Although we have mentioned only trumpets in the title this lecture is really about all the wind instruments, including the pipe organ. One of the main considerations will be the way in which the actual technology involved in making instruments has affected the whole course of musical development. The early trumpets without valves could play tunes with only very high notes; the development of valves has, however, made it possible to play tunes at a much lower pitch. On the early woodwind instruments it was quite difficult to play very rapid passages but the introduction of Boehm's marvellous system of keys has made the instruments much more flexible. The opening clarinet glissando of the "Rhapsody in Blue" would be very difficult on a baroque instrument! The simple ideas of vibrations in tubes soon have to be modified to explain the behaviour of real instruments and there are quite a few surprises. For example it is often said (frequently by the Lecturer!) that the trombone uses the various modes of vibration of the tube to produce the main pitch changes and then, in order to play tunes, the gaps are filled in by altering the overall length with the slide. But a good player can fill in the gaps without using the slide, apparently in defiance of the physics! The design and manufacture of wind instruments is every bit as complicated as that of the string family. For example, in a clarinet the finger holes may seem to be there just to enable tunes to be played; but they perform a vital function in the maintenance of the vibrations, in determining the quality of sound produced and in controlling the way in which the sound produced inside the instrument gets out to the ears of the listeners. The tone quality of the woodwinds makes a fascinating study and we shall find, for example that the note of a bassoon contains virtually no fundamental. The way in which the ear-brain system makes up for this loss is well worth studying. The largest and most splendid of