Wind instruments produce sounds by means of a vibrating column of air in much the same way as a vibrating string on a guitar or piano.

We hear various pitches according to whether a string or column of air is vibrating as a unit through its whole length or in particular fractions of it.  Vibration along the whole length gives the lowest or “fundamental” tone.  Vibrations taking place at various fractions of the length produce higher pitches called harmonics or “upper partials”.  The stationary points along a string or air column (i.e., where the waves cancel each other out) are called nodes. 

In mathematical terms we may say that the frequency of each harmonic is in inverse proportion to the size of the fraction.  This means that the vibration of equal halves of a string produces double the frequency of the whole (and thus sounds an octave higher), the vibration of equal thirds triples the frequency (and therefore sounds an octave and a fifth higher than the fundamental note) and so on.  The range of notes so produced is called the harmonic series.

The above physical laws have great significance for musicians in general and wind band players in particular.  Whether he understands the implications of the harmonic series or not, every brass player takes full advantage of this basic physical law when he uses the same fingering to produce notes of different pitches.  This is done by adjusting his embouchure in such a way that it favours different partials of the same fundamental tone.

The flute, oboe, saxophone and bassoon can produce the same overtone series (harmonics on the fundamental fingering) as brass and stringed instruments.  The clarinet, however, is somewhat different. Unlike most other musical instruments, the clarinet's almost exclusively cylindrical shape means that it acts acoustically as a pipe closed at one end. This means that the vibratory modes of the air column with respect to the fundamental harmonic are different. In fact, it gets every other partial (3,5,7, etc) in the series.  This is the reason we say that the clarinet overblows at a 12^th instead of an octave.

Other wind instruments have either cone-shaped bores [the diameter gradually widens] or at least enough conical tubing to cause them to act acoustically as open pipes and thus get the same harmonics as a guitar or piano string. While this cone-shaped bore is easy to see in the case of tapered sections of brass instruments, it can be less obvious in the case of some woodwinds. It is not often realised, for example, that the flute has a conical headjoint