1. Spectral Analysis Techniques for the French Horn The “hand-stopping” transposition controversy Adam Watts Professor Steve Errede UIUC Dept. of Physics 2009

2. Apparent contradiction in “stopped” horn transposition Normal playing position Hand “stopped” muting position Some claim transposing up works as well. How can it be both? Transpose: change the key of notes played, i.e., raise or lower pitch, preserving intervals between notes Closing hand lowers pitch (note frequency), but horn players taught to transpose DOWN while stopped

3. Goal: Using real horn- playing technique, measure what happens to notes during stopping Previous (lock-in) technique takes ~ 6 hours, too long to use real horn player’s hand Not approx. horn technique: I used fake hand, Backus used rubber stopper Previous experiment using simulation hand Previous work could only use simulation of hand technique

4. Reflection from bell causes standing waves that reinforce player’s lip vibration Adapted from figures courtesy of University of New South Wales Playable notes on the horn are frequencies at which standing waves occur between bell and mouthpiece These frequencies are called “partials” by players, i.e., places where the instrument “locks in”

5. Acoustic Impedance analogous to Electrical Impedance Impedance mismatch means wave reflection, standing waves reinforce player’s lips Complex Electrical Impedance Complex Acoustic Impedance Z of free space constant, therefore, horn |Z in | (input impedance magnitude) maxima correspond to standing waves, i.e., playable notes! Trumpet fig. courtesy Dave Pignotti i.e., (pressure) (particle velocity)

6. Pressure Piezoelectric driver Horn driven by piezoelectric driver, sweeping sine voltage P and U microphones read by HP3562A Spectrum Analyzer Spectrum Analyzer calculates P and U in frequency domain (using FFT) for one valve combination of horn (all valves up) Broadband device means lower settling time compared to previous (lock- in) method, ~5 minutes per measurement without averaging Measuring particle velocity (U) and pressure (P) Particle Velocity (dP integrated in t)

7. Stopping technique “splits” notes in mid-range Draft noise Evidently, players use next partial up while stopping, transpose down. But transposing up from the lower partial works too. Peak freq drops

8. Data shows non-uniform trend So both up/down transposition works in the middle range, but barely any adjustment is needed in upper range. Most horn players apparently play the next partial up from desired note, then transpose down. ~half step transposition NO transposition Frequency Shift (cents) Harmonic #

9. Summary French Horn has spectrum of playable notes (“partials”) for each valve combo “Stopped muting” changes pitch of partials, player transposes using valves to compensate, apparent contradiction in how to do so Acoustic impedance max at frequencies where wave reflection off bell occurs, i.e., playable partials Impedance spectrum data shows that partials are “split” during stopped muting, but effect is not uniform over note range as previously assumed Image source: www.bnl.gov, credit: Tom Harvey

10. Acknowledgments Thank you to Prof. Errede, Toni Pitts, Lance Cooper, Celia Elliot, and the NSF. This work was supported by National Science Foundation Grant PHY-0647885