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.