Spectral Analysis Techniques for the French Horn

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

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

4. Reflection from bell causes standing waves that reinforce player’s lip vibration 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” Adapted from figures courtesy of University of New South Wales

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

6. Measuring particle velocity (U) and pressure (P) P and U microphones read by HP3562A Spectrum Analyzer Horn driven by piezoelectric driver, sweeping sine voltage Piezoelectric driver Particle Velocity (dP integrated in t) Pressure 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

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

8. Data shows non-uniform trend NO transposition ~half step transposition Frequency Shift (cents) Harmonic # 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.

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