Spectral Analysis Techniques for the French HornThe “hand-stopping” transposition controversy

Adam WattsProfessor Steve Errede

UIUC Dept. of Physics 2009

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

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

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”

Acoustic Impedance analogous to Electrical Impedance

Impedance mismatch means wave reflection, standing waves reinforce player’s lips

Complex Electrical

Impedance

ComplexAcoustic

Impedance

Z of free space constant, therefore, horn |Zin| (input impedance magnitude) maxima correspond to standing waves, i.e., playable notes!

Trumpet fig. courtesy Dave Pignottii.e.,(pressure)

(particle velocity)

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)

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

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 thenext partial up from desired note, then transpose down.

~half step transposition

NO transposition

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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

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