102 MUSI G [SCIENTIFIC BASIS. time to time enunciated ; but no theory till that described in the last foregoing paragraph probed the natural prin ciples upon which, unknowingly, masters have wrought, nor distinguished between these and the ingenious artifices whereby in former times musical etymology and syntax were regulated. The development of plan or design in musical composition has been the fruition of the last two centuries, and, in spite of all dispute as to its paramount necessity, hope points to it as the everlasting standard of genuineness in art. To distinguish allusions to the present time in compari son Avith former dates throughout this article, and to mark the period to which its narration reaches, statement must be made that it is completed in 1883. (G. A. M.) PART II. SCIENTIFIC BASIS. Musical sounds reach our ears through the air. This is proved by showing that a sounding body placed in a space void of air, as under the receiver of an air-pump, is unable to emit sound. It will be sufficient for our present pur pose to admit that musical sounds are transmitted through the air with substantially unchanged quality, even to great distances. The law according to which the apparent in tensity of a musical sound diminishes as it spreads itself over an increasing surface of air is as yet uncertain ; we can only say with certainty that it does diminish. The origin of musical sound consists in the regular periodic vibration of some surface in contact with air, Avhereby motion is imparted to the air, and thus transmitted to the ear. Experience tells us as follows : 1. Regular repetition is characteristic of those motions which give rise to musical sounds. 2. The pitch of the note produced depends on the time in which the motion takes place. 3. The loudness or intensity of the note depends on the magnitude of the motion and on the pitch. 4. The quality of the note depends on the form or shape of the motion, that is to say, on the manner in which it is executed within the time in which it takes place. Regu- 1 . Regular repetition characterizes musical notes ; irre- larity. gularity in the movements in successive periods charac terizes unmusical noises. This is most usefully illustrated by cases in which false notes are obtained. Strings, for instance, sometimes cannot be tuned. In these cases the motion can frequently be seen to be irregular. Pitch 2. The time in which the motion takes place is defined defined conveniently by the number of times the whole motion is by fre- re peated in a second. The number which expresses this may be called the vibration number, or the frequency of the note. Pitch, then, is defined by frequency. Notes of different frequencies present sounds to the ear which are essentially different from one another. The physical ana logy based on frequency would compare notes of different pitch to light of different colours ; this analogy does not, however, extend to the nature of the perceptions. The notes of a uniform instrument present a closer analogy with a definite colour in virtue of their uniform quality, so far as perception goes. And from this point of view there is nothing in the perception of colour analogous to the per ception of difference of pitch in music. In speaking of the perception of combinations of notes we shall see that the ear possesses, in a more or less perfect form, the power of analysing combinations and hearing the notes separately. If we admitted the physical analogy between pitch and colour this would correspond to a power of seeing com pound colours analysed into their constituents. This of course does not exist. Though we may know by experi ence what a compound colour consists of, no amount of experience will enable us to see the components separately in the same way in which we hear the notes of a combina tion separately. The modes of perception are therefore wholly different in the two cases. When one note is produced by a motion whose frequency is twice that of another, a relation subsists between the sounds of the two notes which appears not to be capable of further explanation. They are said to form octaves with one another. It is easy to give some account of the formation of the octave regarded as a concord, but the in explicable peculiarity of the relation consists in a sort of quasi-identity between the sounds of the two notes. Many persons cannot distinguish with certainty two notes an octave apart, particularly if the quality of tone employed be one in the use of which the observer is not practised, and this is the case even with ears of considerable acute- ness and cultivation ; but it does not apply to those ears of the highest class which possess the power of the recollec tion of absolute pitch. Such ears can usually distinguish octaves with certainty. But in all cases the similarity of effect between notes differing in pitch by one or more octaves Avill be admitted. It is a purely mental pheno menon, and no explanation can be given of it. If for a moment Ave recur to the physical analogy of colour simply for the purpose of illustration, the whole range of visible colour corresponds to less than an octave. The musical phenomenon of the similarity of octaves is as if part of the invisible spectrum, say in the ultra-red, excited a sensation having some similarity to the sensation of its octave in the visible spectrum, the two sensations being such that there is a continuous change from the one to the other. Nothing of the kind actually exists in the case of light. The actual impression on the nervous system of the ear which is con cerned Avith the perception of pitch is believed to be sub stantially the same in different individuals. But the mental processes attached to this perception differ so Avidely that for all practical purposes the results are different in dif ferent individuals. The chief difference appears to consist in the different development of the memory of the actual sound of definite notes, Avhich we may speak of as the perception of absolute pitch. This is developed in all degrees : from almost complete absence, in which case we have a want of musical ear arising from the failure to retain the pitch of a note heard even for the shortest time, to that highest degree of perfection in. which the memory retains permanently the sound of every note that is once heard. It is not believed that the possession of this memory is capable of cultivation to any considerable ex tent. It appears rather to be a natural gift, as it usually appears at once in childhood Avhere it is possessed at all. Roughly speaking, and in the absence of reliable statistics, we may say that the possession of the perception of ab solute pitch is distributed as follows : say 1 per cent. possess it, 1 per cent, are entirely destitute of it, so as to be said to have no ear, and the remaining 98 per cent, or so possess it in a more or less modified form. Of this usual condition we may take as a type cases in which the mental effect of a musical note can be retained in the memory for some minutes. We have to consider the musical perception of the class Percep- possessing the power, and of the numerically much larger tion of class Avho only possess it in a modified form. A simple al3S lute tune or melody produces the same effect in all cases as far as Ave knoAv, except that those Avho have the perception of pitch. absolute pitch know Avhat notes are employed, while others are only conscious of the intervals, i.e., of the relative pitch. All the analytical perceptions are as a rule much better ve
