hirai@swatsun (Eiji "A.G." Hirai) (12/14/87)
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
haitex@pnet01.cts.com (Wade Bickel) (12/16/87)
As I remember, the original question asked for an endlessly rising
tone. These various plays on cyclic nature of the western scale achieve
a similar effect, but are not quite what was asked for.
Western music is based upon a 12 tone system. These tones are sub-
divided into sets of 7 notes which form scales (usually 7 notes). These
subsets form alternative contours. When progressing through the keys
rather than moving in one tone steps, the 5th member of a given scale
forms the next most obvious key. By doing so the scale being changed
to will contain only one note not found in its predicessor, which ex-
plains why it is the next obvious key. This is layed out clearly
for the ear in J.S. Bach's studies of the well tempered scale.
Taking this into account, it should be possible to derive any
number of always rising progressions. Of course doing so in an
artfull manner requires skill, insight, and talent. What I find
fasinating about Bach's work is the precise control of multiple
modes of the keys.
Interestingly enough, the well tempered scale is not true to
the ear. IE: if I tune my guitar by ear to a given major scale,
it will sound fine in that scale, and its cousins, but degrades
with distance from the original root. Clearly the well tempered
clavier (spelling?) is full of consistent distortions to make the
circle of 5ths fit. At least I think this is so. Any knowlegable
theory experts care to enlighten me?
Thanks,
Wade.
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INET: haitex@pnet01.CTS.COMsmoliar@vaxa.isi.edu (Stephen Smoliar) (12/17/87)
In article <2151@crash.cts.com> haitex@pnet01.cts.com (Wade Bickel) writes: > > As I remember, the original question asked for an endlessly rising > tone. These various plays on cyclic nature of the western scale achieve > a similar effect, but are not quite what was asked for. > I am suprised that no one has cited the "Little Boy Suite" on this topic. I cannot remember the composer's name, although I seem to recall that he was French. This was one of the works composed with Max Mathews' Music V system; and, as I recall, it goes down, rather than up. Nevertheless, the principle is applicable in either direction. The composition was based on a timbre whose Fourier spectrum was periodic. Thus, it could be extrapolated both above and below the limits of human hearing. One could then gradually lower the fundamental, creating the sense of a descending pitch. However, new partials would enter from above as others would drop off below; and the effect was one of an endlessly descending tone. (The dramatic effect was intended to be that of the dropping of the "Little Boy" atomic bomb.) I have heard this referred to as the "fencepost" effect, because it is like driving past a long row of fenceposts with new ones always entering the visual field and no end in sight.
mikulska@beowulf.ucsd.edu (Malgorzata Mikulska) (12/20/87)
In article <4359@venera.isi.edu> smoliar@vaxa.isi.edu.UUCP (Stephen Smoliar) writes: > >I am suprised that no one has cited the "Little Boy Suite" on this topic. >I cannot remember the composer's name, although I seem to recall that he >was French. This was one of the works composed with Max Mathews' Music V >system; and, as I recall, it goes down, rather than up. Nevertheless, >the principle is applicable in either direction. > Jean-Claude Risset, in late 1960's, Bell Labs. He used this and similar effects in some other pieces, too (I think in "Mutations", but I don't remember this for sure right now). As for mentioning this piece(s), I had an impression that wasn't the kind of "perpetuum mobile" the original poster was seeking. Margaret Mikulska ======================== mikulska@sdcsvax.ucsd.edu sdcsvax!mikulska =========================
mmt@dciem.UUCP (Martin Taylor) (12/27/87)
--I am suprised that no one has cited the "Little Boy Suite" on this topic.
--I cannot remember the composer's name, although I seem to recall that he
--was French. This was one of the works composed with Max Mathews' Music V
--system; and, as I recall, it goes down, rather than up. Nevertheless,
--the principle is applicable in either direction.
--...the effect was one of an
--endlessly descending tone. (The dramatic effect was intended to be
--that of the dropping of the "Little Boy" atomic bomb.)
Jean-Claude Risset, published on Decca 710810 "Voice of the Computer" 1970.
(The piece is fine as music, too).
--
Martin Taylor
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