CHAMBERS'S INFORMATION FOR THE PEOPLE. 



of the subject than we have hitherto done. We 

 have seen that the oscillatory movements in water 

 were at right angles to the direction of the motion 

 of the wave, but we can easily conceive of their 

 being in some other direction. For instance, the 

 wave-like oscillation produced by wind upon a 

 field of corn is a familiar phenomenon. Fig. I 



Fig. i. 



shews the nature of this motion. The gust of 

 wind is supposed to be moving from left to right, 

 and to have just reached the point B, the stalk A 

 has just swung back again to its original position. 

 The ears of corn are prevented by their stalks 

 from vibrating more than a limited distance up 

 and down, and the wave produced does not, there- 

 fore, consist entirely of elevation and depression 

 of surface, like a sea-wave, but to a very great 

 extent also of a condition of more closely or less 

 closely packed ears. 



From this illustration (for which we are indebted 

 to Mr Sedley Taylor's excellent book Sound and 

 Music), it becomes quite easy to conceive of a 

 wave-motion in which there is no longer any 

 vibration at right angles to the direction of the 

 wave, but in which the whole vibration is similar 

 to that shewn in the packing of the ears of 

 corn, and therefore in the direction of the wave. 

 Waves of this kind are called waves of alternate 

 condensation and rarefaction, and it is to this 

 class that the sound-waves of air belong. It is 

 obvious that these waves have length, amplitude, 

 and form, just as much as those of water, and also 

 that the rate, extent, and mode of the air-particle 

 vibrations must depend on these just as before. 

 Each air-particle makes little oscillations back- 

 ward and forward along the line of progression 

 of the wave ; and when the wave-motion has 

 ceased, it returns to its original position, just as 

 in the case of water. 



Characteristics of a Musical Sound. 



Every musical sound has three characteristics, 

 which, when known, completely determine it. 

 These are pitch, loudness, and quality. We 

 know of no element in the nature of the sound 

 which does not fall under one of these heads. 

 We find experimentally that these three charac- 

 teristics depend entirely upon the rate, extent, 

 and mode of the air-vibrations which produce 

 that sound. This indeed might almost have been 

 seen a priori, for although we speak of the vibra- 

 t\OT\s producing the sound, yet this is not in reality 

 correct they are the sound. The sound has no 

 other existence, so far as we know ; the vibrations 

 exist, and when they strike our ears, we call them 

 sound. 



The pitch of a musical sound, then (or, in popu- 

 lar language, its highness or lowness), depends on 

 the rate of its vibrations ; the greater their number 



690 



in a given time, the higher the sound. The longest 

 organ-pipe is 32 feet long, and the sound emitted 

 by it (the C 4 octaves below the middle C of the 

 pianoforte) is the lowest which can be distinctly 

 recognised by the ear as a musical sound ; it 

 vibrates 16 times per second.* The highest 

 sound heard in orchestral music is the seldom- 

 used high D of the piccolo flute, which vibrates 

 4608 times per second. It is uncertain what is 

 the highest note actually audible to the ear ; its 

 pitch varies very much in different individuals. 

 Between the limits we have named there is a 

 separate musical note corresponding to every 

 change in the number of vibrations. It is im- 

 portant to bear this continuity of sound in mind, 

 and not to think of musical sounds being discon- 

 tinuous, and occurring only at regular intervals ; 

 like the series of sounds which can be played by 

 the flute, for instance. The ear, however, does 

 not take pleasure in hearing any or every succes- 

 sion of these almost innumerable sounds ; on the 

 contrary, it selects but a small number of them, 

 and hears these with gratification ; while if another 

 sound, varying by a very small amount in its 

 'vibration -rate,' be substituted for one of these, it 

 at once pronounces it to be ' out of tune.' The 

 wrong note is just as much a musical note 

 as the right one ; it is important, therefore, 

 to examine the cause of the unquestionable 

 physical fact, that our ears pronounce a certain 

 sequence of musical notes to be ' in tune,' and any 

 other slightly different sequence to be ' out of 

 tune.' Taking any one sound as a standard (it 

 does not matter in the least what sound), we find 

 that there are certain other sounds which can be 

 combined with it or with each other in melody or 

 harmony, with an effect which is satisfactory to 

 the ear. These sounds have always a fixed rela- 

 tion of pitch to the standard sound, and they are 

 known as the sounds of the ordinary scales of which 

 the standard sound is the key-note. It is also 

 known by universal experience, that ascending or 

 descending the scale from any given key-note, we 

 come (after passing over six notes, which our ears 

 recognise as belonging to that scale) to a note 

 which we at once hear to be identical with the 

 note from which we started in everything except 

 pitch. The interval, or distance between this 

 note and the key-note of which it is the replicate, 

 we call an octave j and the interval between the 

 key-note and any of the intermediate notes is called 

 a second, a third, &c., according to the position of 

 these notes the second being the interval between 

 the key-note and the note next above it. If tl 

 notes forming the intervals of which we have been 

 speaking be sounded successively, it will be at 

 once recognised that some of them are agreeable 

 or consonant, and some disagreeable or dissonant^ 

 the former being called concords, and the latter 

 discords. It will also be noticed that the degree 

 of consonance or dissonance varies some of the 

 discords being harder than others, and some of the 

 concords sweeter than others, so that one or two 

 of the intervals seem to lie on the borderland' 

 between consonance and dissonance, shewing 

 that these two sensations differ only in degree 

 like heat and cold, and not in kind. Further, the 

 two notes forming some of the concords are much 



* This is according to the lowest pitch in use. Unfortunately, 

 there is no unanimity as to what the standard pitch should be it 

 varies as much as half a tone in different countries. 



