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HARMONIC SERIES IN

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Originally appearing in Volume V27, Page 876 of the 1911 Encyclopedia Britannica.
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HARMONIC SERIES IN C ea- _:aac 12 3 4 5 6 7 8 9 10 II121314 15 16 Although the valves of brass wind instruments vary in form and detail according to the makers, the general principles governing their action are the same for all types. The piston placed on some branch of the main tube must be so constructed that on being de-pressed it closes the natural windways through the main bore and opens others into the additional piston length. The piston seated on a spring instantly regains its normal position when the finger is removed. After the actual shape and construction of the valve and its box had been successfully evolved, it was the boring and disposition of the windways which engaged the attention of makers, whose object was to avoid complexity and sharp angles and turns in the tubing. The pitch of all tubes is determined by the length of the column of air set in vibration therein. Any variation in the length of this column of air produces a proportional variation in the pitch of the instrument. When the piston is depressed, there-fore, a partition wall is removed and the column of air within the additional length of tubing representing a definite interval is added to the main column, so that the length of the sound wave is proportionally increased whether the column is vibrating as a whole (when it gives the fundamental or first note of the series) or whether it has been induced to divide into equal portions in which sound waves of equal length are simultaneously generated. The numbers under the notes of the harmonic series represent the aliquot parts into which the column of air must divide in order to produce the harmonics. The length of tubing attached to each valve is there-fore calculated on the basis of the length of the main column, to give for the first piston a tone, for the second a semitone, for the third a tone and a half, and for the fourth two tones. In order to illustrate the working of the pistons, we will take as an example the bombardon or bass tuba in E5. Depressing the second piston lowers the pitch of the instrument to D, giving it the harmonic series proper to that key; the third harmonic, which on the open tube would be B5, now becomes A; the fifth harmonic, which was G, is now F#, and so on. The first piston on being de-pressed similarly transforms the E5 bombardon into an instrument in D5, a tone lower; the third piston lowering the pitch 1-i tones changes the key to C. So far the intonation of the notes produced by means of the pistons is as accurate as that of the harmonics. The variations in the length of the column of air correspond to the positions of the slide on the trombone, the first position being that of the instrument with all valves in their normal position. The use of the three pistons in turn gives the second, third and fourth positions. In order to obtain a complete chromatic compass there must be seven positions or different lengths of tubing available, as on the trombone, each having its proper harmonic series. On valve instruments the three other positions are obtained by means of combinations of pistons; the fifth position consists of a combination of pistons 2 and 3 (z and i tones), which would transpose our bombardon into the key of B; the sixth position consists of a combined use of pistons i and 3, producing a drop in pitch of 21 tones from E5 to B5. In the seventh position all three pistons come into play simultaneously, lowering the pitch three tones. The intonation of the notes obtained in positions 5, 6, 7 is not so faultless as that of notes from the other positions, for the following reason:β€”On the bombardon in E5 piston I lower,: the pitch one tone to D5; in the sixth position, when pistons I and 3 are used simultaneously, the third piston is no longer attached to a bombardon in E5, on which it would produce the effect of C, but to one in D5, on which it lowers the pitch to B5; it is clear, therefore, that the supplementary tubing will not be quite long enough to give the correct intonation, and that the B5 obtained as the 2nd harmonic in the sixth position will be a little too sharp, a defect which the performer corrects as best he can with his lip. The exact differences in length can be found from the table of ratios given by Victor Mahillon in La Trompette, son histoire, sa theorie, sa construction (Brussels and London, 1907), p. 38. This inherent defect of the valve system was understood and explained a few years after the invention of valves by Gottfried Weber,' and the record of the successive endeavours of brass instrument makers to overcome this defect without unduly complicating the mechanism or adding greatly to the weight of the instruments constitutes the history of valve instruments. The accredited inventor and patentee of valves applied to musical instruments was Heinrich Stolzel 2 of Pless in Silesia in 1815. The credit, however, is really due to Blumel,' also a Silesian, who sold his rights to Stolzel. ' Caecilia (Mainz, 1835), xvii. 89–91. 2 See Captain G. B. Bierey in Allg. musik. Ztg. (Leipzig, 1815), p. 309, and idem for patent 1817, p. 814. 