Talk:Logarithmic approximants - Revision history

Sintel at 00:53, 6 May 2026

2026-05-06T00:53:50Z

← Older revision		Revision as of 00:53, 6 May 2026
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			== Cleanup and notes ==

			I cleaned up a lot of the formatting on this page. It is in a much better state now.

			There's some genuinely cool stuff buried in here, and I haven't really taken the time to understand all the details.
			I believe this material can be presented in much better ways. Not sure exactly how to go about this. A good start would maybe be to split off approximants into a more encyclopedic article rather than this essay format. The section on argent tuning is also of high interest, since it relates to what we now call the [[argent comma]].

			– [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 00:53, 6 May 2026 (UTC)

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

2018-10-01T18:02:38Z

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
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	~~= 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.~~

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	~~== Pade(2,1) ==~~
	~~Have you taken a look at the Pade(2,1) approximant? I compute it as $\frac~~{~~1}{4} \frac~~{~~(r-1)(r+5)~~}~~{2r+1~~}$. Calculations show it beats the quadratic approximant on the interval $[1,4]$ at the endpoints of which the two approximants agree. (The two are nearly identical on that interval, with a max difference of $\approx .006$.) The approximants are fairly simple (generally simpler than the Pade(1,2) approximants). E.g. for r = 2/1 we have the approximant 7/5 (ignoring the constant 1/4). A first computation shows that this approximation spots 34EDO by comparing the approximants for 5/4 and 3/2: 25/56 and 13/16 resp. We don't get equality, but minimizing the difference m(13/16)-n(25/56) gives m=11, n=20 with 11(13/16) - 20(25/56) = 1/112, a unit fraction with denominator the LCM of the approximant denominators.

	~~- '''mattyhawthorn''' April 04, 2015, 05:08:22 PM UTC-0700~~
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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

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	= 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.

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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.'''
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== Pade(2,1) ==
Have you taken a look at the Pade(2,1) approximant? I compute it as $\frac{1}{4} \frac{(r-1)(r+5)}{2r+1}$. Calculations show it beats the quadratic approximant on the interval $[1,4]$ at the endpoints of which the two approximants agree. (The two are nearly identical on that interval, with a max difference of $\approx .006$.) The approximants are fairly simple (generally simpler than the Pade(1,2) approximants). E.g. for r = 2/1 we have the approximant 7/5 (ignoring the constant 1/4). A first computation shows that this approximation spots 34EDO by comparing the approximants for 5/4 and 3/2: 25/56 and 13/16 resp. We don't get equality, but minimizing the difference m*(13/16)-n*(25/56) gives m=11, n=20 with 11*(13/16) - 20*(25/56) = 1/112, a unit fraction with denominator the LCM of the approximant denominators.

- '''mattyhawthorn''' April 04, 2015, 05:08:22 PM UTC-0700
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