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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 Instrument s also are categorized as conical or cylindrical, though most in fact have both conical and cylindrical sections. 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. 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. REFERENCES
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