rmonics on the aulos. The credit of
the discovery of this interesting fact is due to A.A. Howard,[5] of
Harvard University; it explains many passages in the classics which
before were obscure (see AULOS). Plutarch relates[6] that Telephanes
of Megara was so incensed with the syrinx that he never allowed his
instrument-makers to place one on any of his auloi; he even went so
far as to absent himself, principally on account of the syrinx, from
the Pythian games. Telephanes was a great virtuoso who scorned the use
of a speaker-hole, being able to obtain his harmonics on the aulos by
the mere control of lips and teeth.

The modern clarinet has from thirteen to nineteen keys, some being
normally open and others closed. In order to understand why, when once
the idea of adding keys to the chalumeau had been conceived, the
number rose so slowly, keys being added one or two at a time by makers
of various nationalities at long intervals, it is necessary to
consider the effect of boring holes in the side of a cylindrical tube.
If it were possible to proceed from an absolute theoretical basis,
there would be but little difficulty; there are, however, practical
reasons which make this a matter of great difficulty. According to V.
Mahillon,[7] the theoretical length of a B flat clarinet (French pitch
diapason normal A = 435 vibrations), is 39 cm. when the internal
diameter of the bore measures exactly 1.4 cm. Any increase in the
diameter of the cylindrical bore for a given length of tube raises the
pitch proportionally and in the same way a decrease lowers it. A bore
narrow in proportion to the length facilitates the production of the
harmonics, which is no doubt the reason why the aulos was made with a
very narrow diameter, and produced such deep notes in proportion to
its length. In determining the position of the holes along the tube,
the thickness of the wood to be pierced must be taken into
consideration, for the length of the passage from the main bore to the
outer air adds to the length of the resonating column; as, however,
the clarinet tube is reckoned as a closed one, only half the extra
length must be taken into account. When placed in its correct
theoretical position, a hole should have its diameter equal to the
diameter of the main bore, which is the ideal condition for obtaining
a full, rich tone; it is, however, feasible to give the hole a smaller