228 lines
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228 lines
10 KiB
Plaintext
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Chaos Corner V03 N08 3 December 1993
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Copyright 1993 by Robert D. Cowles; Ithaca, NY 14850. Permission is
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hereby granted to republish complete issues in unaltered form.
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Republication of partial issues must reference the source and state that
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subscriptions to Chaos Corner are available (free) by sending electronic
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mail to chaos-request@pelican.cit.cornell.edu.
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--------------------------------------------------
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Mailbag - Sites for SCO/Unix software?
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Mark Lednor asked after our last issue about the availability of
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precompiled software for systems that run Xenix from SCO. While Dr.
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Chaos doesn<73>t know himself of any such sites, he suggests that the place
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to look for such information is, where else, rtfm.mit.edu in the
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/pub/usenet/comp.unix.xenix.sco directory.
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--------------------------------------------------
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Mailbag - Bits and Bytes Online
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Jay Machado, author of Bits and Bytes Online, another electronic
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magazine, is please to announce that it is now possible to subscribe and
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unsubscribe by using a listserv.
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To subscribe send a message to listserv@acad1.dana.edu, no subject,
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text: SUBSCRIBE bits-n-bytes
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To unsubscribe send a message to listserv@acad1.dana.edu, no subject,
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text: UNSUBSCRIBE bits-n-bytes
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"The purpose of B&B is to encourage thinking and debate on the effects
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(both positive and negative) of emerging technologies on our lives and
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on our planet."
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--------------------------------------------------
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Mailbag - Musical Notes - Reprise
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It appears that musical note frequencies are an issue that ranks up
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there with USGS maps in terms of reader interest. While Dr. Chaos
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received interesting notes from Michael Salmon and Nick Gimbrone on the
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topic, the most instructive came from David Karr in Cornell's Computer
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Science Department in the area of revision control over occasionally
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connected computer networks (Dr. Chaos claims that that sounds like many
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of the meetings he attends). The following is quoted from David's very
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interesting note:
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I think what Edward Stuebing means is that "just intonation" is
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different from "equal temperament."
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"Just intonation" is related to the harmonics of a tone, that is, when
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you pluck a string you get not only the fundamental frequency but also
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harmonics which are 2 times, 3 times, 4 times, and higher integer
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multiples of the frequency. Doubling the frequency (2x) gives you an
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octave, for example, c to c' (low C to middle C on a piano). The 4x
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harmonic of c is then c'', that is, two octaves higher.
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The frequency ratio 3:2 is a "pure fifth," which in just intonation is
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the ratio between g and c. So the 3x harmonic of c is g' (an octave
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and a fifth higher) and the 6x harmonic of c is g'' (two octaves and a
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fifth higher).
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In between the 4x and 6x harmonics is the 5x harmonic; the 5:4 ratio
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is a "pure major third," the ratio between e and c. So the 5x
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harmonic of c is e'' (two octaves and a major third higher).
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So the major triad c-e-g has frequency ratio 1:(5/4):(3/2). The C
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major scale is constructed by taking this chord (the "tonic"), the
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note c' (the octave above c), and two other major triads: g-b'-d', the
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"dominant," and f-a'-c', the "subdominant," both of which also have
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ratios 1:(5/4):(3/2). Divide the resulting frequency for d' to obtain
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d, and put it all together, and you get the following frequencies
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relative to c:
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c 1
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d 9/8
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e 5/4
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f 4/3
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g 3/2
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a' 5/3
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b' 15/8
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c' 2
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I think there is some tradition for assigning the frequency 256 Hertz
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to c (the C below middle C) in just intonation, but this makes *all*
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your notes about a semitone flat: a'= 426.667 Hertz instead of 440
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Hertz (the current international standard). Then again, Mozart's and
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Handel's tuning forks had a'=422 Hertz (see Harvard Concise Dictionary
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of Music, 1978, under "Pitch"), so maybe that's not so bad.
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The problem with just intonation is that if you tune a piano to it,
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some of the whole steps (such as c-d) have 9:8 ratios and some (such
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as d-e) have 10:9 ratios. Then if you start tuning the black keys
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(sharps and flats) to try to make the musical keys with one, two, or
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three sharps or flats sound right, you end up working yourself into
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a fix where the keys with more sharps or flats sound very strange.
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So, actually, the "tempering" of the musical scale is just a way of
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adjusting just intonation so that all musical keys will be playable
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on a piano.
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The system of equal temperament is one such adjustment, where each
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half-tone is given a ratio of exactly 2(1/12):1. But there's
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apparently some evidence that other "well-tempered" systems have been
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used, for example by Bach for his Well-Tempered Clavier.
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A possibility for computer-generated music would be to produce notes
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of just intonation when playing in a major key (I don't know quite
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what to do in minor keys or other modes). Most of the time when you
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start adding or removing sharps or flats from notes, it's for a key
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change of some sort, in which case you simply produce the just
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intonation for the new key. This should work out for most key
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modulations (if you go all the way around the circle of fifths,
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though, you might run into trouble and have to adjust again). You'd
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have to do something else for truly chromatic music, of course, since
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not all half steps can be in the ratio (16/15):1, but then there are
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lots of other interesting possibilities you could take advantage of,
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like 19-tone or 31-tone scales or other innovations of modern music
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theorists.
