From "Big Brother" Tuning List... ... several weeks, but that will change next week or shortly thereafter ... Yes, of course, this should wait until after the...
Joseph Pehrson
pehrson@...
Nov 8, 2000 2:33 pm
266
Don't forget the microtone festival saturday in NYC. Who's going? I want to meet some of you odd tuning freaks :) Matt ... From:...
Ricardo Sheets
spliffrd@...
Nov 10, 2000 12:06 am
267
Rather than just summing the exponential, N=10000, s=1% dyadic entropies for the six intervals in the tetrad, I wanted to use a function that would give more...
Paul H. Erlich
PERLICH@...
Nov 16, 2000 8:57 am
268
In case anyone didn't know, (exp(entropy))^(6*pi) = exp(entropy*6*pi)....
Paul H. Erlich
PERLICH@...
Nov 16, 2000 6:17 pm
269
I wrote, ... mutually prime Actually that probability is 6/(pi^2). So the Farey series of order N contains about 6*(N/pi)^2 fractions, since, of the N^2...
Paul H. Erlich
PERLICH@...
Nov 16, 2000 8:39 pm
270
Apparently the probability that n randomly chosen integers will be mutually prime is zeta(n), where zeta is the Riemann zeta function (see the current thread...
Paul H. Erlich
PERLICH@...
Nov 16, 2000 9:22 pm
271
I wrote, ... proportional to 1/sqrt(n*d)" rule as >before, but _not_ restricting the possible fractions to be in lowest terms? This thought comes to me a >lot ...
Paul H. Erlich
PERLICH@...
Nov 16, 2000 10:43 pm
272
I wrote, ... that should read: "It's virtually the same shape as the _exponential_ of the harmonic entropy curve obtained . . ."...
Paul H. Erlich
PERLICH@...
Nov 16, 2000 10:44 pm
273
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the harmonic_entropy group. File :...
harmonic_entropy@egro...
Nov 17, 2000 6:53 am
274
Mama mia! http://www.egroups.com/files/harmonic_entropy/Erlich/pizza3.jpg http://www.egroups.com/files/harmonic_entropy/Erlich/pizza2.jpg Still all diadic at...
Paul H. Erlich
PERLICH@...
Nov 17, 2000 7:35 am
275
Hi Paul... Thanks for the new ordering and the delicious new pizza slices. I'm going to listen to the new ordering as soon as I get a chance... Just "off the...
Joseph Pehrson
pehrson@...
Nov 17, 2000 9:16 pm
276
... These mountains are the familiar, consonant triads, as I'm sure you'll see upon further examination . . . the difference between the new pizzas and the...
Paul Erlich
PERLICH@...
Nov 17, 2000 11:00 pm
277
Hello all, I would like to start a discussion of the Ferguson-Forcade algorithm, and related integer relation algorithms, and their application in finding a...
Carl Lumma
CLUMMA@...
Nov 24, 2000 2:53 pm
278
Carl: The book I just returned on multidimensional continued fractions mentioned Ferguson-Forcade only in passing. It did say that Brun's algorithm is...
John Chalmers
JHCHALMERS@...
Nov 24, 2000 4:49 pm
279
Hello John, I'm very interested in that book you red about multidimensional continued fractions. Can you give the reference? ... Question Can one call the...
Peter Mulkers
P.MULKERS@...
Nov 24, 2000 10:09 pm
280
Carl Lumma wrote, ... John Chalmers wrote, ... for ... John, the question Carl brings up is not a simple problem, nor is it a question of speed of convergence....
Paul Erlich
PERLICH@...
Nov 25, 2000 7:11 am
281
I wrote, ... enough ... plane ... Clearly I didn't finish that sentence! It should conclude, "a much more sophisticated approach is needed."...
Paul Erlich
PERLICH@...
Nov 25, 2000 7:18 am
282
http://hissa.nist.gov/dads/HTML/fergusonForcade.html Note the emphasis on the _iterative_ nature of the procedure -- that property seems essential to its...
Paul Erlich
PERLICH@...
Nov 25, 2000 8:05 am
283
The book I looked at is "Multidimensional Continued Fraction Algorithms" by A. J. Brentjes, published by the Mathematisch Centrum, Amsterdam, 1981. I also...
John Chalmers
JHCHALMERS@...
Nov 25, 2000 4:52 pm
284
... and ... Tribonacci! I just posted on that to the tuning list. Actually, that's quite a coincidence -- continued fractions are to the MOSs of the Scale Tree...
Paul Erlich
PERLICH@...
Nov 25, 2000 10:02 pm
285
... CF) a ... This doesn't look very promising from a musical point of view, since it says that, for example, 38/37 is more "rational" than 5/3. And what about...
Paul Erlich
PERLICH@...
Nov 25, 2000 10:11 pm
286
... Peter: Right, I have to review my definition of irrationality. Maybe the number of layers and low integer simplicity in the CF-expansions have to play...
Peter Mulkers
P.MULKERS@...
Nov 26, 2000 2:21 pm
287
There is a measure of regularity or normality of irrational numbers called "approximate entropy" or ApEn developed by Steven Pincus and various colleagues in...
John Chalmers
JHCHALMERS@...
Nov 27, 2000 6:20 pm
288
Peter wrote, ... I prefer to think of the low integer simplicity as the _only_ valid measure of rationality, and then use harmonic entropyu, as Pierre said, to...
Paul H. Erlich
PERLICH@...
Nov 27, 2000 8:42 pm
289
John Chalmers wrote, ... Bizarre! Do you really mean pi and not phi? And do you mean 3 and not sqrt(3)?...
Paul H. Erlich
PERLICH@...
Nov 27, 2000 9:14 pm
290
[John Chalmers wrote...] ... [Paul Erlich wrote...] ... Why don't we focus on the link between the Euclidean algorithm and the mediant process. We won't know...
Carl Lumma
CLUMMA@...
Nov 28, 2000 2:55 pm
291
Paul: Yes, pi is the most random of the irrational numbers measured. The terms regular and irregular are a bit confusing, even in the original papers. I meant...
John Chalmers
JHCHALMERS@...
Nov 28, 2000 3:47 pm
292
Paul: I checked the Science mag note and the order from most random to least of the numbers tested is pi, sqr(2), e, sqr(3). The principal paper in ther series...
John Chalmers
JHCHALMERS@...
Nov 28, 2000 6:09 pm
293
... Of the numbers _tested_. So there could be a "more random" number than pi, or at least one "as random", right?...
Paul H. Erlich
PERLICH@...
Nov 29, 2000 3:25 pm
294
Paul: I don't know if there could be one more random than pi, but possibly there are some as random. --John...
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