Physical Correlates of Brass-Instrument Tones
David A. Luce, Melville Clark · The Journal of the Acoustical Society of America · 1967
Time-dependent Fourier analyses of the attack transients and steady states of about 900 trumpet, trombone, tuba, and French-horn tones yielded the amplitudes and relative phases of the first 11 partials. Relative component amplitudes for all tones of an instrument played at a given dynamic marking are approximately described by a spectral envelope. The partials are conveniently divided into those below a cutoff frequency (Class 1 components) common to all notes of the instrument and those above it (Class 2). Class 1 components have similar attack envelopes and reach approximately equal steady-state values before those in Class 2. The transient periods for Class 2 components increase with frequency of the components, and their steady-state values decrease rapidly with increasing frequency of the components. Amplitude modulations (blips) that last for one or only a few cycles of the modulation occur for all components during the end of the transient, but are larger for Class 2 components. For brasses other than the French horn, spectral envelopes are approximately frequency-scaled versions of each other. Rolloff rates above the cutoff frequency decrease as the average amplitude of a scale of notes increases, and it appears that an increase in radiated power is achieved primarily by an increase in the amplitudes of high-frequency partials. Average rolloff rates in decibels per octave for scales played at an average sound pressure level of 68 dB were: trumpet, 15; trombone, 20; tuba, 17; unstopped horn, 16; stopped horn, 30.