SCIENTIFIC BASIS.] MUSIC 103 developed in the case of those who possess the perception of absolute pitch than in other cases. In those whose perceptions fall below a certain mark the analysis of com binations of notes by the ear fails more or less entirely. In this particular, however, cultivation is generally possible. And this agrees with the assumption that the mechanism of the ear is generally the same. For the perception of differences of pitch is conceived to be due to a mechanism universally present, which effects the analysis of combina tions by the same means by which the pitch is distinguished. The phenomena which give rise to this belief may be stated as follows. If we sound two notes together and cause one of them to change its pitch, we can examine the sensations produced by all sorts of binary combinations. If the two notes have the same pitch at starting, then when they separate beats are heard. Up to a certain point, which is not very far from the point where the two notes are half a semitone apart, the effect in the ear is as if one note was heard, having the alternations of intensity which constitute beats and a pitch generally intermediate between the constituent notes. At this distance of about half a semitone the ear begins to perceive the two separate notes beside the beats. As the distance between the constituent notes increases the two notes become more prominent, the beats grow fainter, and ultimately, Avhen the constituent notes are a little more than a whole tone apart, the beats disappear and the two notes are recog nized as separate and distinct sensations. Now this observation is explained by Helmholtz s hypo thesis of the existence of a resonant mechanism in the ear. Just as a harp, or a piano with the dampers raised, will have the strings corresponding to any sound that reaches it set in vibration, so we suppose that there exists a collection of resonant bodies in the ear which respond to vibrations of pitch nearly coincident with their own. The question then arises, Is the range of sympathy, the distance at which a certain response is excited in the vibrating mechanism of the ear, the same in all cases 1 It is easily seen that, if the above phenomena are sub stantially the same in all cases, the character of the mechanism must also be the same. The interval at which the two notes of a binary combination begin to be sepa rately distinguished can be observed with considerable accuracy, and is critical in the matter. So far as such observations have been hitherto attempted, this interval is very nearly the same in persons of the highest type of ear, who have the perception of absolute pitch in an advanced degree, and in persons occupying a position not high among those who only possess the power of relative per ception. In all cases, moreover, where beats are observed, the beats are the same to all persons, so far as our present knowledge goes. And as some of these beats arise within the ear itself, they depend upon the properties of its mechanism. The result is that, so far as ordinary obser vation goes, the main features of the mechanism of the ear may be safely pronounced to be the same, in the great majority of cases, at all events. Some slight differences in this respect have been observed ; but there can be little doubt that the great differences which exist in the endow ment of the ears of different persons do not arise from differences in the receptive mechanism, but have their source in the nervous or mental actions which lie behind the mechanism. In this we are not referring to the differences which exist between the range of hearing in different individuals. These undoubtedly arise from what may be spoken of as differences in the compass of the re ceptive instrument in different individuals. These differ ences exist both at the upper and lower extremities of the scale. Those in whom the upward range is defective fail to hear the noises of certain insects, and are also unable to hear organ-pipes of very high pitch. The absence of the lower range of hearing is less well established. The complete range of audible musical sounds comprises Range of about nine octaves. It extends from the 32-foot C, two oc- musical taves below the lowest note of a bass voice, to somewhere sounds - about three octaves above C in alt. The upper notes of this range are not audible to some persons. Organ-pipes are made having notes covering this whole range, except about the top half -octave. The position of notes is so fre quently referred to the length of the corresponding organ- pipe that it is convenient here to give these lengths, with the usual notation for the notes to which they correspond. 2 octaves above. f inch. inches. C IV c in altissimo. 3 inches. 6 inches. 1 foot. 2 feet. 4 feet. 8 feet. 16 feet. 32 feet. C c tenor. C Great c. ,C or C .0 or C 2 octaves below. N.B. The letter notation is continued from each C upwards through the octave, and changes at the next C above. The normal perception of pitch does not, however, cover all this range. Its extent varies much in different indivi duals. We cannot assume that pitch can be completely perceived in the normal manner in either the uppermost octave or the lowest octave of the foregoing range. The lower half of the uppermost octave is easily examined, wherever an organ is available, by drawing the fifteenth alone and sounding the notes of the upper half octave of the keyboard. These notes will generally be heard as sounds, but if a bit of a melody be sounded on them, for instance a simple scale passage, it will generally be found unrecognizable. The same is the case with the lowest octave lying between the 16-foot and 32-foot notes. There has been considerable doubt as to the reality of the notes which profess to occupy this position. All instruments sound notes of a complex character, which include sounds of a higher pitch than the nominal note, in fact the har monics, of which the nominal note is the fundamental. And doubts have been raised, which have in some cases proved to be well founded, whether the deep notes in question really contain any of the nominal note or funda mental at all, and do not rather consist entirely of har monics, or of sounds whose real pitch is much higher than the nominal one.
