is heard. It is gradually moved nearer till the tone is heard. The distance apart is noted. Then it is placed close to the first coil, a loud tone being heard, and is gradually moved away till the tone is lost. The average of the two results gives a figure for the deafness of the person.

For rough tests a watch is often used. The watch is steadily brought nearer to one ear (the opposite one being closed) till the tone is heard. The distance of the watch from the ear indicates the threshold for sound, or the degree of deafness. This method is very unreliable, the chief difficulty being the disturbance by outside noises.

A special notation has been invented to indicate tones. The first complete notation for pitch is attributed to Guido Aretino in the eleventh century. Three centuries later the notation for duration was introduced by Jan de Meurs. Naturally the presence of exact means of expression for these two quantities afforded opportunity for progress in the artistic execution on the one hand and for scientific research on the other. The subject of pitch has reached a high degree of development. The duration of tones is also a matter of technique that has been carried to a great degree of precision in practice.

We are all familiar with the staff notation for pitch and duration. Each note indicates a certain tone of a definite pitch lasting through a definite time.

The intensity of tones has been neglected; it must be remembered that we are not speaking of the semiconscious use of the different degrees of intensity in the execution of a piece of music, but to a deliberate use of

the shades of intensity. In music the consideration is confined to the five vague expressions, ff, f, m, p, pp. When a group of tones is to be made rather loud, put an fover it. How loud? just as the performer feels. All of the same loudness? just as the performer is inclined. Are all the tones without these letters to be of the same strength? just as the performer is disposed. These five vague grades cover only a few tones out of the thousands in a piece of music. The composer is powerless to give any indication of the wonderfully delicate shadings in the intensity of the different members. of a group of tones; the performer is left without help. Two good performers on the organ will execute the same music with utterly different effects, because they do as they please with the intensity of the tones. Which effect did the composer intend? Nobody knows.

It is to overcome this difficulty that I propose a system of notes to include shades of intensity. Suppose, for the present, that we agree upon nine grades of in

FIG. 83.-Method of Indicating Intensity in Notes; Loudest by Black, Weakest by White.

tensity between the weakest and the strongest the instrument is successfully capable of. Then we can introduce a system of shading the heads of the notes to indicate grades of intensity just as the heraldist uses shading to indicate colours. Such a system is shown in Fig 83.

The head of the note ought not to be used to

indicate duration. In the present system duration is shown by the hooks on the stems of the

notes, except in the case of the whole and half-notes, where a difference is made in the head of the note. This change in the head of the note is unnecessary for the indication of duration and can be employed to indicate intensity. A very slight change is thus necessary in the present notation; we can retain the usual method of indicating pitch and the usual signs for duration with the exception of the two for the whole note and the half-note. These can be indicated by two lines across the stem of the ordinary quarter-note for the whole note of Notes Ac- and one for the half-note. Consequently Duration. the series of notes as regards duration will be that shown in Fig. 84, representing the whole, half, quarter, eighth, sixteenth, and thirty-second notes respectively.

FIG. 84.-Series

cording to

Now we can use the head of a note to indicate its intensity, and even its form. Suppose we wish to indicate a half-note of medium constant intensity, we have ; ; or an eighth-note of loud intensity and staccato form, ; or a whole note, weak, but of cres

cendo form, f.

Where are the tones we hear? With one ear closed the sounds we hear have no definite position. We know that a certain rattling must be down on the street, because waggons cannot be up in the air the

But a plain Take a seat in hold your head Put your finger

song of a bird cannot be under our feet. tone is nowhere, or rather, anywhere. this high-backed chair; let some one firmly so that you cannot turn it. tightly in one ear and close your eyes. Now I make clicks with a snapper sounder, or I strike a glass with a spoon. Point to where the sound is. If I vary the intensity of the sound so that you cannot reason the the matter out, your answers are generally wrong.

By turning the head you can get an idea of the place because you know that sounds straight out sidewise are stronger than in any other direction.

Open both ears but keep the eyes closed. Now you can tell me just where the sound is. You draw, unconsciously, an inference from the relative intensity of the two sounds from the two ears. But whenever I snap the sounder equally distant from the two ears, you are always wrong. Imagine a sheet of glass passed through the body dividing it into two halves symmetrically. For all sounds in this plane you are utterly at a loss. I snap my sounder under your chin; you declare that it is behind your back. I snap it at your feet; you say it is in front of your nose.

TH

W

CHAPTER XII

COLOUR

HE number of different colours that we can distinguish in nature probably amounts to several hundred thousand. Suppose we had all of them to arrange in a consistent system. We find among them a series of colours ranging from white through grey to black, that show no traces of red, green, blue, or other of the what we have been accustomed to regard as the specific colours. These are the "neutral" colours. With white at one end and black at the other all the neutral colours including the greyish whites, the medium greys and the greyish blacks would be indicated by points along a line ( WBk, Fig. 85).

BK

FIG. 85.-System of Greys or Neutral Colours.

Now let us pick out all the brightest and purest colours and arrange them by likeness. Beginning with red we put next to it a slightly different red, again a slightly dif ferent one, and so on; soon we find that we have passed to orange, From orange we pass to yellow, then to green, blue, and purple. If we use several hundred different colours, the differences between successive