Part 4 (2/2)

The whistling of the wind, the plas.h.i.+ng of water, the rattling of a wagon are noises, but musical instruments give us tones. When, however, many untuned instruments sound together, or when all the keys within an octave are struck on the same time, then it is a noise that we hear. Tones are therefore more simple and regular than noises. The ear perceives both by means of the agitation of the air that surrounds us. In the case of noise the agitation of the air is an irregularly changing motion. In musical sounds, on the other hand, there is a movement of the air in a continuously regular manner, which must be caused by a similar movement in the body which gives the sound. These so-called periodical movements of the sound in the body, rising, falling and repeated at equal intervals, are called vibrations. The length of the interval elapsing between one movement and the next succeeding repet.i.tion of the same movement is called the duration of vibration (_Schwingungsdauer_), or period of motion.

TONE, AND ITS LAWS OF VIBRATION

A _tone_ is produced by a periodical motion of the sounding body--a _noise_ by motions _not_ periodical. We can see and feel the sounding vibrations of stationary bodies. The eye can perceive the vibrations of a string, and a person playing on a clarionet, oboe, or any similar instrument, feels the vibration of the reed of the mouthpiece. How the movements of the air, agitated by the vibrations of the stationary body, are felt by the ear as tone (_Klang_), Helmholtz ill.u.s.trates by the motion of waves of water in the following way: Imagine a stone thrown into perfectly smooth water. Around the point of the surface struck by the stone there is instantly formed a little ring, which, moving outwards equally in all directions, spreads to an ever-enlarging circle. Corresponding to this ring, sound goes out in the air from an agitated point, and enlarges in all directions as far as the limits of the atmosphere permit. What goes on in the air is essentially the same that takes place on the surface of the water; the chief difference only is that sound spreads out in the s.p.a.cious sea of air like a sphere, while the waves on the surface of the water can extend only like a circle. At the surface the ma.s.s of the water is free to rise upward, where it is compressed and forms billows, or crests. In the interior of the aerial ocean the air must be condensed, because it cannot rise. For, ”in fact, the condensation of the sound-wave corresponds to the crest, while the rarefaction of the sound-wave corresponds to the sinus of the water-wave.”[7]

The water-waves press continually onwards into the distance, but the particles of the water move to and fro periodically within narrow limits. One may easily see these two movements by observing a small piece of wood floating on water; the wood moves just as the particles of water in contact with it move. It is not carried along with the rings of the wave, but is tossed up and down, and at last remains in the same place where it was at the first. In a similar way, as the particles of water around the wood are moved by the ring only in pa.s.sing, so the waves of sound spread onwards through new strata of air, while the particles of air, tossed to and fro by these waves as they pa.s.s, are never really moved by them from their first place. A drop falling upon the surface of the water creates in it only a single agitation; but when a regular series of drops falls upon it, every drop produces a ring on the water. Every ring pa.s.ses over the surface just like its predecessor, and is followed by other rings in the same way. In this way there is produced on the water a regular series of rings ever expanding. As many drops as fall into the water in a second, so many waves will in a second strike a floating piece of wood, which will be just so many times tossed up and down, and thus have a periodical motion, the period of which corresponds with the interval at which the drops fall. In like manner a sounding body, periodically moved, produces a similar periodic movement, first of the air, and then of the drum in the ear; the duration of the vibrations const.i.tuting the movement must be the same in the ear as in the sounding body.

THE PROPERTIES OF TONE (KLANG)

The sounds produced by such periodic agitations of the air have three peculiar properties: 1. STRENGTH, 2. PITCH, 3. TIMBRE.

The strength of the tone depends on the greater or less breadth of its vibrations, that is, of the waves of sound, the higher or lower pitch of the tones upon the number of the vibrations; that is, the tones are always higher the greater the number of the vibrations, or lower the less the number of the vibrations.

A second is used as the unit of time, and by number of vibrations is understood the number of vibrations which the sounding body gives forth in a second of time. The tones used in music lie between 40 and 4000 vibrations per second, in the extent of seven octaves. The tones which we can perceive lie between 16 and 38,000 vibrations to the second, within the compa.s.s of eleven octaves.

