des into three equal
parts, producing a triple number of vibrations resulting in the third
note of the harmonic series, at an interval of a twelfth above the
fundamental.[4] In a wind instrument with lateral holes the fundamental
note corresponding to any particular hole is produced when all the holes
below that hole are open and it itself and all above it are closed, the
effective length of the resonating tube being shortened as each of the
closed holes is successively uncovered. In order to obtain a complete
chromatic scale on the clarinet at least eighteen holes are required.
This series produces with the bell-note a succession of nineteen
semitones, giving the range of a twelfth and known as the fundamental
scale or _chalumeau_ register, so called, no doubt, because it was the
compass (without chromatic semitones) of the more primitive predecessor
of the clarinet, known as the _chalumeau_, which must not be confounded
with the shawm or schalmey of the middle ages.

The fundamental scale of the modern clarinet in C extends from
[Illustration]. The next octave and a half is obtained by opening the
speaker key, whereby each of the fundamental notes is reproduced a
twelfth higher; the bell-note thus jumps from E to B#, the first key
gives instead of F its twelfth C#, and so on, extending the compass to
[Illustration], which ends the natural compass of the instrument,
although a skilful performer may obtain another octave by
cross-fingering. The names of the holes and keys on the clarinet are
derived not from the notes of the fundamental scale, but from the name
of the twelfth produced by overblowing with the speaker key open; for
instance, the first key near the bell is known not as the E key but as
the B#. The use of the speaker key forms the greatest technical
difficulty in learning to play the clarinet, on account of the thumb
having to do double duty, closing one hole and raising the lever of
the speaker key simultaneously. In a clarinet designed by Richard
Carte this difficulty was ingeniously overcome by placing the left
thumb-hole towards the front, and closing it by a thumb-lever or with
a ring action by the first or second finger of the left hand, thus
leaving the thumb free to work the speaker key alone.

There is good reason to think that the ancient Greeks understood the
advantage of a speaker-hole, which they called _Syrinx_, for
facilitating the production of ha