Saxophone Acoustics: Harmonic Partials, Pitch Bending, and Multiphonics

Every Harvard undergraduate has a set of courses he or she is required to take to graduate, which are called General Education courses; it's pretty much like distribution requirements, which you find at most 4-year colleges. I elected to take a course this semester called "Why You Hear What You Hear: The Science of Sound and Music" to fulfill a requirement called "Science of the Physical Universe." The course is taught by Eric J. Heller, a professor of chemistry and physics who's best known for his work in quantum mechanics and quantum chaos but has also been interested in the science of sound (he's an amateur trumpet player and also creates digital art on the side). 

The most recent material we've covered in class has been about wind instruments and the voice, and I was asked to demonstrate several sonic properties of the saxophone in class this past Monday. The results were analyzed briefly by Professor Heller, and I thought I'd share the lecture slides here.

The picture to the left is a sonogram that shows the predominant frequencies of overtones (overblown partials) of the lowest note of the tenor saxophone (concert Ab). The picture to the left shows the original Ab with its collection of evenly spaced partials based on a fundamental frequency of 100 Hz. Interestingly, although you hear 100 Hz as the fundamental frequency, the sonogram shows that this partial isn't supported all that strongly (the bottom horizontal band). The picture to the left shows how the lower harmonics are suppressed when you play in the altissimo register of the saxophone, which is comprised largely of upper partials.

To the left: a sonogram visualization of the bending of a pitch. 

The last slide illustrates the harmonic make-up of a multiphonic I lifted from John Coltrane***; it's the second-to-last last note of "I'll Wait and Pray" from Coltrane Jazz (1961). The ending of that tune is especially remarkable because Trane slides from another multiphonic one  half-step above down to the final resting diad. 

In his textbook, Heller distinguishes between "true multiphonics," which are combinations of frequencies belonging to different harmonic series, and "pseudo-multiphonics," which are frequencies belonging to a single harmonic series (having the same fundamental
frequency). Based on the frequency ratios between the two predominant pitches in this particular multiphonic, this example from Trane would fall under the category of true multiphonic. I suppose an example of a pseudo-multiphonic on saxophone would be splitting the overtones of a low note, e.g., playing low Bb and splitting the overtone sound between the fundamental and the F an octave and a half above.

***For tenor players, a fingering that work for me to get this multiphonic is B, bis Bb, and the high E side key.