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From: hirai@swatsun (Eiji "A.G." Hirai)
Newsgroups: comp.sys.amiga,comp.sys.mac,comp.sys.atari.st,rec.music.makers,rec.music.synth,rec.music.classical
Subject: Re: Sonic Holography.
Message-ID: <1480@tulum.swatsun.UUCP>
Date: 14 Dec 87 03:50:33 GMT
References: <7536@eddie.MIT.EDU> <2476@gryphon.CTS.COM> <1239@sugar.UUCP>
Organization: Sun Lab, Swarthmore College PA
Lines: 40
Summary: J.S. Bach's _Musical Offering_

In article <1239@sugar.UUCP> peter@sugar.UUCP (Peter da Silva) writes:
>(Richard Sexton) writes:
>
>See Johann Sebastian Bach's "endlessly rising canon". This is a very old
>illusion, based on the fact that a note sounds very much like the same note
>in the next octave.

	More specifically, this is a piece called "Canon per Tonos" and it's
in J.S. Bach's _Musical Offering.  The canon is able to repeat itself because
Bach made the 'tail' notes of the canon flow smoothly into the 'head' notes
of the canon.  More importantly, the canon starts in the key of C minor
but when we near the end of the piece, it changes to the key of D minor.
So we keep on playing in the key of D minor but when we near the 'tail' again,
it changes to E, and so on and so on...  Eventually, it reaches the key of
C minor, to start all over again!

	Bach's _Musical Offering_ also contains other interesting pieces
too.  Check out Hans Theodore David's _J.S. Bach's Musical Offering_ to
see how involved and beautiful this collection of musical delights is!
The book is devoted exclusively to the analysis of _Musical Offerings_.
Bery bery interesting...

	Another piece which repeats itself is Chopin's _Mazurka in F minor_,
opus 68 posthumous (1849).  You can play this piece without end, though it
doesn't have the neat key changes that "Canon per Tonos" has.

	I posted a query for any pieces the net-readers know about that are
similar to these, but the response so far has been under-whelming.  Oh well.

					-a.g. hirai
					"You have, of course, just begun
					 reading the sentence that you have
					 just finished reading."
						- Peter M. Brigham

-- 
Eiji "A.G." Hirai @ Swarthmore College, Swarthmore PA 19081 | Tel. 215-543-9855
UUCP:   {rutgers, ihnp4, cbosgd}!bpa!swatsun!hirai |  "All Cretans are liars."
Bitnet:       vu-vlsi!swatsun!hirai@psuvax1.bitnet |         -Epimenides
Internet:            bpa!swatsun!hirai@rutgers.edu |         of Cnossus, Crete