Saxotromba - Acoustic Principles

Acoustic Principles

The saxotromba was a half-tube brasswind instrument. It was constructed in such a way that the column of air inside the instrument was capable of vibrating at a number of different pitches that corresponded to the notes of the harmonic series. These pitches are known as the instrument's natural or normal modes of vibration, each one being a natural harmonic or open note. By vibrating his lips at the correct frequency, the player is able to compel the instrument's air column to vibrate at the correct pitch; by lipping, he can correct the minor intonational defects that inevitably arise on account of the discrepancies between the natural harmonic series and the tempered scales of classical music.

Like the modern valve trumpet and cornet, the saxotromba employed harmonics two through eight. Being a half-tube instrument, the fundamental or first harmonic was not available on the saxotromba. Harmonics higher than the eighth were certainly feasible, but it is unlikely that military musicians would ever have been required to venture above the eighth harmonic. The seventh harmonic was too much out of tune to be lipped; this partial was generally avoided by trumpeters and cornet players after the introduction of valves.

In order to provide a saxotromba with a chromatic compass from the second harmonic upwards, it is essential to provide the player with some means of lowering the pitch of the third harmonic by as many as six semitones, this being the size of the gap between the second and third harmonics. Three independent valves will reduce the pitch of a natural or open harmonic by two, one and three semitones respectively. Used singly or in combination, these can bridge the gap between the second and third harmonics, though the player will be required to correct by lipping the faulty intonation produced when independent valves are used in combination. The gaps between the higher harmonics are smaller still, so no more than three valves are required to provide a saxotromba with a full chromatic compass; this is true even if the seventh harmonic is not used.

Furthermore, by using all three valves in combination while overblowing the second harmonic, the player can extend the lower end of the instrument's compass downwards by six semitones to a note three whole tones below the second harmonic:

Presumably the fourth valve, where present, would have lowered the pitch of an open note by a perfect fourth, or five semitones, removing the need to use certain faulty combinations of the first three valves. In the early nineteenth century, when four valves were applied to a half-tube instrument they generally lowered the pitch of a natural harmonic by two, one, three and five semitones respectively. Berlioz notes that in the case of "an instrument with four cylinders, the chromatic compass of the low part of this instrument no longer stops at the F# but goes down to the first C ". He notes, however, that the "first low note of the tube's resonance ... is too bad to be employed". This would seem to imply that the fourth valve of the saxotromba did indeed lower the pitch of a given harmonic by 5 semitones, so that all four valves in combination would lower an open note by a major seventh. It is doubtful, however, whether four independent valves were ever used in combination to produce such low notes.

The fifth valve, where present, probably lowered the pitch of an open harmonic by 6 semitones. Later models of saxotromba were provided with six independent valves, lowering the pitch of an open harmonic by one through six semitones, thus removing completely the need to use any valves in combination.