Xref: utzoo comp.sys.amiga:1354 comp.sys.mac:9895 comp.sys.atari.st:6362 rec.music.makers:1086 rec.music.synth:1967
Path: utzoo!mnetor!uunet!husc6!psuvax1!vu-vlsi!swatsun!hirai
From: hirai@swatsun (Eiji "A.G." Hirai)
Newsgroups: comp.sys.amiga,comp.sys.mac,comp.sys.atari.st,rec.music.makers,rec.music.synth
Subject: Re: Sonic Holography.
Message-ID: <1478@tulum.swatsun.UUCP>
Date: 13 Dec 87 23:59:36 GMT
References: <7536@eddie.MIT.EDU> <2476@gryphon.CTS.COM> <1239@sugar.UUCP>
Organization: Sun Lab, Swarthmore College PA
Lines: 32
Summary: J.S. Bach's _Musical Offerings_

In article <1239@sugar.UUCP> peter@sugar.UUCP (Peter da Silva) 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, it's a piece in Bach's _Musical Offerings_.  Each
of the pieces are intriguing in their own right.  I'm not knowledgeable
enough in music theory but I recently perused over a book that was devoted
exclusively to anaylyzing _Musical Offerings_.  Very interesting!

	The piece starts on one key but after the piece nears the 'end',
it has changed to another key, and the 'end' of the piece runs smoothly into
the start of the piece, this time with the new key.  The key goes on changing
until you've reached the original key, and so on and so on and so on and so...

	A similar work (without the key changes but with the tail -> head
sort of loop) was done by Chopin.  I can't remember what it was called,
though it was a piano piece (big surprise! - for Chopin :-)
If anyone is interested, I can dig it from my notes...

>-- Peter da Silva

						-a.g. hirai
						"You have just begun reading
						 a sentence which you have
						 just finished reading."
-- 
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