The
cone and the
cylinder are the two idealized shapes used to describe the bores of
wind instruments. Other shapes are not generally used, as they tend to produce
dissonant,
anharmonic overtones and an unmusical sound. Instruments may consist of a primarily conical or cylindrical tube, but begin in a mouthpiece, and end in a rapidly-expanding "flare" or "
bell". This flare reduces the
acoustic impedance mismatch between the instrument and the air, allowing the instrument to transmit sound to the air more effectively. These shapes affect the prominence of
harmonics associated with the timbre of the instrument. A bore that flares from the mouthpiece reduces
resistance to the breath, while a bore that narrows from the mouth increases it, compared to a cylinder.
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. Modern brass instruments however generally make use of the full length of the instrument for every pitch, and are therefore significantly affected by the effects of the mouthpiece and
bell. These modify the instrument's resonances to closely resemble that of a conical pipe, even if the bore is mostly cylindrical. Instruments having a cylindrical, or mostly cylindrical, bore include: •
Chalumeau •
Clarinet •
Cornamuse •
Crumhorn •
Flute (
Boehm system — open) •
Recorder (renaissance and some modern recorders) •
Kortholt •
Rackett (renaissance) •
Trumpet •
Trombone 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 approximately equal to 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: •
Alphorn •
Bassoon •
Conch shell •
Cornet •
Dulcian •
Euphonium •
Flugelhorn •
Flute (pre-Boehm) •
French Horn •
Recorder (baroque and most contemporary recorders) •
Oboe •
Rackett (baroque) •
Rauschpfeife •
Saxhorn •
Saxophone •
Shawm •
Trembita •
Tuba •
Uilleann pipes == Woodwinds ==