Tones have, first of all, the character that we call pitch; they lie, that is, up or down in the scale; they belong to the bass or the treble or to a middle region. The word ‘pitch’ means height; it is a term borrowed from perceptions of sight; and we cannot yet say certainly how it came to be applied to tones. Secondly, tones have the character of volume,—another borrowed word! The highest note on the piano seems shrunken, narrowed, pointed, as compared with the deepest note in the bass; and the difference comes out even more clearly with bottle tones. Thirdly, tones show a sort of recurrence. If you run your finger-nail quickly up the keyboard in a glissando, you perceive a change only of pitch and volume; but if you play the notes c, d, e in one octave and then in another and then in a third, you realise that all the sequences are alike; we talk, indeed, of playing the same notes in different octaves. This recurring character of tones is called tonality.
It has recently been stated that tones have a further character, that of vocality. Consider the series of vowels, U, O, A, E, I (voiced approximately as in the words moot, moat, mart, mate, meet); there is no doubt that U suggests a low bottle tone, and I a high whistle tone. Experiments seem to show that, as we go up the scale, the tones say M-M, U, O, A, E, I, S-S, F-F, CH (the sound in the Scotch loch); and, curiously enough, that they say these things at intervals of an octave; so that, when we have found a pure O, we find the pure A just an octave higher, and the tones that lie between give Oa, OA, oA, according to their position. The question is still in debate; for these experiments are opposed by others, and the whole subject of the nature of vowel-sounds is very thorny. It is quite clear that high and low tones sound definitely like U and I; but some of the other vowels are far less distinct; and the point of change from vowel to vowel does not appear to be as sharp and precise as the first experiments indicated. On the whole, we shall do best to suspend judgement.
There are some ten thousand simple tones in the complete tonal scale; but the compound tones employed by music are only about a hundred in number, and are selected from a middle range of hearing. The compound tone, as we have said, breaks up on analysis into simple partial tones; the lowest is called the fundamental, the others the overtones. It is a remarkable fact that the overtones always stand in a definite relation to the fundamental. The various musical instruments do not, however, sound all the overtones alike; their construction favours some, and weakens or destroys others; and that is the main reason why we can tell a harp-tone, for instance, from a tone of the same pitch played on oboe or trumpet. The compound tones thus owe their colour or timbre, in the first instance, to the number and relative loudness of the overtones which accompany the fundamental. Timbre has other factors; but this is the primary source of difference.
Overtones may readily be heard. Strike a c, very lightly, on the piano. When it has ceased to sound, strike loudly the c next below; you can probably, even at the first trial, hear the higher c in the lower. Now strike very lightly the g next above your higher c, and then the lower c again loudly; you will probably hear the g. Helmholtz, working with thin strings, was able to hear no less than fifteen overtones with the fundamental.
This blending of the partial tones in a compound tone, to give a single and unitary impression, is an example of what is called tonal fusion. The best fusion is that of two tones which constitute an octave; here, indeed, the blend is so close that it is often confused with unison; a soprano and a bass singer, told to sing in unison, will start off without hesitation an octave apart. Next after the octave stands the fifth (c and g); boys who think they are whistling the same notes often whistle, in fact, a fifth apart. Other pairs of tones give lesser degrees of fusion.
Tones generate as well as blend. If you sound together two high tones, such as you get from a double bicycle whistle, or from small bottles of different sizes, you hear, besides these tones themselves, a third tone, very much deeper, larger, more booming; this differential tone is easy to find and, once heard, cannot be mistaken. Only, the two tones must not be too nearly alike in pitch; for, if they are, you hear, instead of a differential tone, slow surges or quick rattlings of sound. Take two bottles of the same size, and mistune one of them by pouring in small amounts of water; have them blown steadily together; the course of the beats, as they are called, from a slow surge through a rattle to a harsh blur, may thus be followed.
Noises, which form a class of sensations distinct from tones, are nevertheless aroused by the same sort of stimuli. If a tonal stimulus is sounded for a very brief time, we hear a dry knock; if a large number of tonal stimuli are sounded all at once, we hear a buzz or crash. Noises have pitch; the spit of a pistol is higher than the crack of a rifle, and the sizzle of frying fat is higher than the murmur of falling rain; but no one has yet established a complete scale of noise.
The sensory cells are found in the inner ear, a tiny structure with an extremely complicated mechanism. Many different views of its action have been put forward. That which is most generally accepted was proposed by the German physicist H. von Helmholtz. The ear contains a narrow triangular membrane which carries many thousands of stiffish cross-fibres; and the theory is that the air-waves which impinge on the outer ear play, selectively, upon these fibres; every air-wave throws into vibration the fibre which is tuned to respond to it. A compound tonal stimulus is thus analysed by the membrane into a number of simple tonal stimuli, and every simple stimulus excites the nerve-fibril attached to its particular cross-fibre. This theory explains our ability to analyse compound tones into their simple components.
The ear is, however, more than an organ of hearing. It includes organs, of a very ancient type, which help to regulate our balance in walking, our precision in turning corners or avoiding obstacles, and so on. Each ear, for instance, has three little organs that resemble minute spirit-levels, set in the three planes of space, and that give us the sensation of ‘swimming’ when the head is sharply jerked, and the sensation of dizziness when we twirl on our heels. For the most part these organs act reflexly, without furnishing sensations; or at any rate furnish sensations of little strength, and of a pressure-like kind that blends indistinguishably with the kinæsthetic sensations from the tissues beneath the skin; but in the cases mentioned the swimmy, dizzy sensation may be noticed.
[§ 13]. Sensations from the Eye.—You may study tones by help of the piano and a few medicine bottles; but for the study of lights and colours you must go beyond household appliances, and secure a fairly large set of coloured and grey papers; sample-books may be obtained, very cheaply, from the manufacturers. You will notice, first of all, that as the world of sounds divides into tones and noises, so does the world of looks divide into what we have just called colours and lights. The colourless looks or lights may be arranged in a single straight line that passes from purest white through the greys to deepest black; they are, as sensations, older than colours, just as noise is older than tone. Colours are more varied. Consider, to begin with, the character of colour proper or hue, that is, the differences of colour that show in the rainbow. Hues may be arranged, not in one straight line, but in a square. Setting out, say, from red, you pass through red-yellow or orange to yellow; that is one straight line; setting out again from yellow, you pass through yellow-green to green; from green you pass through green-blue to blue; and finally from blue you come back, by way of blue-red (violet and purple), to the original red. Colours have, besides, two further characters, that bring them into relation with lights. They differ in tint, that is, in darkness or lightness; brown is darker than yellow, sky-blue is lighter than navy-blue. They differ also in saturation or chroma, that is, in poorness or richness of hue; pinks and yellows look faded and washed-out as compared with rich reds and blues. Tint brings colours into relation with lights, because, if we can say that a colour is darker or lighter than a particular grey, we can also find some grey that matches it in darkness or lightness; and chroma brings colours into relation with lights, in the sense that the better chroma is farther off from colourlessness (that is, from grey) than the poorer chroma of the same hue and tint.