Xref: utzoo comp.sys.amiga:1355 comp.sys.mac:9896 comp.sys.atari.st:6363 rec.music.makers:1087 rec.music.synth:1968 rec.music.classical:1818 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,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