The later pianos usually go as low as C1 with 33, or even to A2 with 27 vibrations; mostly as high as a4 or c5, with 3520 and 4224 vibrations. The one lined a, from which all instruments are tuned, has now usually 440 to 450 vibrations to the second in England and America. The French Academy, however, has recently established for the same note 435 vibrations, and this lower tuning has already been universally introduced in Germany.[8]

The high octave of a tone has in the same time exactly double the number of vibrations of the tone itself. Suppose, therefore, that a tone has 50 vibrations in a second, its octave has 100 in the same time; i.e., twice as many. The octave above this has 200 vibrations, &c. The Pythagoreans knew this acoustic law of the ascending tones, and that the octave of a tone had twice as many vibrations in a second as the tone itself, and that the fifth above the first octave had three times as many; the second octave, four times; the major third above the second octave, five times as many; the fifth of the same octave, six times; the small seventh of the same octave, seven times. In notation it would be thus, if we take as the lowest note C, for example:

1:C 2:c 3:g 4:c 5:e 6:g 7:b? 8:c 9:d 16:c 32:c4

The figures below the lines denote how many times greater the number of vibrations is than that of the first tone. In the first octave we find only one tone; in the second, two; in the third, all the tones of the major chord with the minor seventh.

In the fourth octave we find sixteen tones (which, however, we divide in our system of music into twelve). Likewise, we find in the fifth octave thirty-two tones, which number is doubled in the sixth. Hence, the Greeks had quarter and eighth tones, which we in our equal-tempered tuning have done away with.[9]

The production of a higher pitch in a tone rests in all sounding bodies upon the uniform law which we may observe in the strings of musical instruments, whose tones ascend either by greater tension, by shortening, or through a diminution of the density of the strings.

THE TIMBRE (KLANGFARBE) OF TONES

Strength and pitch were the first two distinctions of different tones. The third is the timbre. When we hear one and the same tone sounded successively upon a violin, trumpet, clarionet, oboe, upon a piano, or by a human voice, &c., although it is of the same strength and of the same pitch, yet the tone of all these instruments is different, and we very easily distinguish the instrument from which it comes. The changes of the timbre seem to be infinitely manifold; for, not to mention the fact that we have a mult.i.tude of different musical instruments, all which can give the same tone, letting alone also that different instruments of the same kind as well as different voices show certain differences of timbre, the very same tone can be given upon one and the same instrument, or by one and the same voice, with manifold differences of timbre.[10]

As now the strength of the tone is determined by the breadth of the vibrations, and the pitch by their number, so the varieties of timbre are ascribed to the different forms of the waves of vibration. For as the surface of the water is stirred differently by the falling into it of a stone, by the blowing over it of the wind, or the pa.s.sing through it of a s.h.i.+p, &c., so the movements of the air take different shapes from sounding bodies. The movement proceeding from the string of a violin over which the bow is drawn, is different from those movements caused by the hammer of a piano or by a clarionet.

OVER-TONES (OBERToNE)

That timbre is dependent on the form of the vibrations is confirmed by Helmholtz, and acknowledged as so far correct that every different timbre requires a different vibratory form, but different forms sometimes correspond to nearly the same timbre.

But how far the different forms of vibration correspond with different timbres, Helmholtz shows by a fact which has. .h.i.therto escaped the notice of physicists, although it forms the foundation of all music. We have learned by the stereoscope that we have two different views of every object, and compose a third view from those two. _Just so the ear perceives different musical tones which come to our consciousness only as one tone._

It is in general, and especially in the case of the human voice, very difficult to distinguish these single parts of tone, because we are accustomed to take the impressions of the external world without a.n.a.lyzing them, and only with a view to their use.

But when we are once convinced of the existence of partial tones (_Partialtone_), if we concentrate our attention, we can also distinguish them. The ear hears, then, not only that tone, the pitch of which is determined, as we have shown, by the duration of its vibrations, but a whole series of tones besides, which Helmholtz names ”_the harmonic over-tones_” of the tone, in opposition to that first tone (fundamental tone) which is the lowest among them all, generally the strongest also, and according to the pitch of which we decide the pitch of the tone. The series of these over-tones is for each musical tone precisely the same; they are, namely, the tones of the so-called acoustic series, arising, as already described, from the doubling of the vibrations.

First, the fundamental tone, then its octave with twice as many vibrations, then the fifth of this octave, &c.

The different timbre of tones thus depends upon the different forms of the vibrations, whence arise various relations of the fundamental tone to the over-tones as they vary in strength. The most thorough inquiries have led to the following results, of the first importance in every formation of tone: _that the appropriate form of the vibratory waves which is the most agreeable to the ear, as well as the fullest, softest and most beautiful timbre which corresponds to that form, is produced when the fundamental tone, and the over-tones following it, so sound that the fundamental tone and the over-tones sound together, the former most strongly, while the latter are heard fainter and fainter in the intervals of the major chord with the minor seventh, so that, with the fundamental tone, still further sound seven over-tones_. If the higher harmonic over-tones grow stronger, and even overpower the fundamental tone, the sound grows shriller, but when the discordant over-tones lying close together, higher than the tones just named, overpower the fundamental tone, the timbre becomes sharp and disagreeable.

But these over-tones are not to be confounded with the earlier known combination-tones (_Combinationstone_), which arise from the sounding together of two consonant intervals, and likewise have their own over-tones.

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