of attention given to them by the mind. In general we pay attention to our sensations only in so far as they enable us to form correct ideas of external objects. Thus we can distinguish two comparatively simple tones coming from different instruments. On the other hand when a compound tone is produced by one instrument we disregard the several partials because they do not correspond to different portions of the vibrating body; each portion executes the compound motion corresponding to all the partials at once. Moreover it would hinder our musical enjoyment if we were habitually to concentrate our attention on the upper partials, and we have therefore, in general, no interest in doing so. Hence it must not be supposed that when we fail to distinguish the partials of a compound tone they are not really present, or that when we hear them but faintly their intensity is small. Helmholtz gives an experiment which strikingly illustrates this. He obtained two nearly simple tones an Octave apart, and by listening to each tone in succession he was able to distinguish them when sounding together. But he could do so only for a while, for the higher sound was gradually lost in the lower, and a quality of tone different from either was the result. This happened even when the higher was somewhat stronger than the lower sound.
Notwithstanding the difficulty of hearing the upper partial tones, many musicians have been able to do so by their unaided ears. Thus, Mersenne[1] could distinguish six partials in the tones of strings, and sometimes seven. Rameau[2] also succeeded in perceiving the partials of the voice, which are much harder to distinguish than those of strings. There are several methods[3] by which the ear can be trained to recognise the upper partials. It is better to begin with the uneven tones, Twelfth, Seventeenth, etc., which are easier to hear than the Octaves. Touch the note g′ softly on the piano, damp the string, and strike c loudly. Keep the attention directed to the pitch of the g′, and this note will be heard in the compound tone of c. Similarly by sounding e′′ softly and then c loudly, the latter will be observed to contain the former. It must not be supposed that when these partials are heard it is due to an illusion of the ear, for the note e′′ on the piano as ordinarily tuned is appreciably sharper than the 5th partial of c. The difference of pitch between the two sounds proves that one cannot be the echo of the other. There is another and still better method of directing the attention of the ear to any given partial tone. Touch a vibrating string at one of its nodes, for example at ⅛ of its length, and the 5th partial will be heard, faintly accompanied by the 10th, 15th, etc. It will then be easy to hear the 5th partial in the compound tone of the whole string.
The ear is however hardly able to carry out researches of this kind without mechanical assistance. Hence Helmholtz made use of Resonators, which are hollow globes or tubes of glass or metal, having two openings, one to receive the sound, the other to transmit it to the ear. From the mass of compound tone each resonator singles out and responds to that partial which agrees with it in pitch, but is unaffected by a partial of any other pitch. By this means Helmholtz has shown that the number of the partial tones and their relative intensities vary in different instruments, and even in the same instrument, according to the way it is played. These various combinations are perceived by us as different qualities of tone, by which we distinguish the note of a violin from that of a horn, or the note of one violin-player from that of another. The nearest approach to a simple tone is given by tuning-forks of high pitch. Dr. Preyer[4] was unable to detect any upper partials in forks tuned to g′′ (768 vibrations) or higher. On the other hand, he showed that as many as 10 partials were present in a fork tuned to c (128 vibrations). But these are very weak and can only be heard when great care has been taken to exclude all other sounds. The general effect of such comparatively simple tones is very smooth but somewhat dull, and they seem to be deeper in pitch than they really are. Flutes and wide-stopped organ pipes have few effective partials, and are much inferior in musical effect to open organ pipes and to the piano. The tones of the voice, violin, and horn, are more complex still, and are characterised by fuller and richer qualities. When the partials above the 7th are strong they beat with each other, and the quality becomes harsh and rough as in reed instruments. Mr. Ellis has obtained beats from the 20th partial of a reed and even higher, and Dr. Preyer has proved a reed to possess between 30 and 40 partials.
The clarinet and the stopped organ pipe are exceptions to the general rule, for they give only the unevenly numbered partials 1, 3, 5, 7, 9, etc. Neither of these instruments will set into vibration a resonator an Octave or two Octaves above it in pitch, proving that the 2nd and 4th partials are absent. The resulting quality of tone is hollow and nasal, and may be obtained from a string, by plucking or bowing it in the middle. The effect is to make a Loop there, and hence to prevent the vibrations of the halves, quarters, etc. of the string, which require a Node at that point. [See Node.]
Helmholtz has also discovered that the different vowel sounds are due to various combinations of simple tones, and he verified his theory by reproducing several vowels from a series of tuning-forks set in motion by electricity. Each fork had a resonator the mouth of which could be opened or closed in order to obtain any required degree of intensity.
Bells, gongs, and drums have a variety of secondary tones generally inharmonic with the prime, and the result is that their vibration is not periodic. Hence the sounds they produce
- ↑ 'Harmonie Universelle,' Paris, 1636, pp. 208, 9, and 221 of the 4th book on Instruments. He gives's false ratio for the 7th partial, viz. 20:3 instead of 7:1.
- ↑ 'Nouveau Système de Musique théorique.' Paris, 1726, Preface.
- ↑ Helmholtz, 'Sensations of Tone,' pp. 79–82.
- ↑ 'Akustische Untersuchungen.' Jena, Guslar Fischer, 1879.
