How do musical instruments vary in pitch?

Answer 1

The basics of 'pitch' is what frequency the instrument is playing at. Middle C is tuned (depending whether you're in France, Germany, US or otherwise) at 440Hz, which refers to how fast the air inside the instrument is vibrating.

In a simple sense, the frequency of a tube can be changed (open or closed also reflects the frequency but that's more than what you're asking) by lengthening or shortening it so the air has more length to vibrate before coming out of the holes (in the case of woodwind) where you put your fingers down on keys to achieve this.

Tuning, on the other hand is very different for each instrument but always is lengthening or shortening this tube by some method (such as pulling the mouthpiece, barrel for Clarinet etc out).

Although this air is also vibrated before it goes in the tube, for flute the air hits the edge of the mouthpiece and splits, vibrating, for clarinet the reed vibrates as air hits it and it opens and closes the mouthpiece, so you can also affect this in some way normally with your embouchure that can change it.

Answer 2

Woodwinds are in the class of instruments which traditionally were made with wooden bodies. The group is 'contaminated', if you will, by association with the Woodwind Quartet, which traditionally includes the French horn (or just Horn), which is a Brass instrument, and will not be considered for a 'general woodwinds' question.

The instruments, then, in the woodwind category are the clarinets, oboe, english horn, and bassoon, and Flute. For clarification (as if this actually clarifies anything) the clarinets are single-reed instruments, and so the Saxophone is included in the woodwinds. Similarly, the modern flute family are most often made of metal, but because they were originally wood (and very expensive flutes are still made of wood) they are part of the family.

That said, we have three varieties of woodwind instruments: Ones which are 'actuated' by a flat-cut single piece of reed (arundo donax), ones which use two pieces of reed bound together and shaped to form a small entry, and ones with no reed at all, but rather an opening across which the player blows. The commonality is the fact that the bodies of all of these instruments incorporate holes, which are opened or closed by the player's fingers or by hinged pads operated by keys, which vent the body at strategic positions.

So the general way woodwind instruments change pitch is by these holes, which effectively change the length of the vibrating air column. However, like the brasses, the woodwinds are able to use overtones. A brass instrument (such as the Trumpet) can make many notes without valves or other modification of the physical instrument when the player changes his embouchure (lip position and tension) and blows harder or softer. In the woodwinds, these overtones are generally produced by overblowing, embouchure changes, special fingerings and vent holes.

***So the simple answer to the question is that the woodwind family characteristically changes pitch by the use of opening and closing holes along the length of the body of the instrument, to effectively change the length of the vibrating air column inside.***