... Helaman Ferguson ... << Ferguson is exactly that abstract artist who fully possesses and has cultivated his ability to express his mathematical conceptions...
Pierre Lamothe
plamothe@...
May 1, 2001 8:12 am
386
... Description of PSLQ ... Proceedings of the Organic Mathematics Workshop Recognizing Numerical Constants David H. Bailey and Simon Plouffe The PSLQ Integer...
Pierre Lamothe
plamothe@...
May 1, 2001 8:13 am
387
The kind of two-dimensional generalization of the Farey series we're interested for calculating the harmonic entropy of triads is discussed in ...
PERLICH@...
May 5, 2001 7:46 am
388
... Great! How'd you find it? So triads will be represented as points on the coordinate plane? Assuming yes... ... Both coordinates for each point in ^F_n...
Carl Lumma
carl@...
May 9, 2001 1:30 am
389
I only included "Eureka part I" because I'm waiting for Paul and other mathematically inclined list members to decode that paper for me. As members of the...
Robert C Valentine
BVAL@...
May 9, 2001 7:56 am
390
Carl wrote, ... Google search for "Farey web". ... How could it be otherwise? I presume you're up to speed on my triangular triad plots? ... Yes, but the...
Paul H. Erlich
PERLICH@...
May 9, 2001 8:44 pm
391
... Google strikes again. ... I was vaguely up to speed as of December 2000. ... You mean that taking k=2 combinations of F_n gives a superset of ^F_n because...
Carl Lumma
carl@...
May 9, 2001 9:22 pm
392
Robert Valentine wrote, ... Can I ask you where this is coming from? I always get something like 194¢ as best. ... Why don't you reproduce the calculation...
Paul H. Erlich
PERLICH@...
May 9, 2001 11:03 pm
393
Carl wrote, ... That sounds right. ... Major: (6,4) (5,4) Minor: (12,10) (15,10) Although the coordinates simply reduce to (3/2),(5/4) or vice verse, the major...
Paul H. Erlich
PERLICH@...
May 9, 2001 11:08 pm
394
... Whoa. Each chord is a line segment? I thought each chord was a point, ie Maj=(5/4, 3/2) Min=(6/5, 3/2). ... It says, "Theorem 2 (Monkemeyer) Let...
Carl Lumma
carl@...
May 10, 2001 7:19 pm
395
... Nope. ... Correct. My ordered pairs were (y,x) (z,x), and the point corresponding to them is (y/x, z/x). ... You have to calculate it!...
Paul H. Erlich
PERLICH@...
May 11, 2001 6:55 pm
396
... Okay- I guess I'm just not familiar with this usage of "ordered pairs". Anyway, according to the paper, yx and zx must be in lowest terms, so how are you...
Carl Lumma
carl@...
May 11, 2001 7:02 pm
397
... Where do you see that? No, x:y:z must be in lowest terms. ... Because x=10....
Paul H. Erlich
PERLICH@...
May 11, 2001 7:12 pm
398
... Ah, right. ... Check. So, the fact that triangulations aren't unique means that a given pair of points may be consecutive with more than one third point? ...
Carl Lumma
carl@...
May 11, 2001 7:38 pm
399
... No, it doesn't mean that. Any pair of points is simply a member of an ordinary Farey series. It's with triples of points that the complexities come in....
Paul H. Erlich
PERLICH@...
May 11, 2001 7:42 pm
400
... I guess I don't understand how to construct a triangulation, then. For a given ^F_n, the points are fixed. Every pair of points must participate in ____...
Carl Lumma
carl@...
May 11, 2001 8:05 pm
401
Every pair of neighboring points must form an edge for two regular triangles. I guess I misunderstood what you meant by "consecutive". ... From: Carl Lumma...
Paul H. Erlich
PERLICH@...
May 11, 2001 8:09 pm
402
... Cool. I guess I'm waiting for part 2, then. Thanks, Paul! -C....
Carl Lumma
carl@...
May 11, 2001 8:15 pm
403
Carl, are you aware of the MIRACLE/blackjack developments over on the Tuning List? It's all possible because of you. I think you'd be more than interested!...
Paul H. Erlich
PERLICH@...
May 11, 2001 8:16 pm
404
Hi all. I've been looking through the files and there's a lot to study. Very nice Bob Helsloot Age 44 - Living in the Netherlands, Purmerend 20 km from...
Bob Helsloot
bhelsloot@...
May 13, 2001 7:04 pm
405
... Very nice ... Our friend Manuel Op de Coul, the world's premier microtonal scale curator and software engineer, also lives in the Netherlands. Perhaps you...
PERLICH@...
May 13, 2001 7:47 pm
406
Our friend Manuel Op de Coul, the world's premier microtonal scale curator and software engineer, also lives in the Netherlands. Perhaps you two should meet ....
Bob Helsloot
bhelsloot@...
May 13, 2001 8:44 pm
407
Subject: Re: complexity measures ... I did some more investigation over the weekend. The most successful experiment I did was to insert a complexity cap. This...
Robert C Valentine
BVAL@...
May 14, 2001 6:55 am
408
Hi Robert, ... We've gone over this several times. I'll be glad to do whatever it takes to get you up to speed, but for now, perhaps you can review the...
Paul H. Erlich
PERLICH@...
May 14, 2001 6:46 pm
409
Hi Paul, I may take a look some time and try to catch on what it all is about. However, meanwhile, if you want me to code it quickly, you could specify the...
Robert Walker
robert_walker@...
May 15, 2001 1:48 pm
410
See http://groups.yahoo.com/group/harmonic_entropy/message/350 and follow the thread from there....
Paul H. Erlich
PERLICH@...
May 15, 2001 6:26 pm
411
Or if you don't want to, I can just send you the values! Or put them in a file, like Manuel has already done....
PERLICH@...
May 19, 2001 8:54 pm
412
... Well, that would get it into my program in a jiffy. If you had it in excel or a text file, it would be a cinch. If its a big effort, then don't make it for...
Robert C Valentine
BVAL@...
May 20, 2001 12:31 pm
413
Hi Robert, Since you include local mimima for rather complex ratios, and you're looking at scales in an octave-equivalent sense, I decided to give you the data...
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