lurker revealed

Another lurker's confession:

I studied physics in college. Somehow I got turned on to the musical
connection when the wave equation and normal modes of oscillation came up. I
dragged my Jr. High guitar out from under the bed & played with harmonics &
tuning for the next few years. I started using the frets after a while. Never
have got any good at playing any sort of music, but I still keep the guitar
next to my chair & play around often enough, mostly just pentatonic
meandering.

In college I posed myself the problem, is there a better equal-step scale
than the common one based on 2**(1/2)? I wrote a program to evaluate a
"quality of scale" function for various step sizes, the function being a sum
over overtones of how close the scale hits the overtone. I printed asterisks
next to the local minima. When lots of lines got flagged, I zoomed in - and
still lots of asterisks! Then I saw the same function in a math book as an
example of a continuous function nowhere differentiable. Huh, never knew
about that before. Kept on tuning that guitar, amazing what structure can
unfold from just a couple of strings.

Started getting into rational approximations to irrational numbers in
grad school, triggered somewhat by the Fibonacci patterns in sunflowers. At one
point I remember surprising a Jewish friend by asking about 19 year cycles in
the lunar calendar. Irrational numbers are everywhere! Also started looking at
close calls in large products of small integers as a way to generate
scales. Became a fan of 10**(1/90) as a generating interval. On guitar played
a bit with scales built on the same old 2**(1/12), only so much one can do
with frets, but with periods based not on the octave but the fifth, fourth,
etc.

What kind of instrument might be useful for playing 10**(1/90) music? How
about a surface covered with hexagonal keys? Hey, the same thing could be
used for other scales, too, good old 2**(1/12) or even just tuning!!

C D E F# G# A# C D E
A B C# D# F G A B C# D#
G# A# C D E F# G# A# C
F G A B C# D# F G A B
E F# G# A# C D E F# G#
C# D# F G A B C# D# F G
C D E F# G# A# C D E
A B C# D# F G A B C# D#
G# A# C D E F# G# A# C
F G A B C# D# F G A B
E F# G# A# C D E F# G#
C# D# F G A B C# D# F G

I enjoy this newsgroup because even though I've only been subscribed a couple
of weeks, people have gone far beyond any of my ideas in all directions!
Anyway I put up this key pattern just for everyone's amusement. Probably all
old hat as well, but my just tuning version is based on a pattern with three
keys to a unit cell, the various cells run through all (2**n)(3**m), while
the keys in the unit cell are related by, well, maybe 4/5, 1, 5/4, or??? I
imagine a control panel sort of like organ stops, where one can reset the
relationship between the keys in each cell, so one could even walk the
progression 5/4, 25/16, etc.

Next problem, how to notate. Of course I have zip music training, I moved out
of the school district in 8th grade just as they were about to catch me
singing the melody line in chorus instead of whatever the sheet music
said. Anyway I took a couple of Bach's harmonized chorals and used the colors
of the spectrum to denote which just-tuned note I might want to play, the
choices being in a series of 81/80 intervals. Well, I couldn't really finish
the exercise, but I got some really cool looking scores, and the exercise
seemed to reveal some interesting structure in the music, a gradual
accumulation of tension and then resolution: I didn't seem too far off track
at least.

I was completely amazed to see similar geometric patterns of fractions in
Ernest McClain's books THE MYTH OF INVARIANCE etc. I also read one of Alain
Danielou's books, not (yet) the one recently published by Inner Traditions
- MUSIC AND THE POWER OF SOUND - but something about musicianship in the
Orient, I forget the title. I also ran across a very similar analysis of the
misfit of just tuning in 19th century Western music in THE STRUCTURE OF
RECOGNIZABLE DIATONIC TUNINGS.

My more recent playing around with continued fractions has enamored me of the
2**(1/53) scale. I am hoping to use simulated annealing algorithms to
generate some reasonably structured random "melodies" in this and other
scales. One musical friend doubts that rational intervals really sound
better. For him I want to generate melodies in the scale generated by the
cube root of the golden ratio, which ought to sound "perfectly horrible".

I listen to all sorts of music - Captain Beefheart, Johnny Dyani, Paul
Hindemith. Sometimes Harry Partch, Ben Johnston, Joe Maneri, or Music of Iran
on Lyrichord.

Not long ago I spent some time training in a Tibetan Buddhist tradition &
learned some basics of liturgical music: drum, cymbals, gyaling (a shawm),
and ratung (a long straight horn). A very different style of music!

I've gone on way too long! Thanks for continuing to open music up, the
possibilities seem inconceivably vast!

(These days I'm a computer programmer, developing tools for digital circuit
designers.)

Jim Kukula

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