Simple Tones and Their Basic Properties

Beiträge zur Akustik und Musikwissenschaft, edited by C. Stumpf:

1. W. Köhler, Acoustic Investigations I, 1909, no. 4.
2. P. Liebermann and G. Revers, On Orthophony, 1909, no. 4.
3. W. Köhler, Acoustic Investigations II, 1911, no. 6.
4. C. v. Maltzew, The Recognition of Successively Presented Musical Intervals in the Outer Tone Regions, 1913, no. 7.
5. C. Stumpf, On Recent Investigations in Tone Theory, 1915, no. 8.

Simple tones differ from one another in their strength and pitch. This, it would seem, uncontroversial proposition has in recent times undergone a certain substantial change in the circles of psychologists: to the simple tone, besides its strength and pitch, certain other primary qualities are ascribed. Most of the works belonging here were produced in the laboratory of Professor C. Stumpf in Berlin and printed in his journal;² below are summaries of these works.

If, beginning with some initial simple tone, we proceed successively to increase the number of its vibrations, then we shall pass to tones differing more and more from the initial tone. Soon, however, we shall notice that the progressive raising of the tone leads to the fact that it begins more and more to resemble the original tone, and this resemblance reaches a maximum when the two tones stand to one another in octave relations. Transposing some musical phrase by an octave does not essentially change it. Wishing to sing some familiar melody for us, we not infrequently make a mistake by one or two octaves, quite without noticing it. The facts enumerated and similar ones lead to the thought that two tones standing in octave relations differ from one another, but at the same time also have something common, similar. That which two octave tones have in common psychologists attribute to their quality (Qualität); that which distinguishes two octave tones from one another psychologists now ordinarily call not pitch, but brightness (Helligkeit).

The circumstance that octave sounds have something in common and at the same time something that differentiates them has long been known, and if psychologists have now found themselves compelled, on this basis, to distinguish the quality and brightness of a tone, this is connected with certain new facts. In work 2 a case is cited of a pathological change of hearing, when the principal properties of the tone, brightness and quality, were separated from one another. In one intelligent patient with good musical hearing it could be established that one of his ears, at times, during attacks of the illness, did not distinguish any interval properties within the limits of \(g^2—dis^4\), while distinctions of pitch remained unchanged. One must suppose that such a separation is encountered not only in pathological cases; to this there evidently also belongs the extensive class of “unmusical” people, who without difficulty distinguish brightness (pitch), but do not understand the quality of sounds. At the extreme limits of sounds for our hearing we all suffer from this: above the sounds \(c^5\) we still catch that one sound is higher than another, but the quality of the sound seems ever more and more dimmed. Especially interesting is the region passing over to the higher sounds, when we are still capable of distinguishing quality and interval, i.e. in the second half of the fourth octave and the first half of the fifth octave: here, as the pitch rises, the tone is judged to be lower, and in connection with this the interval between two octaves as closer than corresponds to the number of vibrations. E. Maltseva dealt with this question, presenting a very thorough investigation (4). Maltseva proved that if to the tone \(c^4\) we take a tone with a doubled number of vibrations, then the result obtained is not the interval of an octave, but an interval judged by us as a major seventh. Similar relations Maltseva also assumes in the regions of sounds passing over to the low limiting sounds.

Besides the noted “quality” (Qualität) of the tone, another fundamental property is ascribed to the latter—namely “vocality” (Vokalität). If we wished to arrange our vowels in a certain order, then, as has already often been noted before, for the most part we would arrive at this order: У, О, А, Е, И—in this order it would seem to us that we pass from a lower sound to a higher one. The majority of acousticians have encountered the fact that in a simple tone there is sometimes heard a cha-

character of a vowel sound; thus, for example, a tuning fork sounds on the vowel “U.” It has long been maintained that, if one raises the tone successively, one can hear the whole series of vowels: U, O, A, E, I. This question has been worked out in great detail by Köhler (1 and 3). Köhler proves that at certain points of a continuously rising series of tones we hear vowels with complete distinctness, and these definite points are separated from one another by an octave. Vowels are heard well and distinctly only at tones of a definite pitch, namely: $c^1$—“U,” $c^2$—“O,” $c^3$—“A,” $c^4$—“E,” $c^5$—“I.” If we take not the indicated tones but intermediate ones, for example, then we shall hear an indefinite vowel, since it will be intermediate between U and O. In exactly the same way, $g^1$ gives a vowel intermediate between O and A. Thus it is evident that only in a few definite places can we distinctly perceive the principal character of a tone; for the most part it is difficult to determine. This also explains why, up to now, this new quality of tone, its Vokalität, has not been established with certainty. The many-sidedness of tone, with its properties of brightness and quality, leads Stumpf (5) to the thought that these two properties developed against the background of the evolution of animal forms at different times. The same, as is now becoming clear, should be accepted with regard to light sensations: a colorless sensation is of earlier origin than a colored one. The earliest form of auditory irritation was probably noise; periodic vibration, especially sinusoidal vibration, is a later product. Together with the appearance of smooth, even sounds there must have developed the capacity to distinguish the pitch (brightness) of a sound. Physiological experiments of recent times teach that animals, for example dogs, distinguish sounds extremely finely by their pitch; but in them the capacity to distinguish quality is still absent or poorly developed. Subsequently, together with the development of the central nervous system in the direction of the hemispheres, in man the capacity to distinguish quality in tones becomes more and more definite and, in the historical epoch of our life, leads us to the establishment of our musical intervals.

A. Samoilov.