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 128 NEW BOOKS. phenomena of art we may get an answer to all the chief problems of metaphysic. It is misleading of the author to intimate that his metaphysic is " founded on aesthetic ". It is assumed without any foundation at alL We do not get anything about art till after a prefatory section full of violently mysterious assumptions about reality. " Le r^el est done mysteVieux dans sa nature," argues the writer, and mystery or fogginess is the dominant impression of the book. Mr. Peres has undoubtedly a genuine interest in his subject, but he must study clearness of thought and expression. It is a mistake to write in sentences longer than those of the "judicious " Hooker (one in the introduction runs to 140 words),, interspersed with aphorisms more cryptic than the fragments of Hera- cleitus. Beitrdge zur Akustik und Musikwissenscha/t. Herausgegeben von Dr. CARL STUMPF. 1 Heft, C. Stumpf : Konsonanz und Dissonanz. Pp.. , vi., 108: Leipzig, Earth, 1898. Prof. Sturnpf tells us in the Preface to this brochure that its appear- ance is due to a decision which he has formed not to publish the two remaining volumes of the Tonpsychologie in this form, but in that of separate investigations. He has done, it would seem, with the psycho- logical foundations, and will henceforth appeal to a more musical public. The first number, written by himself, deals with the theory of Harmony and Discord. Although now and again it makes a pretty lengthy ex- cursion into the physical side of acoustics, and into the more technical department of music, this first instalment is in the main psychological. It grows, indeed, as a kind of natural sequence out of the methodical inquiry into the analysis by the ear of tone masses which form the main problem of the second volume of the Tonpsychologie. Its theme may be described as the theory of fusion and analysis set forth in this volume applied to the explanation of the most fundamental contrast in modern, if not in all, music. The essay begins with a critical examination of some of the more prominent traditional theories. Here the author deviates from the his- torical order, beginning with an examination of the latest of the com- manding theories, viz., that of Helmholtz, according to which dissonance arises from beats, and harmony means freedom from beats. The criticism of this hypothesis is particularly searching ; the writer succeeds in showing that Helmholtz gives two definitions of harmony the beat theory to fit the case of simultaneous tones or accords, and the theory of affinity, as determined by the coincidence of partial tones, to fit the case of the sequent tones of melody. He examines each of these. His argument is well prepared and forcible. It seems almost incredible that a great physicist great alike in his mastery of the material and in his reasoning power as Helmholtz undoubtedly was, could have gone so far wrong as he must have done if the facts are as Prof. Stumpf here de- scribes them ; he seeks to show that there is no discoverable relation between the amount of beat-effect of a pair of tones and its place among harmonious and dissonant combinations. As a piece of critical dialectic this sifting of the truth from the error in Helmholtz's explanation is quite up to the level of the writer's earlier performances. It is penetrat- ing, unsparing in its thoroughness, finely discriminating, and immensely convincing. After examining the ' unconscious arithmetic ' theory of Leibniz, which places the value of harmony in a sub-conscious apprehension of the