Bore Profile and Tube Termination in Wind Instruments

How two independent variables — bore shape and end condition — determine which harmonics a wind instrument can produce.

The acoustic behavior of a wind instrument is governed by two independent variables: bore profile (cylindrical vs conical) and tube termination (whether each end is open or closed). These are separate axes. Changing one does not imply anything about the other, and the combination of both determines which harmonics the instrument can produce.

Tube Termination

A tube open at both ends supports a complete harmonic series — resonances at every integer multiple of the fundamental frequency. A tube with one closed end and one open end supports only odd harmonics, with the fundamental an octave lower than the equivalent open tube of the same length.

The flute is the only common wind instrument that is both cylindrical and open at both ends. The embouchure hole acts as an open end acoustically; the far end is open. The result is a complete harmonic series with a well-supported fundamental.

This can be confirmed directly by experiment. Capping the far end of a flute converts it to a closed cylinder: the fundamental drops an octave and only odd harmonics sound — exactly what the model predicts.

The clarinet is the other cylindrical case. The reed acts as a closed end, and together with the cylindrical bore this produces a tube that supports only odd harmonics. The instrument overblows at a twelfth rather than an octave. This is covered in Harmonic Series With Wind Instruments.

Bore Profile

Bore profile introduces a separate variable. In a conical bore, the geometry of the tube produces wave equation solutions that support all integer harmonics. A conical instrument with a closed reed end produces a full harmonic series — the combination of conical bore and closed end yields the same resonance series as an open-open cylinder.

This is why the oboe and the saxophone — both conical, both with a closed reed end — overblow at the octave rather than the twelfth. It is also why the saxophone overblows at the octave despite being mechanically similar to the clarinet in its use of a single reed. The difference is entirely in the bore profile.

Brass Instruments and Hybrid Bores

Brass instruments fall between purely cylindrical and purely conical. Where they fall on that continuum has direct consequences for the pedal tone.

The flugelhorn is predominantly conical. Its resonances, including the fundamental, align well. The pedal tone is strong and in tune.

The trumpet is a hybrid: substantial cylindrical tubing through the main bore, combined with a conical mouthpiece and a flared bell. The bore is specifically designed to bring the upper partials into alignment, and it succeeds at this. But the cylindrical sections pull the fundamental flat relative to that aligned series. The trumpet's pedal tone is not merely difficult to produce — it is genuinely flat, displaced from where a complete harmonic series would place it.

This represents a tradeoff rather than a flaw. The same cylindrical bore geometry that displaces the pedal tone also extends the upper register, making the extreme high range more accessible than on a predominantly conical instrument. The flugelhorn does not share this characteristic.

Summary