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13-limit EDOs
"In the opinion of some 46et is the first equal division to deal adequately with the 13-limit, though others award that distinction to 41edo."
I have a question concerning the above. Is there a sequence of EDOs such that each EDO approximates 13-limit JI "better" (I guess less total "error"?) than the one before it and is the smallest EDO (larger than the one before it in the sequence) that does this? I suspect 41 and 46 would be next to each other in this sequence. Is there a place I could find a list like this?
Thanks,
Andrew
- Andrew_Heathwaite August 20, 2011, 12:12:22 PM UTC-0700
That depends on all kinds of things--do you use absolute or relative error, do you use logflat weighting, do you use 13 odd limit or 15 odd limit or neither, and so forth. Maximum 13 odd limit error, leaving off anything below 9, gives 9, 10, 15, 19, 22, 24, 26, 29, 41, 46, 58, 72, 80, 87, 94, 111, 130, 159, 190, 198, 224 ...
- genewardsmith August 20, 2011, 03:36:37 PM UTC-0700
Thanks, Gene, that's helpful!
I have another question about 46edo. I notice that it seems to do very well in the 17-limit, but that's not mentioned on the page. Is there any particular reason for that?
- Andrew_Heathwaite August 24, 2011, 05:25:05 PM UTC-0700
...it's also got a good 21 and 23, but not so good 19...
- Andrew_Heathwaite August 24, 2011, 06:06:35 PM UTC-0700
I guess I just got lazy after 13.
- genewardsmith August 24, 2011, 06:28:13 PM UTC-0700
Can we add higher limit intervals? 46 looks even better when one looks at the 23-prime limit, or maybe 27-odd limit. Maybe I'll make another column with some slightly higher complexity ratios 46 does well at?
- iamcamtaylor January 30, 2016, 04:06:39 PM UTC-0800
My lists could be helpful too. Here are my lists with various parameters set. It calculates up to 65536.
Target 3, 5, 7, 11, 13:
1 2 3 4 5 6 7 9 10 15 16 17 19 20 22 24 26 31 37 46 50 53 63 77 84 87 130 140 161 183 207 217 224 270 494 851 1075 1282 1578 2159 2190 2684 3265 3535 4573 5004 5585 6079 8269 8539 13854 14124 16808 20203 22887 28742 32007 37011 50434 50928 51629 54624 56202 59467 64471 65052
Target 3, 5, 7, 9, 11, 13:
1 2 3 4 5 6 7 10 13 15 16 17 22 24 31 37 41 53 77 87 124 130 171 183 217 224 270 441 494 1012 1282 1395 1506 1578 1848 1889 2190 2460 2684 3178 3696 4190 4573 4843 5361 5585 6079 8269 8539 14124 20203 28742 44849 47933 48545 50434 54624 65052
Target 3, 5, 7, 9, 11, 13, 15:
1 2 3 4 5 6 7 9 10 16 17 19 20 21 22 24 31 41 53 77 87 118 130 171 183 224 270 407 431 441 494 1106 1171 1236 1395 1578 1848 1889 2159 2190 2460 2684 2954 3265 4190 4349 4843 5585 6079 8539 11664 14124 16808 17302 20203 22887 37011 37505 41854 47933 48545 54624 65052
- PiotrGrochowski September 30, 2016, 06:47:08 AM UTC-0700