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If you are interested in other frequency charts, David Karr recommends
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the charts in the CRC Handbook of Chemistry and Physics. Look in the
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Index under "Musical".
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--------------------------------------------------
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Mailbag - Congratulations on Doctorate!
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Walter Wehinger sent his congratulations on Dr. Chaos being awarded an
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honorary doctorate, and say that for a paltry DM 50.000 donation the
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University of Stuttgart he could become a permanent member of the
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academic senate. It looked attractive until I pointed out to Dr. Chaos
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that the German way of marking off numbers is reversed from the
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convention used here ... 50,000 looks like a much larger quantity to us!
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Dr. Chaos has been monitoring the exchange rate via Deutsche Welle and
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points out that if current trends continue, the 50,000 number may not be
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too bad (currently more than 1.7 DM per USD as opposed to 1.4 DM per USD
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about a year ago).
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--------------------------------------------------
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Correction to address for accessing FEDWORLD BBS
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Art McGee points out that while "fedworld.doc.gov" will work for now,
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you should really use the "official" name of "fedworld.gov" ... the
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first name will stop working at some point in the future.
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--------------------------------------------------
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Apologies for mailing snafu
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Dr. Chaos set new records for snarling up the mailing of the last issue.
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The first problem was a bad character ( a ") buried in the subscription
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list that meant it was not clear how many people had received the first
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mailing (addresses seem to be processed in reverse order). In any case,
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Dr. Chaos got rattled in the processing of getting that fixed and failed
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to (1) specify a "Reply-to:" field, and (2) neglected to disable the
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list to prevent others using it. While it may be a surprise to those
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who received many copies of ccv03n07, it is possible that not everyone
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got a copy. Be assured that this mailing is going to go out "the
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regular way" without trying for any "improvements".
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--------------------------------------------------
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Lists of available articles mentioned in Chaos Corner
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As recent subscribers know, there is now a list of articles mentioned in
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Chaos Corner and still available on request from Dr. Chaos. The lists
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are available via anonymous FTP from pelican.cit.cornell.edu in the /pub
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directory. Look for the files v1.files, v2.files and v3.files. If you
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see something you like, send your electronic mail request to Dr. Chaos
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at chaos-request@pelican.cit.cornell.edu. If you do not have direct
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access to FTP, send a mail file containing the single word "help" (no
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quote marks) to ftpmail@grasp.insa-lyon.fr (European users only), or
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bitftp@pucc.princeton.edu (this may be limited to BITNET users).
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--------------------------------------------------
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Electronic Mail access to Gopher
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Are you frustrated by hearing about the wonders of Gopherspace when you
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don't have access to it? Request help from gophermail@ncc.go.jp (Japan)
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or gophermail@calvin.edu. According to Scott Yanoff, maintainer of the
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Internet Services List, if you visit one Gopher, it should be the one at
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english-server.hss.cmu.edu.
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--------------------------------------------------
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Electronic version of The Journal of Irreproducible Results
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Mark Dionne, editor of the Journal of Irreproducible Results, has
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announced the Mini-JIR:
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The Mini-Journal of Irreproducible Results publishes news
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about overly stimulating research and ideas. Specifically:
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A) Haphazardly selected superficial (but advanced!)
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abstracts of research news and satire from the Journal of
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Irreproducible Results (JIR). JIR itself is a print journal,
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which since 1955 has been publishing irreproducible science
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humor from laboratories around the world and elsewhere.
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B) News about the annual Ig Nobel Prize Ceremony. Ig Nobel
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Prizes honor "achievements that cannot or should not be
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reproduced." A public ceremony is held at MIT, in Cambridge
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Massachusetts, every autumn. The ceremony is sponsored
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jointly by JIR and by the MIT Museum. The first issue of
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Mini-JIR contains a list of the 1993 Ig Nobel Prize winners.
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C) News about other science humor activities conducted by
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the MIT Museum and JIR.
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The Mini-Journal of Irreproducible Results is an electronic
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publication, available over the Internet, free of charge. It
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is distributed as a LISTSERV application. We expect to
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publish 6-12 issues per year.
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To subscribe, send an E-mail message to:
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LISTSERV@MITVMA.MIT.EDU
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The body of your message should contain ONLY the words
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"SUBSCRIBE MINI-JIR" followed by your name.
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--------------------------------------------------
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Get your Free Subscription Here!
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Just send a message to Dr. Chaos - chaos-request@pelican.cit.cornell.edu
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and ask to be put on the subscription list. From CompuServe, use the
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address INTERNET:chaos-request@pelican.cit.cornell.edu. It's that easy.
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Don't delay ---- act now!
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Dr. Chaos
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.
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