conical converging in the direction from mouthpiece to bell;
No. 3, cylindrical—No. 1 gives a fundamental tone somewhat
higher, No. 2 somewhat lower, than No. 3. Victor Mahillon[1]
adds that the rate of vibration in such conical tubes as the horn
is slightly less than the rate of vibration in ambient air; therefore,
as the rate of vibration (i.e. the number of vibrations per second)
varies in the inverse ratio with the length of the tube, it follows
that the practical length of the horn is slightly less than the
theoretical, the difference for the horn in B♭ normal pitch
amounting to 13.9 cm. (approximately 512 in.).
The tube of the horn behaves as an open pipe. E. F. F. Chladni[2] states that the mouthpiece end is to be considered as open in all wind instruments (excepting reed instruments), even when, as in horns and trumpets, it would seem to be closed by the lips. Victor Mahillon, although apparently holding the opposite view, and considering as closed the tubes of all wind instruments played by means of reeds, whether single or double, or by the lips acting as reeds, gives a new and practical explanation of the phenomenon.[3] The result is the same in both cases, for the closed pipe of trunco-conical bore, whose diameter at the bell is at least four times greater than the diameter at the mouthpiece, behaves in the same manner, when set in vibration by a reed, as an open pipe, and gives the consecutive scale of harmonics.[4]
In order to produce sound from the horn, the performer, stretching his lips across the funnel-shaped mouthpiece from rim to rim, blows into the cavity. The lips, vibrating as the breath passes through the aperture between them, communicate pulsations or series of intermittent shocks to the thin stream of air, known as the exciting current, which, issuing from them, strikes the column of air in the tube, already in a state of stationary vibration.[5] The effect of this series of shocks, without which there can be no sound, upon the column of air confined within the walls of the tube is to produce sound-waves, travelling longitudinally through the tube. Each sound-wave consists of two half-lengths, one in which the air has been compressed or condensed by the impulse or push, the second in which, the push being spent, the air again dilates or becomes rarefied. In an open pipe, the wave-length is theoretically equal to the length of the tube. The pitch of the note depends on the frequency per second with which each vibration or complete sound-wave reaches the drum of the ear. The longer the wave the lower the frequency. The velocity of the wave is independent of its length, being solely conditioned by the rate of vibration of the particles composing the conveying medium: while one individual particle performs one complete vibration, the wave advances one wave-length.[6] The rate of particle vibration or frequency is therefore inversely proportional to the corresponding wave-length.[7] Sound-waves generated by the same exciting current travel with the same velocity whatever their length, the difference being the frequency number and therefore the pitch of the note. As long as the performer blows with normal force, the same length of tube produces the same wave-length and therefore the same frequency and pitch. By “blowing with normal force” is understood the proper relative proportions to be maintained between the wind-pressure and the lip-tension—a ratio which is found instinctively by the performer but was only suspected by the older writers.[8] If the shocks or vibrations initiated by the lips through the medium of the exciting current be sharper owing to the increased tension of the lips, and at the same time succeed each other with greater velocity, the wave-length breaks up, and two, three or more proportionally shorter complete waves form instead of one, and traverse the pipe within the same space of time, producing sounds proportionally higher by an octave, a twelfth, &c., according to the character of the initiatory disturbance. We may therefore add this proposition: the rate of vibration of a tube varies as the number of segments into which the vibrating column of air within it is divided. In order to obtain the fundamental, the performer’s lips must be loose and the wind-pressure gentle but steady, so that the exciting current may issue forth in a broad, slow stream. To set in vibration a column of air some 16 or 17 ft. long is a feat of extreme difficulty; that is why it is quite exceptional to find a horn-player who can sound the fundamental on the low C or B♭ basso horns. In the organ, where even a 32 ft. tone is obtained, the wind-pressure and the lip-opening controlling the exciting current are mechanically regulated for each length of pipe—only one note being required from each. In order, therefore, to induce the column of air within the tube to break up and vibrate in aliquot parts, the exciting current must be compressed into an ever finer, tenser and more incisive stream. There is in fact a certain minimum pressure for each degree of tension of the lips below which no harmonic can be produced.
It is often stated that the harmonics are obtained by increasing the tension of the lips and a crescendo by increasing the pressure of the breath.[9] Victor Mahillon[10] accounts for the harmonics by increased wind-pressure only. It is evident that the greater the tension of the lips, the greater the force of wind required to set them vibrating; therefore the force and velocity of the air must vary with the tension of the lips in order to produce a steady or musical sound. D. J. Blaikley considers that the ratio of increase in lips and breath follows that of the harmonic series. The tension of the lips has the effect of reducing the width of the slit or aperture between them and the width of the exciting current. While increasing its density the energy of the wind must, therefore, either expend itself in increasing the rate of vibration, or frequency of the pulses, which influences the pitch of the note; or else in increasing the extent of excursion or amplitude of the vibrations, which influences the dynamic force of the sound or loudness.[11] If the aperture be narrowed without providing a proportional increase of wind-pressure, the harmonic overtone may be heard, but either the intonation will suffer or the intensity of the tone will be reduced, because the force required to set the tenser membrane in vibration is insufficient to give the vibrations the requisite amplitude as well as the frequency. If the force expended be excessive, i.e. more than the maximum required to ensure the increased frequency proportional to the increased tension, the superfluous energy must expend itself in increasing the amplitude of the vibrations so that a note of a greater degree of loudness as well as of higher pitch will be produced. The converse is equally true; the lower the pitch of the note the slower the pulses or vibrations and therefore the looser the lip and the gentler the force of current required to set them vibrating. To draw a parallel from organ-pipes: as long as even wind-pressure is maintained, the mouthpiece being fixed proportional to the length of tube, the pipe gives out one note of unvarying dynamic intensity; increase the pressure of the wind and harmonics are heard, but it is impossible to obtain a crescendo unless the mouthpiece be dispensed with and a free reed (q.v.) adapted.
Reference has already been made above to the difficulty of obtaining the fundamental on tubes of great length and narrow bore like the horn. The useful compass of the horn, therefore, begins with the note that an open pipe half its length would give; the Germans term instruments of such small calibre half instruments, and those of wide calibre, such as bugles and tubas, whole instruments,[12] since in them the whole of the length of the tube is available in practice.
The harmonic series of the horn, or the open notes obtainable without using valves or crooks, is written as for the alto horn in C of 8 ft. tone, which forms the standard of notation. Notes written in the bass clef are generally, for some unexplained reason, placed an octave lower than the real sounds.
| Written. | Sounded. | Written and sounded. |
 | ||
| Very difficult. | ||
- ↑ Les Instruments de musique au musée du Conservatoire royal de musique de Bruxelles, “Instruments à vent,” ii., “Le Cor, son histoire, sa théorie, sa construction” (Brussels and London, 1907), p. 28.
- ↑ Die Akustik (Leipzig, 1802), p. 86, § 72.
- ↑ Op. cit. p. 13, § 20, and p. 15, §§ 24 and 25. This apparent discrepancy between an early and a modern authority on the acoustics of wind instruments is easily explained. Chladni, when speaking of open and closed pipes, refers to the standard cylindrical and rectangular organ-pipes. Mahillon, on the other hand, draws a distinction in favour of the conical pipe, demonstrating in a practical manner how, given a certain calibre, the conical pipe must overblow the harmonics of the open pipe, whatever the method of producing the sound.
- ↑ See Gottfried Weber, loc. cit.
- ↑ See Ernst Heinrich and Wilhelm Weber, Wellenlehre (Leipzig, 1825), p. 519, § 281, and A Text-Book of Physics, part. ii., “Sound,” by J. H. Poynting and J. J. Thomson (London, 1906), pp. 104 and 105.
- ↑ See Sedley Taylor, Sound and Music (1896), p. 21.
- ↑ Id. pp. 23-25.
- ↑ See Gottfried Weber, op. cit., pp. 39-41, and Ernst H. and Wilhelm Weber, op. cit. p. 522, end of § 285.
- ↑ See A. Ganot, Elementary Treatise on Physics, translated by E. Atkinson (16th ed., London, 1902), p. 266, § 282, “In the horn different notes are produced by altering the distance of the lips.” Such a vague and misleading statement is worse than useless. See also Poynting and Thomson, op. cit. p. 113.
- ↑ “Le Cor,” p. 22; p. 11, § 18; pp. 6 and 7, § 8.
- ↑ The phraseology alone is here borrowed from Sedley Taylor, (op. cit. p. 55), who does not enter into the practical application of the theory he expounds so clearly.
- ↑ See Dr Emil Schafhäutl’s article on musical instruments, § iv. of Bericht der Beurtheilungs Commission bei der Allg. Deutschen Industrie Ausstellung, 1854 (Munich, 1855), pp. 169-170; also F. Zamminer, op. cit.
