source file: mills2.txt Date: Tue, 25 Jun 1996 15:01:14 -0700 Subject: Post from McLaren From: John Chalmers From: mclaren Subject: Paul Erlich's insightful comments -- Kudos to Paul Erlich. Having seived through hundreds of my posts and thousands of my posted quotes, references, tables, numbers, equations and citations, he has succeeded in finding 2 errors. (Actually one of 'em is not an error, but a sly joke.) The 1ere error in question involves my calling phi a transcendental number. As Paul astutely points out, phi is the solution of a simple algebraic equation with rational coefficients and real rational exponents: x^2 - X - 1 = 0. This means that phi is by definition an algebraic irrational, rather than a transcendental irrational number. Thanks, Paul. As mentioned on many another occasion, Your Humble E-Mail Correspondent is a mathematical idiot. This means I make plenty of flubs when it comes to math--like my infamous statement that "i is the square root of -1." (Of course -i also qualifies, as Manuel Op de Coul pointed out.) This also means that I'll make plenty of mathematical flubs in the future. Thanks in advance to everyone who'll be on the lookout for my math errors. It's important, when speaking about mathematics, to catch the errors before they propagate. Here's Erlich's reaction to my little joke (which he must have misunderstood as an error): "Brian McLaren wrote: >As the final and most bizarre demonstration of the properties >of extended Wilson CPS scales, observe the tuning which >falls out of the 3,8 [1.22222, 2.33333, 3.444444, 4.55555, >5.666666, 6.777777, 7.888888, 8.99999]. >According to Manuel Op de Coul's SCALA program, this >Wilson CPS produces the 9-tone equal-tempered scale. >--mclaren "It does not. However, [2^1.22222, 2^2.33333, 2^3.444444, 2^4.55555, 2^5.666666, 2^6.777777, 2^7.888888, 2^8.99999] is all the notes in the 9-tone equal tempered scale, and combination product sets of this will, trivially, produce 9-tone equal tempered scales. Nothing bizarre about it. Brian McLaren reminds me of a Ludwig Plutonium on some of the sci. newsgroups, and Albert Silverman on rec.music.compose. Long, self-aggrandizing posts filled with factually incorrect and useless examples and lots of whining about the establishment, accompanied by a complete lack of ability to communicate with the other members of the group." -- Paul Erlich, Tuning Digest 719 Let us re-examine EXACTLY what I said: "According to Manuel Op de Coul's SCALA program, this Wilson CPS produces the 9-tone equal-tempered scale." -- mclaren My statement above is correct as it stands. There's a bug in Manuel's SCALA program version 1.0 which produces a fairly humorous result for the CPS function when you input a Wilson 3,8 CPS with generators [1.22222, 2.33333, 3.444444, 4.55555, 5.666666, 6.777777, 7.888888, 8.99999] It doesn't take a rocket scientist to figure out that these generators cannot possibly produce a 9-TET scale--or so I assumed. It seemed so obvious to me that the result I gave was comically wrong, that it would be immediately apparent to any forum subscriber that I was poking a tiny bit of fun at the beta version of Manuel's SCALA program. The tip-off, of course, being the last sentence of my post-- a sentence which Erlich deliberately left off when he misrepresented my post: "According to Manuel Op de Coul's SCALA program, this Wilson CPS produces the 9-tone equal-tempered scale. It is left as an exercise for the enterprising xenharmonist to determine why and how. --mclaren" My expectation was that at least one "enterprising xenharmonist" would actually feed my numbers into SCALA, discover that SCALA gave an incorrect result, and report that fact in the properly amused tone. Instead, Erlich compares me to someone called "Ludwig Plutonium," whoever that is. Let us re-read the last sentence of my post: "It is left as as an exercise forthe enterprising xenharmonist to determine why and how." -- mclaren This is peculiar way of describing what should be a straightforward scale-generation procedure. Tongue in cheek, anyone? The "why" is simple: there's a bug in SCALA 1.0. The "how" is less simple-- it appears to involve an ADA routine which assumes that only integers will be entered. I did not expect anyone to penetrate that deeply into the arcana of my sly little joke; and of course no one did. Thus, when Erlich complains (Tuning Digest 719) about "Long, self-aggrandizing posts filled with factually incorrect and useless examples..." it is of some interest to examine his plaint. Presumably Erlich wants people to believe that my posts are "filled" with "factually incorrect" examples. Yet out of my hundreds of posts and thousands of facts, Erlich has been able to find only 2 errors--one of which wasn't even an error. Out of my thousands of facts and hundreds of posts, Erlich pounces on 1 (one, count it--one) error. (I incorrectly identified phi as a trascendental irrational rather than an algebraic irrational.) On the basis of this 1 (one, count it--one) error, Erlich rants: "Brian McLaren reminds me of a Ludwig Plutonium on some of the sci. newsgroups..." Okay. Now I think we've all got the picture. Make 1 error out of several hundred posts, and you're a charlatan. One (count it, 1) error identified out of thousands of facts, tables, quotes, citations...and *this* means that my posts are "filled" with "factually incorrect" examples. Need I say more? Does *anyone* out there require convincing that Paul Erlich is less concerned with the facts than with ad hominem attacks on Your Humble E-Mail Correspondent? While we're on the subject of errors, turnabout is fair play. So let's examine one of Paul Erlich's own posts, and see whether it contains any "factually incorrect" examples... Paul Erlich stated in Tuning Digest 718 that subharmonics are not present in the spectra of acoustic instruments. This is not only false, it demo hates that Erlich has not done little (if any) Fourier analysis of real-world instrument sounds. One of the hard facts is that book learning will only take you so far when you apply DSP techniques to the study of real sounds. Then you've got to get your hands dirty out in the real world and find out that 90% of what you learned in those books applies only in special cases, or doesn't apply at all. Ralph David Hill has written a Fourier analysis/ resynthesis software system which is capable of detecting, analyzing, and resynthesizing quasi- harmonic sounds. Yesterday I visited Dave at his home and he ran me through a demo of his system. He resynthesized a trombone note with and without the octave-below and 2-octaves below subharmonic. The notes resynthesized without both subharmonics sounded noticeably different from the original sound, and significantly less realistic. Dave reported this at the 1982 ICMC, so it's very old news. Clearly Paul Erlich needs to learn something about signal processing, real-world timbres, and the limitations of using off-the-shelf Fourier analysis software. -- --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 26 Jun 1996 05:19 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id UAA02106; Tue, 25 Jun 1996 20:19:06 -0700 Date: Tue, 25 Jun 1996 20:19:06 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu