Logarithmic approximants: Difference between revisions

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This article is based on original research by [[Martin_Gough|Martin Gough]]. See [[:File:Bimod_Approx_2014-6-8.pdf|this paper]] for a fuller account of bimodular approximants.

~~The~~ tuning ~~referred~~ to ~~here as argent~~ tuning appears to have been ~~discovered 'about 1950'~~ by Erv Wilson, who ~~named~~ it [http://anaphoria.com/meruthree.pdf ~~2-zig/2-zag~~]'. It was later ~~rediscovered~~ independently by [[~~Graham_Breed|~~Graham Breed]] and Paul Hahn, who described it in posts ([https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12592.html#12599 #12599], [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12637.html#12670 #12670]) to the Yahoo tuning list on 10 and 12 August 2000.

Argent tuning is based on the continued fraction convergents of <math>sqrt{2}</math>, which have been known since ancient times.

This application to tuning appears to have been first made by [[Erv Wilson]], who described it under the name '2-zig/2-zag' in a [http://anaphoria.com/meruthree.pdf note] dated December 1996, with a comment claiming it as his answer to [[Joseph Yasser]] "at about 1950".

The same construction was later arrived at independently by [[Graham Breed]] and Paul Hahn, who described it in posts ([https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12592.html#12599 #12599], [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12637.html#12670 #12670]) to the Yahoo tuning list on 10 and 12 August 2000.

Thanks to [[Gene_Ward_Smith|Gene Ward Smith]] for the Gelfond-Schneider result.

[[Category:Essays]]

@@ Line 839: / Line 839: @@
 This article is based on original research by [[Martin_Gough|Martin Gough]]. See [[:File:Bimod_Approx_2014-6-8.pdf|this paper]] for a fuller account of bimodular approximants.
-The tuning referred to here as argent tuning appears to have been discovered 'about 1950' by Erv Wilson, who named it [http://anaphoria.com/meruthree.pdf 2-zig/2-zag]'. It was later rediscovered independently by [[Graham_Breed|Graham Breed]] and Paul Hahn, who described it in posts ([https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12592.html#12599 #12599], [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12637.html#12670 #12670]) to the Yahoo tuning list on 10 and 12 August 2000.
+Argent tuning is based on the continued fraction convergents of <math>sqrt{2}</math>, which have been known since ancient times.
+This application to tuning appears to have been first made by [[Erv Wilson]], who described it under the name '2-zig/2-zag' in a [http://anaphoria.com/meruthree.pdf note] dated December 1996, with a comment claiming it as his answer to [[Joseph Yasser]] "at about 1950".
+The same construction was later arrived at independently by [[Graham Breed]] and Paul Hahn, who described it in posts ([https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12592.html#12599 #12599], [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12637.html#12670 #12670]) to the Yahoo tuning list on 10 and 12 August 2000.
 Thanks to [[Gene_Ward_Smith|Gene Ward Smith]] for the Gelfond-Schneider result.
 [[Category:Essays]]