Chaos Corner V03 N08 3 December 1993 Copyright 1993 by Robert D. Cowles; Ithaca, NY 14850.

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Chaos Corner V03 N08 3 December 1993 Copyright 1993 by Robert D. Cowles; Ithaca, NY 14850. Permission is hereby granted to republish complete issues in unaltered form. Republication of partial issues must reference the source and state that subscriptions to Chaos Corner are available (free) by sending electronic mail to -------------------------------------------------- Mailbag - Sites for SCO/Unix software? Mark Lednor asked after our last issue about the availability of precompiled software for systems that run Xenix from SCO. While Dr. Chaos doesnĘt know himself of any such sites, he suggests that the place to look for such information is, where else, in the /pub/usenet/comp.unix.xenix.sco directory. -------------------------------------------------- Mailbag - Bits and Bytes Online Jay Machado, author of Bits and Bytes Online, another electronic magazine, is please to announce that it is now possible to subscribe and unsubscribe by using a listserv. To subscribe send a message to, no subject, text: SUBSCRIBE bits-n-bytes To unsubscribe send a message to, no subject, text: UNSUBSCRIBE bits-n-bytes "The purpose of B&B is to encourage thinking and debate on the effects (both positive and negative) of emerging technologies on our lives and on our planet." -------------------------------------------------- Mailbag - Musical Notes - Reprise It appears that musical note frequencies are an issue that ranks up there with USGS maps in terms of reader interest. While Dr. Chaos received interesting notes from Michael Salmon and Nick Gimbrone on the topic, the most instructive came from David Karr in Cornell's Computer Science Department in the area of revision control over occasionally connected computer networks (Dr. Chaos claims that that sounds like many of the meetings he attends). The following is quoted from David's very interesting note: I think what Edward Stuebing means is that "just intonation" is different from "equal temperament." "Just intonation" is related to the harmonics of a tone, that is, when you pluck a string you get not only the fundamental frequency but also harmonics which are 2 times, 3 times, 4 times, and higher integer multiples of the frequency. Doubling the frequency (2x) gives you an octave, for example, c to c' (low C to middle C on a piano). The 4x harmonic of c is then c'', that is, two octaves higher. The frequency ratio 3:2 is a "pure fifth," which in just intonation is the ratio between g and c. So the 3x harmonic of c is g' (an octave and a fifth higher) and the 6x harmonic of c is g'' (two octaves and a fifth higher). In between the 4x and 6x harmonics is the 5x harmonic; the 5:4 ratio is a "pure major third," the ratio between e and c. So the 5x harmonic of c is e'' (two octaves and a major third higher). So the major triad c-e-g has frequency ratio 1:(5/4):(3/2). The C major scale is constructed by taking this chord (the "tonic"), the note c' (the octave above c), and two other major triads: g-b'-d', the "dominant," and f-a'-c', the "subdominant," both of which also have ratios 1:(5/4):(3/2). Divide the resulting frequency for d' to obtain d, and put it all together, and you get the following frequencies relative to c: c 1 d 9/8 e 5/4 f 4/3 g 3/2 a' 5/3 b' 15/8 c' 2 I think there is some tradition for assigning the frequency 256 Hertz to c (the C below middle C) in just intonation, but this makes *all* your notes about a semitone flat: a'= 426.667 Hertz instead of 440 Hertz (the current international standard). Then again, Mozart's and Handel's tuning forks had a'=422 Hertz (see Harvard Concise Dictionary of Music, 1978, under "Pitch"), so maybe that's not so bad. The problem with just intonation is that if you tune a piano to it, some of the whole steps (such as c-d) have 9:8 ratios and some (such as d-e) have 10:9 ratios. Then if you start tuning the black keys (sharps and flats) to try to make the musical keys with one, two, or three sharps or flats sound right, you end up working yourself into a fix where the keys with more sharps or flats sound very strange. So, actually, the "tempering" of the musical scale is just a way of adjusting just intonation so that all musical keys will be playable on a piano. The system of equal temperament is one such adjustment, where each half-tone is given a ratio of exactly 2(1/12):1. But there's apparently some evidence that other "well-tempered" systems have been used, for example by Bach for his Well-Tempered Clavier. A possibility for computer-generated music would be to produce notes of just intonation when playing in a major key (I don't know quite what to do in minor keys or other modes). Most of the time when you start adding or removing sharps or flats from notes, it's for a key change of some sort, in which case you simply produce the just intonation for the new key. This should work out for most key