March 11, 2008

Mother, Superior

Today's episode marks the 500th post here on Soho the Dog.

Last spring I had occasion to mention the 1970 book The Computer and Music, edited by Harry B. Lincoln. Here's another excerpt from the book that grabbed my eye:
Another composition of a much different sort was produced in 1964 by Mother Harriet Padberg of Maryville College of the Sacred Heart outside St. Louis....

Her compositional method is based on the idea of first subdividing the octave into twenty-four steps. These are not tones in equal temperament, however, but rather the 24th to 47th harmonic partials of a fundamental of 18.333 cps. It follows, therefore, that the 24th partial is 440 cps. The 48th partial is, of course, the octave of this, and the steps within the octave are separated by equal numbers of cycles per second.... Second, Mother Padberg associated a letter of the alphabet with each note of this scale, doubling up V and W and associating Y with either I or Z. Third, she defined a tone row by means of any 12-letter meaningful phrase and further defined ways of developing rhythms from ratios of consonants to vowels. With the addition of further rows for dynamics and voicing or orchestration, she was then ready to write computer programs for generating compositions based on these schemes. Mother Padberg first wrote a computer program in FORTRAN for an IBM-1620 computer to enable her to write a canon for two or four voices. Later, however, she was able to expand and generalize this idea by writing a more generalized program for an IBM-7072 computer. This latter program permitted her to generate canons in two or four voices based on one to three tone rows with the further option of producing a "free fugue." The construction of this "free fugue" was based on the idea that a tone row and its transformation constitute a "group" to which transformations of group theory are applicable.

—Lejaren Hiller, "Music Composed with Computers—
A Historical Survey," in The Computer and Music,
Harry B. Lincoln, ed. (Cornell University Press, 1970)

Sister Padberg's "Canon and Free Fugue" sounds like one of the coolest pieces of all time. Hiller gets most of the basics right, although the tone rows can range anywhere from 5 to 12 notes in length—the computer separates the input into blocks based on word breaks, which are then converted into rows. The use of text as the generating material isn't just for ease of input, in other words; the linguistic structure becomes a main factor in the musical results. The rhythmic patterns are fairly intricate, based on prime number relationships derived not only from the consonant-to-vowel ratio, but also the comparative lengths of the resulting word blocks. You can get all the details in Sister Padberg's dissertation, available through ProQuest.

It's fun how many contemporary musical threads the "Canon and Free Fugue" seems to echo, however distantly. The use of language as not just an inspiration, but a guiding factor in the actual compositional building blocks of the music, relates to a similar current in other avant-garde music of the 1960s, from the serious investigation of the inherently musical qualities of phonemes in Luciano Berio's Circles or Sinfonia, to the playful embedding of Bach's name—via Morse code—within Lukas Foss's Baroque Variations. The program's ability to turn any phrase of suitable size into music also gives it a kinship with aleatoric developments. And the intricacy and ingenuity of the scheme points towards the fascination with process that would lead to early Minimalism. But even on its own, the "Canon and Free Fugue" intrigues, the way the step-by-step transformation of written language into a musical result parallels the computer's translation of programming language into purposeful electronic activity.

Sister Padberg taught mathematics and music at Maryville University for 24 years, starting their music therapy program in 1973. Though retired from teaching, she continues to volunteer as a music therapist (and pick up awards now and then). She relates via e-mail that the only realization of the piece was fairly "primitive"; for her thesis defense, she played examples that were synthesized from punch cards that she sent to Bell Telephone Labs. Her dissertation contains the complete FORTRAN code for each program, as well as sample data outputs, if anyone with more computer savvy than me is interested in attempting a full realization. If you'd like to play around with the 24-tone scale, the frequencies are reproduced below (click to enlarge):

For an idea of how technologically spoiled we are when it comes to electronic music, Sister Padberg writes:
It is interesting that a few weeks ago an "alum" of those days was reminiscing about how the students had helped me get some idea of the "sound" by filling Coke bottles with the correct amount of water and blowing into them!!! How times have changed!!
That image of a bunch of college students pouring water in and out of Coke bottles until they whistle at the proper frequencies is irresistible—the low-tech, hands-on, trial-and-error origin of the digital sound world we live in now.



You wrote, "But even on its own, the 'Canon and Free Fugue' intrigues, the way the step-by-step transformation of written language into a musical result parallels the computer's translation of programming language into purposeful electronic activity."

It's an interesting connection, but don't these parallels run in opposite directions? The programming language is constructed based on what the computer can do. Padberg uses patterns of English spelling (not inherently meaningful) to construct musical sounds. It's logical that the programming language would be useful and meaningful for its purpose. It doesn't follow that the words Padberg chooses would produce interesting music. Maybe if she got a thousand monkeys on a thousand typewriters to input the words we'd get "The Musical Offering."

Mark said...


I teach at Maryville and never knew this at all nor have I ever met Sister Mary.

Of course, I'm still a part-timer of course, but it's certainly going to lead me to do a bit of investigation.

Lisa Hirsch said...

(Just catching up with this particular posting, which I read initially when it was published...)

Holy moly!

I'd love to know who her contact was at Bell Labs!

Ariza said...

I wanted to let you know that my article, featuring a comprehensive investigation into Sister Padberg's work, is now available:

Many thanks for your assistance in helping to get in touch with her!