Math and Music – Harmonious Connections, by Trudi Hammel Garland and Charity Vaughan Kahn, is the clearest introduction to the subject I have come across. It has a rather interesting explanation of the Pythagorean tuning ; also touches upon the concept of self-similarity, which I also refer to as ‘dinergy’ (see article on the subject on my web site: www.elodielauten.net/articles & concepts). This book also offers a chronology of music/mathematics thinkers, from Pythagoras to Ptolemy, Euclid, Boethius, Kepler, Pascal, Gauss, Mersenne, Euler and for the 20th century, Joseph Schillinger who taught both math and music at Columbia University in the 1920s… which brings me to a new book by a similar personality: Serge Donval, who teaches both science at the University of Paris and music at the Conservatoire. His book,
Histoire de l’Acoustique Musicale, (a history of musical acoustics), and I would look forward to its publication in the English language, as it is uniquely comprehensive and concise, as well as widely researched; I was particularly interested in Donval's presentation of Zarlino’s scale (1558), a largely forgotten early temperament system. Donval also uncovers a vast array of multicultural models. I stared for a long time at the ‘
first microtonal scale in history’, a triangular 17-tone matrix conceived in the 13th century. This is an excellent and thorough reference book for anyone interested in microtonality, the history and geography of temperament, and other music-math connections. In
The Math Behind the Music, by Leon Harkleroad, I found some unique information about chance music and probability systems. What I would like to see in a future on math and music is more information about Hans Cousto, Benoit Mandelbrot, and the musical implications of their work. Also what I haven’t yet found is a comprehensive presentation of the relationship between color and sound.
The sound/color equation, at first glance, seems exciting, but even though it has triggered an incredible amount of interest in this over the centuries, no one seems to agree on what color matches what sound. This particular area of exploration intrigued Isaac Newton; then in the 18th century Louis Bertrand Castel started building eccentric ‘color harpsichords’ that would pop a colored card with each note – a wonderful salon gadget, not doubt, for the aristocrats of the Enlightenment period; Castel used a simple correspondence scheme based on the color spectrum; but then Rameau stepped in and introduced the concept of color harmony: for instance, the primary colors, yellow, blue and red would be lined up with a major chord. This complicated matters somewhat in terms of the sound/color correspondence. Later Helmholz looked into the subject, and Alexander Scriabin seems to have been the first to use the color/sound correspondence approach as a compositional device, and from there a new school of thought has emerged: ‘spectral music’ based on the light spectrum correspondence.
At one point, I experimented with a light/sound correspondence for the matrix of an orchestral piece (shown above); the scheme that made the most sense to is the basic mathematical correspondence between Angstrom (light units) and Hertz (frequencies) which places the violet with G, indigo with A, blue with B, green with C, yellow with D, orange with E and F with red. On the other hand, I didn’t really find this correspondence scheme too useful in composition, because it is so limiting, and I used it mostly for determining tonal centers. In a multimedia piece, however this could possibly make sense, provided one goes for a ‘rainbow’ sort of look, with a balance of colors… or one would have to go monochromatic with a single tone held for a long time…
I found some information at
http://www.rhythmiclight.com/, authored by Fred Collopy.
Does math make jack a dull fellow... not necessarily, and we microtonal mathheads are having a fest at of all places the Bowery Poetry Club - it doesn't get much more highbrow than this... Dates are April 29, May 2 and May 9 at 10 PM. I am eagerly awaiting the first performance of my Ecocity for woodwinds and percussion - I keep wondering why I wrote such a piece... no fear of tunings though I am using ear-friendly temperaments 0nly. More infor at:
www.afmm.org.
Composer/keyboardist/producer 
