Talk:13-limit - Revision history

Mike Battaglia: 1 revision imported: Moving archived Wikispaces discussion to subpage

2018-10-01T18:02:30Z

1 revision imported: Moving archived Wikispaces discussion to subpage

← Older revision	Revision as of 18:02, 1 October 2018
(No difference)

WikispacesArchive>Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-10-01T18:01:16Z

Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' <span style="color:#800000">''...

← Older revision		Revision as of 18:01, 1 October 2018
Line 1:		Line 1:
	~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~		{{WSArchiveLink}}
	~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

	~~<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.~~

	~~----~~

	~~== 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~~
	~~----~~

Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-09-20T07:00:49Z

← Older revision		Revision as of 07:00, 20 September 2018
Line 1:		Line 1:
	= ARCHIVED WIKISPACES DISCUSSION BELOW =		= ARCHIVED WIKISPACES DISCUSSION BELOW =
	'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''		'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''

			<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.

	----		----

PiotrGrochowski: cut the doubles

2018-09-18T09:39:54Z

cut the doubles

← Older revision		Revision as of 09:39, 18 September 2018
Line 51:		Line 51:

	- '''PiotrGrochowski''' September 17, 2016, 03:10:07 AM UTC-0700		- '''PiotrGrochowski''' September 17, 2016, 03:10:07 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, 03:10:09 AM UTC-0700~~
	~~----~~
	~~Doubling makes anything look stupid.~~

	~~- '''PiotrGrochowski''' January 26, 2018, 12:05:21 PM UTC-0800~~
	~~----~~
	~~Doubling makes anything look stupid.~~

	~~- '''PiotrGrochowski''' January 26, 2018, 12:05:24 PM UTC-0800~~
	~~----~~
	~~Doubling makes anything look stupid.~~

	~~- '''PiotrGrochowski''' January 26, 2018, 12:05:25 PM UTC-0800~~
	----		----

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

New page

= ARCHIVED WIKISPACES DISCUSSION BELOW =
'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
----

== 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
----
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, 03:10:09 AM UTC-0700
----
Doubling makes anything look stupid.

- '''PiotrGrochowski''' January 26, 2018, 12:05:21 PM UTC-0800
----
Doubling makes anything look stupid.

- '''PiotrGrochowski''' January 26, 2018, 12:05:24 PM UTC-0800
----
Doubling makes anything look stupid.

- '''PiotrGrochowski''' January 26, 2018, 12:05:25 PM UTC-0800
----