Talk:13-limit/WikispacesArchive

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ARCHIVED WIKISPACES DISCUSSION BELOW

All discussion below is archived from the Wikispaces export in its original unaltered form.
Please do not add any new discussion to this archive page.
All new discussion should go on Talk:13-limit.


EDOs good for 13-limit

I think it doesn't stop at 65052. How can I calculate this list?

I think it would be good to add a hint here (and maybe limit the enumeration, but link each of the samples to its wiki page)

- xenwolf September 16, 2016, 02:47:19 AM UTC-0700


I calculated it up to 65536. To calculate this list, simply check the errors of log(3), log(5), log(7), log(11) and log(13) compared to closest approximation in each edo added together, then check if it has lower error than smaller edos. The list can vary a bit, since I used 3/2 instead of 3 for example, and it's not logarithmic check (7/5 is closer than 10/7 to sqrt(2)).

- PiotrGrochowski September 16, 2016, 05:07:44 AM UTC-0700


Edo steps are represented as n/edo (fraction)

- PiotrGrochowski September 16, 2016, 05:08:29 AM UTC-0700


Thanks for the clarification. Is there consensus about calculating the relative error? I mean there are also such lists on other p-limit pages in this wiki.

- xenwolf September 16, 2016, 05:18:54 AM UTC-0700


Well, I changed them to my calculated lists. For 3-limit page, both are included. There is more than one method of calculating relative error. I used linear error. Some people use logarithmic (cents for example). Some calculate error of all intervals in tonality diamond, some calculate error of primes only.

- PiotrGrochowski September 17, 2016, 01:48:54 AM UTC-0700


I was wrong. I actually used logarithmic error calculation, resulting in (cent error) / 1200.

- PiotrGrochowski September 17, 2016, 02:06:27 AM UTC-0700


With a bit of code modification, I can generate five types of n-limit good edo lists: soft, normal, strict, very strict and 5-cent tolerability. Normal just uses the described error, strict weights the error by multiplying it by edo number, very strict multiplies it by square of edo number. Soft weights the error by dividing it by edo number. 5-cent tolerability instead calculates list by checking for 5 cent error. (This was made to qualify 17 as good)

3-limit examples:

Soft: 1 2 3 4 5 7 10 12 24 29 41 53 106 147 159 200 253 306 359 612 665 1330 1995 2660 3325 3990 4655 5320 5985 6650 7315 7980 8286 8951 9616 10281 10946 11611 12276 12941 13606 14271 14936 15601 31202 31867 47468 63734

Normal: 1 2 3 5 7 12 29 41 53 200 253 306 359 665 8286 8951 9616 10281 10946 11611 12276 12941 13606 14271 14936 15601 31867

Strict: 1 2 5 12 41 53 306 665 15601 31867

Very strict: 1 2 12 53 665

5-cent: 1 12 17 24 29 34 36 41 43 46 48 51 53 55 58 60 63 65 67 68 70 72 73 74 75 77 79 80 82 84 85 86 87 89 90 91 92 94 96 97 98 99 101 102 103 104 105 106 107 108 109 110 111 113 and every edo above 113

I have some other types of lists but I won't explain them for length.

- PiotrGrochowski September 17, 2016, 03:07:52 AM UTC-0700


It included 1 in 5-cent because it's hard-wired to include 1 when generating lists. (Otherwise a division by 0 error would occur)

- PiotrGrochowski September 17, 2016, 03:10:07 AM UTC-0700