modulations (if you go all the way around the circle of fifths, though, you might run into trouble and have to adjust again). You'd have to do something else for truly chromatic music, of course, since not all half steps can be in the ratio (16/15):1, but then there are lots of other interesting possibilities you could take advantage of, like 19-tone or 31-tone scales or other innovations of modern music theorists. If you are interested in other frequency charts, David Karr recommends the charts in the CRC Handbook of Chemistry and Physics. Look in the Index under "Musical". -------------------------------------------------- Mailbag - Congratulations on Doctorate! Walter Wehinger sent his congratulations on Dr. Chaos being awarded an honorary doctorate, and say that for a paltry DM 50.000 donation the University of Stuttgart he could become a permanent member of the academic senate. It looked attractive until I pointed out to Dr. Chaos that the German way of marking off numbers is reversed from the convention used here ... 50,000 looks like a much larger quantity to us! Dr. Chaos has been monitoring the exchange rate via Deutsche Welle and points out that if current trends continue, the 50,000 number may not be too bad (currently more than 1.7 DM per USD as opposed to 1.4 DM per USD about a year ago). -------------------------------------------------- Correction to address for accessing FEDWORLD BBS Art McGee points out that while "" will work for now, you should really use the "official" name of "" ... the first name will stop working at some point in the future. -------------------------------------------------- Apologies for mailing snafu Dr. Chaos set new records for snarling up the mailing of the last issue. The first problem was a bad character ( a ") buried in the subscription list that meant it was not clear how many people had received the first mailing (addresses seem to be processed in reverse order). In any case, Dr. Chaos got rattled in the processing of getting that fixed and failed to (1) specify a "Reply-to:" field, and (2) neglected to disable the list to prevent others using it. While it may be a surprise to those who received many copies of ccv03n07, it is possible that not everyone got a copy. Be assured that this mailing is going to go out "the regular way" without trying for any "improvements". -------------------------------------------------- Lists of available articles mentioned in Chaos Corner As recent subscribers know, there is now a list of articles mentioned in Chaos Corner and still available on request from Dr. Chaos. The lists are available via anonymous FTP from in the /pub directory. Look for the files v1.files, v2.files and v3.files. If you see something you like, send your electronic mail request to Dr. Chaos at If you do not have direct access to FTP, send a mail file containing the single word "help" (no quote marks) to (European users only), or (this may be limited to BITNET users). -------------------------------------------------- Electronic Mail access to Gopher Are you frustrated by hearing about the wonders of Gopherspace when you don't have access to it? Request help from (Japan) or According to Scott Yanoff, maintainer of the Internet Services List, if you visit one Gopher, it should be the one at -------------------------------------------------- Electronic version of The Journal of Irreproducible Results Mark Dionne, editor of the Journal of Irreproducible Results, has announced the Mini-JIR: The Mini-Journal of Irreproducible Results publishes news about overly stimulating research and ideas. Specifically: A) Haphazardly selected superficial (but advanced!) abstracts of research news and satire from the Journal of Irreproducible Results (JIR). JIR itself is a print journal, which since 1955 has been publishing irreproducible science humor from laboratories around the world and elsewhere. B) News about the annual Ig Nobel Prize Ceremony. Ig Nobel Prizes honor "achievements that cannot or should not be reproduced." A public ceremony is held at MIT, in Cambridge Massachusetts, every autumn. The ceremony is sponsored jointly by JIR and by the MIT Museum. The first issue of Mini-JIR contains a list of the 1993 Ig Nobel Prize winners. C) News about other science humor activities conducted by the MIT Museum and JIR. The Mini-Journal of Irreproducible Results is an electronic publication, available over the Internet, free of charge. It is distributed as a LISTSERV application. We expect to publish 6-12 issues per year. To subscribe, send an E-mail message to: LISTSERV@MITVMA.MIT.EDU The body of your message should contain ONLY the words "SUBSCRIBE MINI-JIR" followed by your name. -------------------------------------------------- Get your Free Subscription Here! Just send a message to Dr. Chaos - and ask to be put on the subscription list. From CompuServe, use the address It's that easy. Don't delay ---- act now! Dr. Chaos .


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