The bore of a wind instrument is the interior chamber in which air is set into vibration to produce musical sounds. The term is used both for instruments made of wood and instruments made of metal, though of course only in the case of wood instruments is the bore typically produced by boring. A wind instrument is a musical instrument that contains some type of resonator (usually a tube), in which a column of air is set into vibration by the player blowing into (or over) a mouthpiece set at the end of the resonator. ...

There are two musically useful idealized shapes for the bore of a woodwind instrument, conical and cylindrical. While real world instrument bores intentionally deviate from these shapes, generally they closely approximate one or the other. Brass instruments also are categorized as conical or cylindrical, though most in fact have both conical and cylindrical sections. A woodwind instrument is a wind instrument in which sound is produced by blowing through a mouthpiece against an edge or by a vibrating reed, and in which the pitch is varied by opening or closing holes in the body of the instrument. ... A brass instrument is a musical instrument whose tone is produced by vibration of the lips as the player blows into a tubular resonator (mouthpiece). ...

The diameter of a cylindrical bore remains constant with distance from the end of the instrument. 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 normal harmonic is one third that, i.e. the 4/3 length of the cone, so its pitch is an 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. Normal modes in an oscillating system are special solutions where all the parts of the system are oscillating with the same frequency (called normal frequencies or allowed frequencies). ... The fundamental tone often referred to simply as the fundamental, is the lowest frequency in a harmonic series. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... Overblowing is producing a different note in a wind instrument by forcing air harder. ...

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; but most actual instrument bores approximate a frustum of a cone. In either case, 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. A frustum is the portion of a solid â€“ normally a cone or pyramid â€“ which lies between two parallel planes cutting the solid. ...

References

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