Late C18 Boxwood Clarinets, one showing advances in mechanisation.
Acoustics
It is a common mistake to suppose that wind instruments require vast amounts of air. In fact, comparatively little air passes through an instrument: most of it goes to waste. Acoustically, its only function is to energise the air already in the instrument into the rapid vibrations which we recognise as musical sound, and in theory it would be better disposed of elsewhere.
The simple act of blowing into an instrument will not produce a musical sound. A regular air stream cannot pulsate the air inside. The agent which does is called the generator, and wind instruments employ three broad types:
Lip activated generator - air escapes intermittently through a narrow aperture between the player's lips, muscularly sprung to act as a resistive valve. This causes the lips to vibrate, as in the blown 'raspberry' or 'bronx cheer'. This type of generator is associated with instruments loosely called 'brass'. The mouthpiece of a brass instrument is not, strictly speaking, a generator, but a lip support.
Reed generator - the narrow aperture is between two springy blades of vegetable tissue, plastic or metal (double reed) or one blade and a rigid surface (single reed). The oboe and bassoon have double reeds, the clarinet and saxophone, single reeds. The 'squeakers' children make from grass blades or plant stems are homely examples of either type.
Edge tone generator - an air stream is shaped into a flat ribbon which develops eddies, of the same type which appear in cigarette-smoke. When these are passed ever a sharp edge, they are marshalled into order and become capable of producing sound. The edge itself does not vibrate. Familiar examples include blowing across a pen top or bottle. This type of generator is associated with the vast flute family. The air stream may be shaped and directed by the lips alone, as in the orchestral flute (where the sharp edge is the 'opposite' side of the blowing hole), or by passing it through a notch or duct which directs it automatically to the sharp edge, as in the recorder, or the flute pipes of an organ.
It is useful to regard a generator as a means of producing vibration rather than sound. For a musical sound, it must be linked to a suitable mass of air. This is called the resonator. In wind instruments it is usually (though not necessarily) a column, largely defined by the tube which contains it. Together, generator and resonator form a coupled system, in which each component influences the other. The resonator, however, is usually considered to be the dominant partner, as it exerts a powerful back-effect on the generator's vibrations and determines the pitch and character of the notes heard.
A resonator is capable of stable modes of vibration at a number of frequencies. In wind playing, the desired frequency is selected primarily by exciting the air column so that the frequencies below it become unstable and drop out. This overblowing is an indispensable part of brass and woodwind technique, though in the latter case it is often assisted by opening small vents in the tube to discourage the lower notes from sounding.
These frequencies are called harmonics and have fixed ratios. If the lowest, or fundamental, is called the lst harmonic, the 2nd will have twice its number of vibrations, the 3rd three times, and so on. Together they make up the Harmonic Series, whose ratios are shown in approximate musical notation in the diagram. For convenience, only the first 16 harmonics are shown, and the diagram is based on a low C corresponding to an open tube length of about 8 feet. Longer or shorter tubes would give the same series, but at lower or higher pitches. For example, a flute or oboe, at about a quarter of the length, gives it about two octaves higher.
The series does not correspond with the scales used in western music. It has massive gaps at its lower end, and though these become narrower until it is running approximately scale-wise from the 7th harmonic, there are several mistuned notes. Moreover, the series as shown is theoretical: in practice, fewer notes may be available from a given tube. A tube which is wide in relation to its length may only give the first part of the series, while a narrow one, designed to facilitate the upper harmonics, may be incapable of the lower. The details of the generator-resonator system are important too: a single reed and cylindrical tube sound the odd-numbered harmonics only.
Some simple wind instruments employ only a limited number of practicable harmonics. The bugle, for example, only gives harmonics 1 to 8, with 1, produced with slack lips, a poor note, and 7 and 8 only exceptionally available. Bugle calls, therefore, merely ring the changes on five pitches or fewer. Many other brass instruments were similarly circumscribed until the advent of mechanisation in the eighteenth century.
One method of producing complete scales is to use an array of generator-resonator systems, each sounding one note. This is the principle of the organ, and of bundle and raft pipes, such as 'pan pipes'.
In many wind instruments, scales are built by sounding a partial harmonic series from different lengths of tube. Brass players add fixed lengths of supplementary tubing called crooks, or bring different lengths into play instantly by means of valves. The telescopic slides of the trombone represent another solution, and various brass instruments have been given side holes and keys, though with little permanent success.
Characteristically, woodwind instruments have tubes which are broad in relation to length, and they employ the lower harmonics. With a few marginal exceptions, such as the piston-stopped pitch pipes here, they use a 'shortening hole' system. The opening of side holes has an effect nearly equivalent to cutting off successive lengths of the tube. With six or seven holes a scale can be produced, usually from 1st harmonics. Normally other ranges of notes are available by overblowing to higher harmonics. Fingering using the 2nd harmonic will be substantially the same as those using the 1st, as they are an octave apart, but those in higher ranges will be significantly different. Many of the notes produced by overblowing are uncertain in pitch or quality, and fingering technique therefore normally selects the best-sounding of the several alternative ways in which a note can be produced. However, the player may substitute a version derived from a different harmonic for effect, or to ease the problems of rapid finger movement.
The clarinet is a special case, as its single reed and cylindrical tube make it behave as a stopped pipe. The notes is produces are an octave below those of other instruments of equivalent length, and its even harmonies are so weak that in effect it skips directly from 1st to 3rd; a pitch distance of a twelfth. It therefore needs different fingerings in its first two registers, as well as additional mechanism to bridge the gap, and employs harmonics as high as the 11th.
The twelve semitones of the octave may be produced on all woodwind instruments from fewer holes by cross- or fork- fingering. This is a method of flattening notes by approximately a semitone by covering holes further down the tube than the open one, or by partly closing the open hole itself. In the past, this technique was also used to observe enharmonic distinctions of pitch which are now largely discounted: for example, the difference between G#/Ab. The fork fingerings which remain in use today are often vented to improve their quality. The desire to avoid their uncertainties had an important bearing on the woodwind's mechanisation.
An instrument's characteristic tone is conveyed through the harmonics. Pure tones of a single frequency scarcely exist in Nature. The unsettling electronic whistles broadcast by the BBC as test tones indicate their sound. Normally, every sound we hear consists of many simultaneous frequencies. When a musical instrument sounds a note, it may be emitting up to twenty harmonics in addition to the fundamental (normally, the lowest frequency) which the mind usually interprets as being responsible for the pitch. The number, distribution and intensity of these, together with their rise and decay times, give the sensation of timbre, or tone. The broad details of tone - what makes a flute sound different from an oboe, and both from a clarinet - are largely fixed by the nature of the generator-resonator system as described above. In addition, the elasticity of the tube contributes secondary details, as do the player's internal air cavities.
The player is, of course, the third element in the acoustic system. All wind instruments are very imperfect, and can be heard to be so in the hands of a beginner. If they eventually 'discourse most eloquent music' - and Hamlet is being ironical in suggesting that technique stops at governing the ventages with finger and thumb - it is because of the player's sensitive control of the system through lip and air stream. He or she is constantly monitoring the acoustical effect and compensating, with minute muscular adjustments, for imperfections by a largely subconscious 'feedback' process