source file: mills2.txt Date: Tue, 26 Nov 1996 20:21:59 -0800 Subject: lurker revealed From: James Kukula 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 Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 27 Nov 1996 11:03 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09047; Wed, 27 Nov 1996 11:05:22 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA09540 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id CAA15795; Wed, 27 Nov 1996 02:05:20 -0800 Date: Wed, 27 Nov 1996 02:05:20 -0800 Message-Id: <199611271101.LAA30846@teaser.teaser.fr> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu