conical bore

Bore (wind instruments)

The bore of a wind instrument is its interior chamber that defines a flow path through which air travels and is set into vibration to produce sounds. The term is used both for instruments made of wood and instruments made of metal, though only in the case of wood instruments is the bore typically produced by boring. The shape of the bore has a strong influence on the instruments' timbre.

Bore shapes

The cone and the cylinder represent two musically useful idealized shapes for the bore of a wind instrument. As discussed below, these shapes affect the harmonics associated with the timbre of the instrument. For example, the conical bore is associated with a timbre that corresponds to a generally triangular waveform, which is rich in both even and odd order harmonics. The cylindrical bore is corresponds to a generally square waveform, which is rich on odd harmonics.

Cylindrical bore

The diameter of a cylindrical bore remains constant along its length. The acoustic behavior depends on whether the instrument is stopped (closed at one end and open at the other), or open (at both ends). For an open pipe, the wavelength produced by the first normal mode (the fundamental note) is approximately twice the length of the pipe. The wavelength produced by the second normal mode is half that, that is, the length of the pipe, so its pitch is an octave higher; thus an open cylindrical bore instrument overblows at the octave. This corresponds to the second harmonic, and generally the harmonic spectrum of an open cylindrical bore instrument is strong in both even and odd harmonics. For a stopped pipe, the wavelength produced by the first normal mode is approximately four times the length of the pipe. The wavelength produced by the second normal mode is one third that, i.e. the 4/3 length of the pipe, so its pitch is a twelfth higher; a stopped cylindrical bore instrument overblows at the twelfth. This corresponds to the third harmonic; generally the harmonic spectrum of a stopped cylindrical bore instrument, particularly in its bottom register, is strong in the odd harmonics only.

Instruments having a cylindrical, or mostly cylindrical, bore include:

Conical bore

The diameter of a conical bore varies linearly with distance from the end of the instrument. A complete conical bore would begin at zero diameter—the cone's vertex. However, actual instrument bores approximate a frustum of a cone. The wavelength produced by the first normal mode is approximately twice the length of the cone measured from the vertex. The wavelength produced by the second normal mode is half that, that is, the length of the cone, so its pitch is an octave higher. Therefore, a conical bore instrument, like one with an open cylindrical bore, overblows at the octave and generally has a harmonic spectrum strong in both even and odd harmonics.

Instruments having a conical, or approximately conical, bore include:

Woodwinds

Bores of real-world woodwind instruments overall may approximate a cone or a cylinder. However, portions of the bores may deviate from these idealized shapes. For example, though oboes and oboes d'amore are similarly pitched, they have differently shaped terminal bells. Accordingly, the voice of the oboe is described as "piercing" as compared to the more "full" voice of the oboe d'amore.

Although the bore shape of woodwind instruments generally determines their timbre, the instruments' exterior geometry typically has little effect on their voice. In addition, the exterior shape of woodwind instruments may not overtly match the shape of their bores. For example, while oboes and clarinets may outwardly appear similar, oboes have a conical bore while clarinets have a cylindrical bore.

Brasses

Brass instruments also are sometimes categorized as conical or cylindrical, though most in fact have cylindrical sections between a conical section (the mouthpiece taper) and a non-conical, non-cylindrical flaring section (the bell). Benade gives the following typical proportions:

Trumpet Trombone Horn
Mouthpiece taper 21% 9% 11%
Cylindrical part 29% 52% 61%
Bell 50% 39% 28%

To complicate matters these proportions vary as valves or slides are operated; the above numbers are for instruments with the valves open or the slide fully in. Therefore the normal mode frequencies of brass instruments do not correspond to integer multiples of the first mode. However, players of brasses (in contrast to woodwinds) are able to "lip" notes up or down substantially, and to make use of certain privileged frequencies in addition to those of the normal modes, to obtain in-tune notes.

See also

Notes

References

  • Nederveen, Cornelis Johannes, Acoustical aspects of woodwind instruments. Amsterdam, Frits Knuf, 1969.

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