is for 5ths above 700, not "meantone" 5ths.
the data:
(701.0 to 703.5 is central range, higher edos must be more accurate to make list)
"multiples" (edos that are some multiple of edos that *do* show up) that don't show up on LMSO cmd search:
12, 24, 36, 48
29, 58, 87, 116
41, 82, 123
53, 106, 159
EDOs by "5th" (or 3/2) size:
numbers in (parentheses) are thought to be too inaccurate for their size, at least in the 3-dimension
700 -- 12edo
700.2 -- 12, (257, 269, 281,293)
700.4 -- 12, (137, 149, 161, 173, 185, 197, 209, 221, 233, 245)
700.5 -- 12, 101, (113, 125, 137, 149, 161, 173, 185, 197)
700.7 -- 12, 77, 89, 101, (113, 125, 137, 286)
700.9 -- 12, 65, 77, 89, 101, (113)
===========================
701.0 -- 12, 53, 65, 77, 89, 101, (368)
701.1 -- 12, 53, 65, 77, 89, (368)
701.2 -- 12, 53, 65, 77, 89, (166)
701.3 -- 12, 41, 53, 65, 77
701.4 -- 12, 41, 53, 65, 77, 142
----------
701.5 -- 12, 41, 53, 65, (272, 337)
701.6 -- 12, 41, 53, 65, (183, 248, 313)
701.7 -- 12, 41, 53, 65, 118
701.8 -- 12, 29, 41, 53, 171, 224, 277
701.9 -- 12, 29, 41, 53, (995)
701.91 - 12, 29, 41, 53, (730)
701.92 - 12, 29, 41, 53, 359
701.93 - 12, 29, 41, 53, 306, 359, (465)
701.94 - 12, 29, 41, 53, 253, 306, 359
701.95 - 12, 29, 41, 53, 200, 253, 306, 359
----------------------------------------------
701.955- 12, 29, 41, 53, 200, 253, 306
plus pure 5/4 @ 386.314 -- 53, 118, 289, 323, 441,
plus temp 5/4 @ 384 -- 147, 200
plus temp 5/4 @ 387 -- 65, 118, 183, 282
----------------------------------------------
701.96 - 12, 29, 41, 53, 200, 253
701.97 - 12, 29, 41, 53, 147, 200, 253
701.98 - 12, 29, 41, 53, 147, 200, 253
701.99 - 12, 29, 41, 53, 147, 200
702.0 - 12, 29, 41, 53, 147, 200
---------------------------------------
702.05 - 12, 29, 41, 53, 94, 147
702.1 - 12, 29, 41, 53, 94, (335)
702.15 - 12, 29, 41, 53, 94, (323)
702.2 - 12, 29, 41, 94, 135, (311)
702.25 - 12, 29, 41, 94, 135, (311)
702.3 - 12, 29, 41, 135, 176, 217
702.4 - 12, 29, 41
702.5 - 12, 29, 41, (275)
702.6 - 12, 29, 41, 111
-----------------------------
702.7 - 12, 29, 41, 70, 111
702.8 - 12, 29, 41, 70, (181)
702.9 - 12, 29, 41, 70, (239)
703.0 - 12, 17, 29, 70, 99, (268, 367)
703.1 - 12, 17, 29, 70, 99, 128, (227)
703.2 - 12, 17, 29, 99, 128, (157),
703.3 - 12, 17, 29, (157, 186, *215*, 244, 273)
703.4 - 12, 17, 29, (476)
703.5 - 12, 17, 29,
=========================
703.6 - 12, 17, 29, 162
703.7 - 12, 17, 29, 104, (133), (162)
703.8 - 12, 17, 29, 75, 104, (237)
703.9 - 12, 17, 29, 75, 104, 179
704. - 12, 17, 29, 46, 75,
-------------------------------------------
704.1 - 12, 17, 29, 46, 75, 121, 196,
704.56 -- 109!
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