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Old 24th April 2013, 12:07 PM   #104
calebprime
Penultimate Amazing
 
Join Date: Jul 2006
Posts: 13,001
Originally Posted by calebprime View Post
...
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!

Last edited by calebprime; 24th April 2013 at 12:10 PM.
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