Hi,
Just to bring a different persepective here:
More interesting to me than alternate tunings, are simply the types of unpredictable variances when gets when real instruments go "out of tune". To me, music that is accidentally "out of tune" sounds quite rich and interesting.
I used PD recently to generate long tones in eight instruments on a very simple set of four pitch classes, in any one of three octaves. However, a simple Markov chain allows the pitch to drift either up or down by some randomly chosen amount (something between 0 and a quarter tone I believe). The sound turned out to be far richer than I imagined. The best thing is, that the same algorithm can also generate the events for my score of
real instruments, though I think I must draw the score by hand to get
the right look. So I will probably have PD generate text files. I might even generate images for the score with GEM, but I don't know how to make curves that have the randomness of the ones I draw, so in this case I'd probably trace the images and humanize the look of the lines.
John Cage "Ryanji" pieces were something of an inspiration for this - where he draws pitch curves using the edges of rocks.
~David
On 8/10/06,
Chuckk Hubbard <badmuthahubbard@gmail.com> wrote:
I have to disagree with this.
You could play music that sounds just as natural using a series of 6
or 8 perfect fifths. *Any* number of notes separated by fifths sounds
natural.
12-tone equal temperament is useful because 2^(7/12) is close to 3/2.
In 19-tet, 2^(5/19) is close to 6/5 (minor third), 2^(6/19) is close
to 5/4 (major third), and 2^(11/19) is close to 3/2. That makes these
exponential divisions of 2 useful for *fooling* the ear, but in all
cases they are approximations, and 19-tet's substitute for 3/2 is
farther from it than 12-tet's.
I say if you want 3/2, use 3/2.
I don't think 5-tone equal temperament is a substitute for the
pentatonic scale. The pentatonic scale is made up of decidedly uneven
intervals. Javanese gamelan tuning is notoriously non-standardized,
adjusted individually for different ensembles. They usually don't
even use octaves. http://www2.hmc.edu/~alves/laras.html
Also, it is not true that all intervals are based on fifths. Anceint
Chinese theorists suggested this, but their anceint Chinese secret was
that the Ch'in used intervals not derived this way, such as 8/7.
Ptolemy and Didymos both suggested tuning thirds based on the 5th
harmonic, 5/4, rather than Pythagoras' 81/64, which is more out of
tune than 12-tone equal temperament.
Islamic theorists used intervals like 18/17, 81/68, and 27/22,
supposedly because it was simply easier to tell people where to put
the frets that way.
This part is more against the Jeans quote than the article, though.
BTW, he mentions the idea of 7 plus or minus 2. George Miller's essay
on this idea is awesome:
http://www.well.com/~smalin/miller.html
One thing he mentions, that I think dispels the idea that the 7-tone
scale is inviolable, is that folks can recall longer and longer series
if they form a vocabulary of smaller parts, i.e., become more familiar
with the material. How else could we differentiate 26 letters, or
remember 10-digit phone numbers? Or recognize hundreds of people on
sight? Cross-categorizing- Identifying a fat, bald man in a blue
shirt is far easier than recognizing someone based on any one of those
criteria. A melody is far easier to recognize than a single note.
-Chuckk
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