However, these problems of strength of materials are by no means all of the pretty mechanics in the piano. The really fine work that goes into the nicely balanced levers between the keys struck by the pianist's fingers and the hammers that strike the strings is the result of centuries of invention, and reached perfection only comparatively a few years ago. It requires fully fifty parts to this mechanism for every single key of a fine piano.

Tuning a piano requires not only knowledge and skill but a fine "ear" able to detect close shades of pitch. When two strings of almost but not quite equal pitch are sounded together they produce not only a discord but what are called "beats," which are alternate loud and soft impulses of sound. For suppose at a certain instant they vibrate together; then the denser and rarer layers of air formed by the two come together, and the sound is loud. But as the string of quicker vibration gains on the other, presently it will send out a rare layer of air when the other string sends a denser layer, and the combined sound will be very weak. The nearer the two strings agree in pitch, the slower will be the beats, until they come so far apart as to be lost. Piano tuners hear the beats very much clearer than other people do and use them to aid in tuning the many double and triple string groups to unison.

If any scale is tuned exactly right, the numbers of vibrations would be related as follows:

But now suppose the scale of C on the piano should be tuned just as above. Then consider what would happen to the scale of G which would begin on Sol of the scale of C. From Sol to La of the C scale becomes Do to Re of the G scale, but the numbers of vibrations are as 36 to 40, or 9 to 10, while they should be as 24 to 27, or 8 to 9.

Similar troubles would come at every point in the tuning of a piano. The tuning that is exactly right for any one scale is all wrong for all the others. Piano tuners get over this difficulty by tuning all of the scales a little wrong so that while none of them will be perfect the error will not be large enough to be disagreeable to the ears of most people. On this scheme we have the following as the best possible relations of the vibration numbers, which may be compared with those just given and now repeated.

Do Re Mi

Sol La

Fa Si Do Tempered Scale 24 26.939 30.238 32.036 35.959 40.363 45.306 48 True Scale..... 24 27 30 32 40

36

45 48

The upper row of numbers gives what the great composer Bach called the "well-tempered scale." The lower row is the true scale. Probably no piano tuner gets his scales exactly like these figures in the top row, but they give what he should aim for. Once he tunes one octave properly, all the others can be tuned from it very easily, for the notes of the same letters must sound in unison together.

As a practical thing in tuning, the interval from Do to Fa is tuned just a bit sharp and that from Do to Sol

just a bit flat, and every note of the whole keyboard can be covered by stepping off with these two intervals. Organs, of course, like pianos must be tuned with tempered scales.

The human voice is attuned in a manner very different from that of any common musical instrument. For instead of having many strings or pipes or keys, it has but one device for all its pitches. It tunes instantly from pitch to pitch by altering the tension of two elastic bands situated edge to edge in the larynx. One can feel the larynx as a hard lump in the neck. It stands at the upper end of the windpipe, the tube which brings up the air from the lungs. As the air is forced between the two elastic bands just mentioned, the sound of the voice is made. These bands, called the vocal chords, are about half an inch long in women and three quarters of an inch in men. They are also thicker in men's vocal organs. This greater length and greater thickness combined give the lower pitch to men's voices. Similarly, the low pitch strings of the piano are heavy and long, compared to those of the treble.

CHAPTER XVI

THE STORY OF THE OLD SHOES

One Sunday two old shoes sat in a cobbler's window. A colored man had brought them in to mend, but the cobbler had not finished them on Saturday as he had promised. So the two old shoes sat looking rather seedy and melancholy waiting for something to hap pen to them.

"Hey, old gentlemen," said a smart pair of newsoled shoes that some one had failed to call for. "You have a foreign appearance, as if you had been born in another country. It is tiresome to wait all day in this stuffy shop. Tell us a story. We'll warrant you remember something interesting."

"That we do," said the old shoes, "for we were made in England from South American leather and worn first in Sweden. We have forgotten some of the sights we have seen, but you American shoes would surely be surprised at the things we could tell you."

"Oh! fine! Go ahead," said the smart new-soled shoes; and a pair of girl's pumps that had come for a few stitches exclaimed: "How interesting! We love to hear about travels. How we wish we could dance with the First Officer's shoes on an ocean steamer like a pair of pumps we know!"

Naturally the poor old shoes felt quite proud to receive all this attention from the young folks and so they began their tale as follows:

"Far down the map of South America there is a land called Patagonia, owned partly by Chile and partly by Argentina. The Chileans have a fast-growing little city called Punta Arenas down at the very tip end of Patagonia. Near by there, on a great ranch almost in sight of the Strait of Magellan, lived the steer who gave us our first pair of soles.

"One day our steer, with many others, was driven onto a big rowboat called a lighter and after being tossed about in a strangely sickening way while some men with very long oars rowed the boat out a little way from land, our steer, to his prodigious astonishment, was jerked up by a rope slip-noose over his long horns. After swinging for a moment in a terrifying manner high in air, he was lowered very quickly and found himself on all four legs again inside a dark evilsmelling sort of stable on a lower deck of a little steamship.

"Then began for him a horrible experience. He had lived on a vast open prairie-like place, swept by fine free winds, warmed by plentiful sunshine. Now began a voyage which soon led into a terrible ocean where the waves were like mountains, the rain came in torrents, and the sun hardly ever shines.

"Some of the cattle died, but the others, though they grew sad-looking and lost their wild free ways, at