Scan 16
The New Encyclopedia Of Music And Musicians, 1929
28 lines. Read by computer on 18 September 2026. No printed page number was found. See the scan on archive.org.
1between nodes (points relatively at rest) and loops (points relatively in motion or agitation).
3Musical Acoustics is that part of the larger science which deals with sound-phenomena as employed in the practical art of music. It confines itself almost wholly to the study of tones and tone-production, the latter being effected through various materials, natural or artificial, having the property of elasticity. The topics in this field that call for emphasis here are (1) the essential characteristics of tones, by which they are defined and classified for artistic purposes, (2) the special systems of tones that music uses in forming melody and harmony, and (3) various points about tone-producing agencies (instruments), including the factor of resonance.
5(1) Tones may be compared (a) in pitch, (b) in quality or timbre, (c) in loudness and (d) in duration. When assembled in music they have the general aspects of 'tune' and 'time,' the former involving features of pitch and quality, the latter those of loudness (accent) and duration (metric units and patterns).
7(a) Pitch depends on the frequency or rate of the tone-producing vibrations. If the rate is relatively quick, the tone is acute or 'high,' but if relatively slow, the tone is grave or 'low.' Any given tone can be designated by its vibration-number (the number of vibrations per second required to produce it) or by some technical name or description that connects it with the customary nomenclature of musical theory. In the latter case the pitch is defined by stating what is its acoustical relation to an accepted tone of reference or system of tones. Such relation is expressed either by the ratio between the vibration-numbers of the tones in question or by naming the 'interval' by which the ear regards them as 'separated.'
9The use of terms of space, like 'interval' or 'distance,' as well as 'high' and 'low,' is obviously metaphorical. Tones have no location except as represented by notes on a page or keys on a keyboard.
11Common tones of reference are 'middle C' (theoretically 256 or 264 vibrations per sec.) and 'standard A' (435 vibrations, by international agreement).
13The pitch-range or compass of the human voice (men and women) extends from about 40 to 2000 vibrations (including extreme cases). Ordinary chorus-music ranges from about 80 to 875 (low E to high A). The orchestra ranges from about 35 to over 4500 (double-bass to piccolo), which is also approximately the range of the piano and the organ.
15Many remarkable cases of voices of wide range have occurred in the history of operatic singing. To these is now added that of an Austrian man who has command of a range of five octaves and a third (f₁—a₂).
17The interval (or relation) between tones having the same vibration-numbers is called that of the unison or prime (1:1 or 1/1). Such tones tend to blend into complete unity. If two tones have vibration-numbers in the ratio of 1:2 or 2/1, the interval between them is called that of the octave. Such tones seem to the ear repetitions or replicates, differing in plane or register rather than in character. Hence in classifying intervals it is usual to take only those less than an octave, since all larger ones can be reduced to these.
19Within an octave the number of possible tones is theoretically infinite. But practical music undertakes to use at any one time only certain sets of tones having definite relations with each other. Such a set of tones, arranged in order of pitch, is called a scale. The total schedule of selected tones is called a system. See Scale and also under (2) below.
21(b) Quality, Timbre or Tone-Color depends on the form of the tone-producing vibrations. Tones are rarely produced by simple or typical vibrations—those which, when plotted, have a uniform contour (what is called a curve of sines). The general motion to and fro is periodic, but the details within the period are usually highly complex, and this complexity persists in tones of a given character. Analysis shows that the complexity results from compounding or superimposing two or more simple vibrations. This is confirmed by the fact that a tone that the ear at first accepts as a unit can often be resolved into two or more component tones, and also by the fact that a tone of a given character can be synthetically produced by uniting two or more simple ones.
23Hence arises the theory that differences of quality are due to varying unions of partial-tones (also called, less happily, overtones or harmonics). The differences depend on what partials are included and in what relative intensity or loudness. It appears, further, that the partials are regularly taken from a series whose vibration-numbers are proportional to the numbers 1, 2, 3, 4, 5, 6, 7, 8, etc. (i.e., with any fundamental tone, 1, may be grouped its octave, 2, its second and third octave, 4, 8, and certain other tones, 3, 5, 6, 7, etc.). The first eight partials are most important, but the character of many tones is due to the presence of higher partials.
25(c) Loudness, Intensity or Force depends on the amplitude of the tone-producing vibrations and this in turn on the degree of energy in the force producing them. There is no practical way of defining the contrasts and gradations of force used in music except by such loose terms as forte and piano, crescendo and diminuendo, etc. Yet it is evident that relative loudness plays a large part in the complex artistic device of rhythm, which is common to both music, verse and dancing. In music, tones in succession are gathered into groups by means of accent or stress (relatively great loudness), and that which gives effect to nuances is largely a skillful distribution of different intensities.
27(d) Duration is properly not a characteristic of tone, but one of its accidents. Yet in music both the absolute and the relative time occupied by tones is critically significant, since music is a time-art (like dancing and versification) and not a space-art (like sculpture and drawing). The tempo or pace of performance depends on the absolute duration adopted for the time-units in construction, and many effects are produced by studied gradations or contrasts in this absolute rapidity. Furthermore, the order and in-
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