Page:Popular Science Monthly Volume 15.djvu/868

848 survival of the fittest, is made admirably clear by the graphical method of plotting the scale on paper; using the logarithms of the intervals for magnitudes. By the same method the complexities of the chromatic scale and of equal temperament are made easily comprehensible to careful reading.

After briefly considering the questions of time and form (Chapter XIII.) the structure of music (Part III.) is taken up. What use is made of the scales whose origin is traced in Part II.? What is due to natural laws, what to aesthetical influences? The position taken with regard to melody does not seem as strong as it might be. "The earliest forms of music probably arose out of the natural inflections of the voice in speaking." This is Spencer's theory. It is not mentioned that Darwin combats this, placing the origin of melody in the love-songs of man's early ancestors, before speech began; or that Helmholtz attributes the expressiveness of melody to its motion, which translates into vocal ordinates, as it were, the varying intensities of the emotions. It is shown in the "American Naturalist" (April, 1879, "Animal Music," etc.) that if the overtone structure of sounds has impressed itself upon the internal ear, the most easy progression of a melody will be along the intervals existing between overtones, viz., octaves, fifths, fourths, etc. This offers a much more natural basis for melody and scale origin than the theory of Helmholtz, repeated by Mr. Pole, according to which a certain connection is established between notes, an octave, a fifth, etc., apart by the. mind's recognition of their possessing common overtones. This is a psychological, not a physiological basis.

In treating harmony, the natural element, viz., the rough beating of dissonant tones, is given due emphasis, and the dominance of aesthetical arbitrariness over this natural element fully shown. The fallacy of the argumentum, ad aurem, so much used by theoretical musicians, is exposed. In the simplest elements of music the ear has no doubt been the guide, but the appeal to the ear is often carried too far. "We approve certain things not because there is any natural propriety in them, but because we have been accustomed to them, and have been taught to consider them right," and vice versa with our disapprovals. Chapter XVIII. greatly simplifies thorough bass by analyzing all the chords into their binary components, and investigating the harmonic character of these; not assuming in the usual way that every chord must have one root, but accepting Rameau's more rational view that there may be two. The last three chapters comprise harmonic progressions and counterpoint simply treated, and a good summary of the whole book.

The only improvements that could be wished are that the radical importance of the physical basis had been more firmly insisted upon, for, whatever may be the after changes, this basis permeates and controls everywhere; and that the aesthetic influence had not been made to seem so entirely an incalculable matter of chance. This influence has laws of its own, and has been quite successfully investigated by James Sully in the two chapters of his "Sensation and Intuition" entitled "The Aspects of Beauty in Musical Form," and "The Nature and Limits of Musical Expression." These chapters, written in a most quiet and unassuming way, are rich in penetrating analysis made in full sympathy with the artistic side of music, yet with all the exactness and fertility of the scientific method. A brief showing of their trend would have enriched Mr. Pole's work, and have made his treatment more complete.

name of Professor Bloxam is the best assurance of the merit of this volume. The book does not presuppose any knowledge of chemistry on the part of the pupil, and does not enter into any theoretical speculations. It dispenses with the use of all costly apparatus and chemicals, and is divided into separate exercises or lessons with examples for practice to facilitate the instruction of large classes. The method of instruction followed has been adopted by