2 Ibid. 1818, p. 531. The first valves made by Stolzel worked in large square brass boxes and consisted of square blocks of solid brass through which the windways were bored in the same horizontal plane. A trumpet having two valves of this make is preserved in the museum of the Brussels Conservatoire (No. 1310 in catalogue). In 1825 Stolzel had improved upon this primitive valve, making it tubular and calling it Schub-Ventil: its action was lighter and more rapid than that of the original valve. Charles Sax of Brussels took up the manufacture of these valves and applied them to the cornet with two pistons. The scale of instruments with only two pistons had several gaps, and could not be strictly termed chromatic. In order to complete the scale, C. A. Muller of Mainz constructed a trumpet in the early 'thirties which not only had three valves, but also tuning-slides for all three additional lengths of tubing 4 and key crooks, for which corresponding piston lengths could be inserted. This was, therefore, the first attempt at compensation, for which the honour is due to Germany. The early improvements and modifications of Stolzel's invention may be briefly 2 summed up as follows: In 1824 John Shaw, of Glossop, invented a system of valves known as transverse spring slides, both ascending and descending, i.e. respectively having pistons which cut off certain lengths of tubing, thereby raising the pitch, or pistons adding certain lengths, and lowering the pitch thereby. These transverse slides were afterwards improved by Schott in 1830, and became known as the Wiener Venlil, which had an enormous success on the continent of Europe, and were applied to all kinds of brass instruments. In 1827 Blumel invented the rotary valve or cylinder action known as Dreh or cylinder Ventil, a system still in use in Germany and Austria, and preferred to piston systems by many. In 1833 J. G. Moritz (who was associated with Wieprecht, inventor of the batyphone and bass tuba) made the large pistons of generous diameter known as Berliner Pumpen. In 1835 John Shaw patented a variation of the rotary valve, known as patent lever. In 1839 Perinet of Paris invented the most modern form of valve, called by his name, similar to the Schub-Ventil and Berliner Pumpen, but of a diameter between the two. In 1851 and 1852 Dr J. P. Oates made his equilateral valves adopted by Antoine Courtois for his' cornets; the same clever acoustician invented a piston with four straight windways, afterwards patented by A. Sax of Paris. Various attempts to improve the windways and get rid of angularities were made by Gustave Besson in 1851, 1854 and 1855, when a system was devised having the same bore throughout the windways. This decided improvement forms the basis of the present system of the same firm. Until now efforts had mainly been directed towards the improvement of the technical construction of valves and windways. The first attempt since Miiller's (which appears to have passed unnoticed in France and England) to remedy by compensation the inherent defect of the valve system when pistons are used in combination was made in 1850, when Adolphe Sax devised a system of six pistons, one for each position, in which it was impossible to use any two pistons in combination: this system was ascending instead of descending. Gustave Besson's registre in 1856–57 followed, providing a large horizontal piston, which, by connecting other duplicate lengths of tubing of the proper theoretical length, gave eight independent positions. In 1858 G. Besson and Girardin produced the transpositeur, in which two extra pistons when depressed automatically lengthened the slides of the three usual pistons to the required length for combination. In 1859 came the first suggestion for automatic compensation made by Charles Mandel in his book on the Instrumentation of Military Bands, p. 39. It does not appear that he put his suggestion into practice or patented it. In this ingenious system the valves were so constructed that when two or three pistons were used simultaneously the length of tubing thrown open was automatically adjusted to the correct theoretical length required. The same ingenious principle, elaborated and admirably carried out in practice, was patented by D. J. Blaikley in 1878. The working of his device differs from the action of ordinary valves only when the pistons are used in combination. The exact theoretical length is then obtained by bringing into use extra compensating lengths of tubing corresponding to the difference between the piston length for a semitone, a tone and one and a half tones on the open tube and on the tube already lengthened by means of one of the other pistons. The value of this invention, enhanced by the advantage of leaving the fingering unaltered, is more especially appreciated on the large brass instru ments, in which correction of faulty intonation by means of the lips is more difficult to accomplish satisfactorily than on the smaller instruments. A similar device was patented in France in 1881 by Sudre. Victor Mahillon, who had been for some years at work on similar lines, did not patent his invention till 1886, when his piston 4 Gottfried Weber, op. cit. p. 98. 6 Fuller accounts maybe derived from Captain C. R. Day, Descriptive Catalogue of Musical Instruments (London, 1891), pp. 182 seq.; Victor Mahillon, Catalogue descriptif, vol. i. 2nd ed. pp. 282 seq.; and from the pages of the Allg. musik. Ztg. (Leipzig) and Caecilia (Mainz). regulateur was introduced : this first device was not automatic, and was shortly afterwards improved and patented as the automatic regulating pistons. A later valuable development in the history of valve systems is the enharmonic, invented by Messrs Besson & Co., in which they have perfected and simplified the principle of independent positions tried in the registre of the fifties. In the enharmonic valve system each position has its independent length of tubing theoretically accurate, which comes into play as the valves are depressed, and there is besides a tuning slide for the open notes. Finally, there is an improvement in a different direction to he chronicled, unconnected with compensation, in Rudall Carte & Co.'s system (Klussmann's patent) of conical bore throughout, the open tube and the valve slides, which by means of ingeniously combined joints and slides preserve the tone without loss of air. This system has been applied to all valve instruments, and has been found to produce a remarkable improvement in the timbre. (K. S.)
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