On the Sensations of Tone (Dover Books on Music)
Language: English
Pages: 608
ISBN: 0486607534
Format: PDF / Kindle (mobi) / ePub
On the Sensations of Tone
is one of the world's greatest scientific classics. It bridges the gap between the natural sciences and music theory and, nearly a century after its first publication, it is still a standard text for the study of physiological acoustics — the scientific basis of musical theory. It is also a treasury of knowledge for musicians and students of music and a major work in the realm of aesthetics, making important contributions to physics, anatomy, and physiology in its establishment of the physical theory of music. Difficult scientific concepts are explained simply and easily for the general reader.
The first two parts of this book deal with the physics and physiology of music. Part I explains the sensation of sound in general, vibrations, sympathetic resonances, and other phenomena. Part II cover combinational tones and beats, and develops Helmholtz's famous theory explaining why harmonious chords are in the ratios of small whole numbers (a problem unsolved since Pythagoras).
Part III contains the author's theory on the aesthetic relationship of musical tones. After a survey of the different principles of musical styles in history (tonal systems of Pythagoras, the Church, the Chinese, Arabs, Persians, and others), he makes a detailed study of our own tonal system (keys, discords, progression of parts).
Important points in this 576-page work are profusely illustrated with graphs, diagrams, tables, and musical examples. 33 appendices discuss pitch, acoustics, and music, and include a very valuable table and study of the history of pitch in Europe from the fourteenth to the nineteenth centuries.
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whereas the low compound tone itself cannot be considered as the partial of another much higher tone. In the first half of last century, when the minor chord was first used as a close, composers endeavoured to give pro minence to the tonic by increasing the loudness of the tonic note in comparison with its minor Third. Thus in Handel’s oratorios, when he concludes with a minor chord, most of the conspicuous vocal and instrumental parts are concen trated on the tonic, while the minor Third is
equally well distinguishable by our sensations. Such a graduation is possible for all our sensations, as Fechner has shewn in his investigations on psychophysical laws. We find such graduations used for the divisions of musical rhythm, and the astronomers use them in reference to the intensity of light in determining stellar magnitudes. Even in the field of musical pitch, the modern equally tempered chromatic scale presents us with a similar graduation. But although in certain of the less usual
reaches a maximum and then decreases. To express this, the value of s must be also multiplied by a factor, which vanishes when the number of beats is small, attains a maximum for about 30 beats in a second, and then diminishes, and again vanishes when the number of such beats is infinite. Suppose then that the roughness rp, due to the pth partial tone, is expressed by The factor of sp reaches its maximum value = 1, when ; and becomes = 0, when δ, that is, half the interval between the two tones
strike the opposite wall, are again reflected, and so on till they die out. We have to imagine that from the mouths of men and from the deeper musical instruments there proceed waves of from 8 to 12 feet in length [c to F], from the lips of the women waves of 2 to 4 feet in length [c″ to c′], from the rustling of the dresses a fine small crumple of wave, and so on; in short, a tumbled entanglement of the most different kinds of motion, complicated beyond conception. And yet, as the ear is able
tones are really agitating the membrane, we must after all place the bottle with its mouth downwards and strew sand on the membrane. However, when the bottle is of the right size, and the membrane uniformly stretched and fastened, it is only the prime tone of the membrane (slightly altered by that of the sympathetically vibrating mass of air in the bottle) which is easily excited. This prime tone can be made deeper by increasing the size of the membrane, or the volume of the bottle, or by
