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Physics at Hamilton |
Brass instruments (which may be made of a several different metals and may be any color) are driven by a double reed formed by the lips of the player. This is the most flexible of all reeds becuase the extensive mulsculature of the players lips allow for wide variations in the tension and Q of the lips during normal playing. The lips normally operate in an intermediate Q region where the pitch of the instrument is primarily set by the length of the resonator but the player can both select which normal mode will sound and can alter the pitch up to about 1 semitone around the tube resonance. Thus the pitch is determined by a co-operation between the lips and the tube.
Brass instruments fall into two families, those with a generally cylindrical bore and those with a basically conical bore. In both cases, the actual bore shape varies along the length of the tube in ways that have been found historically to give the best performance. Trumpets, trombones, and french horns use basically cylindrical tubes with flaring bells and, in the trumpets and french horn, a short conical leader tube. Cornets, flugle horns, alto horns, baritones, euphonia, and tubas use tubes that have significant conical sections.
Brass instruments use a small, cup-shaped (a long conical cup for the french horn) mouthpieces. The cup serves as a support for the lips and. along with the narrow exit hole, create a mildly resonant chamber that significantly enhances the tuning of the instrument.
A basically cylindrical length of tube with a lip-reed at one end should act like a tube closed at one and an have a set of normal modes missing the even harmonics. The combined effects of the bell, mouthpiece and leader pipe alter the frequencies of the partials, rasing the lower ones and lowering the upper ones to make the final modes, apart from the very lowest, form a harmonic series. The lowest mode still lies well below the apparent fundamental of the new series and the instruments are played on harmonics 2 and above. The Fundamental, called a pedal tone, is very hard to play and very hard to make even close to in tune.
Apart from the trombone, which uses a very simple slide mechanism to alter the physical length of the tubing, most brass instruments use a series of valves to insert and remove short sections of tubing into the air path. This alters the acoustic length of the tubing and allows the instrument to play all the notes between the harmonics. Because the lowest note is harmonic #2, the next lowest basic note is harmonic #3, a fifth above. Thus the valve system needs to span only 7 semitones. It does this with three valves that lower the pitch by 1, 2, and 3 semitones so that, by combining valves, you can lower harmonic #3 by as many as 6 semitones, filling in the gap between it and harmonic #2, 7 semitones below. The tube lengths for the different valves cannot be correct both for single valves and for combinations of valves. Thus the player must use his lip to bring the other notes into tune. Better trumpets feature small slides for two of the valves, worked by the thumb and little finger of the left hand to imporove the tuning. Tuba players reach over their instruments and pull the tubes in and out by hand.
Historically, there were isntruments that used finger holes to shorten the length of the instrument instead of valves. These included the cornett, the serpent, the keyed bugle, and the ophicleide. Cornetts were important treble instruments in the renaisance and serpents survived as bass instruments into the beginning of the 19th century.
In 1810 the large holes covered by pads operated by keyes were successfully added to bugles and the idea was extended to build complete families of keyed brass. Keyed bugles and the larger family of instruments called ophicleides were very popular in the late 18th and early 19th centuries and only disappeared at the end of the 19th century.
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Physics at Hamilton |