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 chaos-request@pelican.cit.cornell.edu.

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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 doesnt know himself of any such sites, he suggests that the place 
to look for such information is, where else, rtfm.mit.edu in the 
/pub/usenet/comp.unix.xenix.sco directory.

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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 listserv@acad1.dana.edu, no subject, 
text: SUBSCRIBE bits-n-bytes 

To unsubscribe send a message to listserv@acad1.dana.edu, 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."

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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".

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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).  

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Correction to address for accessing FEDWORLD BBS

Art McGee points out that while "fedworld.doc.gov" will work for now, 
you should really use the "official" name of "fedworld.gov" ... the 
first name will stop working at some point in the future.

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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".


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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 pelican.cit.cornell.edu 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 chaos-request@pelican.cit.cornell.edu.  If you do not have direct 
access to FTP, send a mail file containing the single word "help" (no 
quote marks) to ftpmail@grasp.insa-lyon.fr (European users only), or 
bitftp@pucc.princeton.edu (this may be limited to BITNET users).

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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 gophermail@ncc.go.jp (Japan) 
or gophermail@calvin.edu.  According to Scott Yanoff, maintainer of the 
Internet Services List, if you visit one Gopher, it should be the one at 
english-server.hss.cmu.edu.

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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.

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