Trombone Directivity

Document Type

Musical Instrument Directivity

Publication Date



The directivity function of a played musical instrument defines the angular dependence of its acoustic radiation, as well as diffraction about the instrument, the musician, and the musician's chair. It is an essential aspect of sound production that affects sound throughout a rehearsal or performance space and detected signals in audio systems. Because high-resolution, spherically comprehensive measurements of played musical instruments have been unavailable in the past, the authors have undertaken research to produce and share such data for studies of musical instruments, simulations of acoustical environments, optimizations of microphone placements, and other applications. The presented data were acquired from a single instrument repeating chromatic scales at mezzo-forte in an anechoic chamber. The musician was seated on a subject-rotation system with his or her instrument in a normal playing position. The chair height and horizontal displacement were adjusted so that the geometric center of the radiating portion of the instrument fell at the circular center of a 1.8 m-radius, semi-circular array of 37 microphones. The microphones were spaced with 5-degree polar-angle increments. Azimuthal rotations also progressed in 5-degree increments, meaning the data were acquired at 2,522 unique positions over a sphere. They were likewise acquired at three positions within the rotating reference frame for subsequent signal processing. Several steps were taken to mitigate issues associated with variations in repeated scales. Transfer functions between reference and array microphones and other calculations were employed to derive the directivities from the measurements. The results are available under Additional Files and may be updated periodically.


While higher resolutions could be derived from the raw measurement data, those currently available are presented in third-octave bands and based on degree-10 spherical-harmonic expansions. Coefficients were derived using a least-squares method. The CSV file provides results in a generic format, organized by third-octave bands. Columns represent the 37 polar sampling angles, while rows represent the 72 azimuthal sampling angles, all with 5-degree increments. The GLL file may be opened using the AFMG EASE GLL Viewer, currently available at The MP4 file is an animation of the directivity balloons rotating 360 degrees for each third-octave band. These data should be useful for many applications and are presented here for general usage. The authors request that the work be cited as suggested under Recommended Citation.

Trombone.gll (307 kB)
Trombone.csv (278 kB)
Trombone.mp4 (92476 kB)

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