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 harmonics 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♭ 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 diameter, altering its position by placing it nearer the mouthpiece. These laws, which were likewise known to the Greeks and Romans,[8] had to be rediscovered by experience in the 18th and 19th centuries, during which the mechanism of the key system was repeatedly improved. Due consideration having been given to these points, it will also be necessary to remember that the stopping of the seven open holes leaves only the two little fingers (the thumb of the right hand being in the ordinary clarinet engaged in supporting the instrument) free at all times for key service, the other fingers doing duty when momentarily disengaged. The fingering of the clarinet is the most difficult of any instrument in the orchestra, for it differs in all four octaves of its compass. Once mastered, however, it is the same for all clarinets, the music being always written in the key of C.
The actual tonality of the clarinet is determined by the diatonic scale produced when, starting with keys untouched and finger and thumb-holes closed, the fingers are raised one by one from the holes. In the B flat clarinet, the real sounds thus produced are
being part of the scale of B flat major. By the closing of two open keys, the lower E flat and D are added.
The following are the various sizes of clarinets with the key proper to each:
E flat, a minor third above the C clarinet.
B flat, a tone below the C clarinet.
The high F, 4 tones above the C clarinet.
The D, 1 tone above the C clarinet.