Steve Wilkinson Responds to Questions

How do you feel math has infuenced your playing style? Do you approach it more methodically, or more as a free flow of feeling?
Math doesn’t influence my playing style at any conscious level. I approach playing more as a free flow of feeling.
Have you ever considered teaching a gen. ed course on math and music?
I taught an honors section of MAT 115 (a gen ed course) on math and music twice. However, it’s tough to devote an entire course to math and music when you can’t impose prerequisites that would make it easier to discuss more topics. For instance, it is limiting to discuss math and music if you cannot assume students have some knowledge of trigonometry. I find it easier to just incorporate certain topics in math and music from time to time in regular general education math classes.
I'd love to know how the frets on the guitar being separated logarithmically helps make the best sound. Why aren't they separated some otherway?
Frets on a guitar are separated not so much logarithmically as exponentially. The pitches one gets on a guitar are the same pitch one gets on a piano or even-tempered tuning. Since the frequency at one note must be doubled to get what we hear as an octave, and western music divides one octave into 12 half-steps, to go from one note up one half step, multiply the original frequency by 2^(1/12). That means if you start with frequency f, then a twelve-step chromatic scale up from f would be 2^(0/12)f, 2^(1/12)f, 2^(2/12)f, 2^(3/12)f, 2^(4/12)f, 2^(5/12)f, 2^(6/12)f, 2^(7/12)f, 2^(8/12)f, 2^(9/12)f, 2^(10/12)f, 2^(11/12)f, 2^(12/12)f = 2f.
Was it hard to learn to correlate different notes to their frequencies?
When I play, I don’t think in terms of frequencies. I think in terms of half-steps. The one exception to that is when I tune my instrument to others. In that case I’m adjusting the lengths of the tubing of my trumpet to better match the frequencies of others. There are some interesting techniques like “beats” one can use to help in these adjustments. The idea of beats is an interesting topic in differential equations.
Regarding octaves and the relationship one octave has to another (halving or doubling): Is that a pattern that was discovered first and then the math behind it was understood later, or was it a mathematical relationship that was understood first and then later the halving or doubling relationship was applied to music?
No one knows for sure why octaves are so basic, but it is assumed that it comes from the fact that adult male human voices tend to be an octave lower than female human voices. Although the mathematical nature of octaves was probably noticed by others, the first historical record for this fact that I am aware of was from ancient Greece’s Pythagoras (500 B.C.)
Is it easier to make money as a mathemusician or as a musician? [I think that this one may be tongue-in-cheek...:) ael]
Speaking from experience, I’ve made much more money doing mathematics that includes some music over doing only music. In fact, I’m pretty sure I’m running a deficit on the music.
What is your favorite song?
My favorite tune depends on what kind of mood I’m in, what I’m currently thinking about, and lots of other variables. I will say that flamenco music is my favorite genre, and the instrument I enjoy HEARING the most is guitar. (Okay, if you twist my arm, I might say my favorite tune is “Volaré” especially as performed by The Gypsy Kings. Wait, no, my favorite song is Samuel Barber’s “Adagio for Strings.” On the other hand, maybe my favorite is …)
Have you ever made a full composition using tools like Mathematica?
It depends on what you mean by a full composition. I have used Mathematica for music composition in two ways.
a. Entering the melody line of an existing tune, from it generating the probabilities of which notes follow which notes, then generating a new melody based on those probabilities and random number generators.

b. Entering four parts from an existing tune and using musical compositional techniques like transpositions (translations) and an inversions (reflections) to create new music.
Can you swing dance?
I play in the band so I don’t have to dance. In other words, I can’t swing dance.
What research on Math within Music have you read that is interesting?
The Math Behind the Music by Leon Harkleroad is probably the most interesting book I have read on math and music. I wouldn’t call it research, but more an overview of some areas of commonality between the two disciplines. In terms of research:
a. Professor Long and I met Maria Mannone about a year ago. She has advanced degrees in both physics and music, and her interests include how math and music mix. She has written some books: Cool Math for Hot Music and The Topos of Music III: Gestures - Musical Multiverse Ontologies. I haven’t yet read these books, but I’ve heard her talk on these subjects.

b. There is a CS professor at Transylvania University, Robert England, who has done some interesting things with computer generated music. I followed him several years ago, but not recently. I don’t know if he is still working this line of research or not.

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