TRUMPET TRANSIENTS: Theoretical Aspects of Trumpet Design © Part 3 of 21

“Parts of this discussion are based upon information regarding acoustic transients, presented in The Physics of Musical Instruments, by Fletcher & Rossing (1998).

Luce and Clark (1967) measured transient properties of brass instruments and found that partials (harmonics other than the fundamental) below cutoff frequency built up together and reached their steady-state values nearly simultaneously.  Partials with frequencies above cutoff built up in amplitude more slowly and reached their steady states at times that were longer the higher their frequencies lay above cutoff.

Risset and Mathews (1969) reached a similar conclusion both by analysis of instrument sounds and by subsequent synthesis of subjectively matched sounds using a computer.  However, they found that for a short trumpet note, the first three harmonics reached their maximum values after only about 20 ms (milliseconds) while harmonics above the fifth took from 40 to 60 ms, with higher harmonics being longer delayed.

The Risset & Mathews finding that the first 3 harmonics reached maximum value in about 20 ms is corroborated considering 3 round-trips at about 6.7 ms per round-trip.  Their finding that the first 6 harmonics reached maximum value in about 40 ms is also corroborated considering 6 round-trips at about 6.7 ms per round-trip.  Reaching maximum value in 60 ms suggests 9 harmonics, and 9 round trips at about 6.7 ms per round-trip.

From the above, notes containing the first 3 harmonics reach maximum value in 3 round-trips.  Notes containing the first 6 harmonics reach maximum value in 6 round-trips.  And, notes containing the first 9 harmonics reach maximum value in 9 round-trips.  Thus, the number of harmonics present requires an equal number of round-trips for those harmonics to become evident.  Cutoff frequency is not relevant in such a process.”