take the timbre of o, and the most skilful artists are not able to sing all the vowels in these tones with equal clearness and purity. The female voice, therefore, has only a few tones more than an octave, upon which every one of the vowels can be distinctly sung; and again, all these tones do not afford an equally sonorous tone with every vowel.
As unfortunately our Song composers do not always keep this fact in view, as the old Italians did, and since words with the most unfavorable vowels often underlie the notes, it as often becomes necessary to mingle with the unfavorable vowel something of the sound (Klang) of the vowel properly belonging to the note; as, for example, in the word “ring” upon f2
, to sing the i with a mixture of the sound (Klang) of a. Artists do this in a way of which they are for the most part unconscious, and which is always unobserved by the hearer. That in every voice there are several tones upon which every vowel sounds well, finds an explanation in an observation of Professor Helmholtz. The ear is attuned to a certain tone, designated as e4 f4. To persons with very susceptible nerves these tones are often insupportable, and we often see dogs, whose sense of hearing is especially acute, run howling away when the above e4 is struck upon a violin, while to other tones they seem wholly insensible. But all the tones which are accompanied by that tone as an over-tone to which the ear is attuned, sound harmonious even with unfavorable vowels.
PARTIAL TONES
But beside the over-tones, which sound with every good, simple sound, there are other partial tones, which, like the long-known combination tones, do not usually present themselves to our consciousness. Combination tones were first discovered in 1745 by the organ-builder, Sorge. By an act of concentrated attention one hears these tones at the accord of two different tones. They lie always lower than the interval to which they belong, and arise from the meeting of the nodes of vibration of the tones producing the interval. The node of vibration is the name of that place where, after every completed vibration, the sounding body returns to its former position. When, for instance, we give the third c1 e1, we hear the c, lying an octave lower than the third, sounding at the same time as a combination tone. For the tone c1 a string has two vibrations, while in the same space of time e1 has three. The vibration node of the c1 will thus, after two vibrations, coincide with the vibration node of the e1. By the coincidence of these nodes of vibration is produced the number of vibrations requisite for the c below. Besides these combination tones there are summation tones, discovered by Helmholtz, which arise from the vibrations collectively (Gesammtzahl) belonging to the above interval, and are higher than the interval. Both kinds of partial tones have again their faint over-tones.
BEATS (DIE SCHWEBUNGEN)
We have explained the movements of the waves of sound by the movements on the surface of water, and we know that, instead of the billows and hollows that we have in the water, the air is condensed and rarefied. We know further that if two different lines of waves run along with one another, their crests and hollows fall together, and their crests become as high again and their hollows as deep again. So two tones from different sources of sound are twice as strong when they are both equally high, and a new tone of the same height added to them will still further increase the sound. But when two agitations of the surface of the water so move that the crests of one fall into the hollows of the other, their movements neutralize each other. The same thing happens in tones when one is not struck until half the vibrations of the preceding tone are concluded. But if the sounding bodies vary in only a small part of a vibration sound, they will be alternately stronger and weaker, and this is termed beats (Schwebungen), which are only produced by tones very near to each other. Those intervals whose combination and over-tones so fall together that many beats are produced, sound harsh and disagreeable, and we call them dissonances.
Those intervals in which few or no beats occur are called consonances. As the combination or interfering tones, as well as the beats, have importance and interest only in harmonizing several voices, in tuning pianos, as well as in composition in general, and as we have in view in these pages only the culture of single voices, we cannot further enlarge on these discoveries, interesting as they are. According to the purpose of this little work, I introduce only so much of the latest investigations and discoveries as will help to show the prevailing evils of our mode of teaching singing, and, by their practical application to the business of instruction, serve to improve the vocal art. But whoever has an interest in this branch of science will find in the invaluable work of Helmholtz, “Die Lehre von den Tonempfindungen,” an abundance of most interesting observations and of the most thoroughly scientific illustrations of the theory of music, and of those processes in the domain of tone which we have hitherto always felt, but never understood.