A theory of harmony by Ernst Levy, Siegmund Levarie

By Ernst Levy, Siegmund Levarie

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Levarie, Siegmund publisher : State University of New York Press isbn10 | asin : 0873959922 print isbn13 : 9780873959926 ebook isbn13 : 9780585068282 language : English subject Harmony. 3 subject : Harmony. A Theory of Harmony SUNY Series in Cultural Perspectives ANTONIO T. DE NICOLAS, EDITOR A Theory of Harmony Ernst Levy Edited by Siegmund Levarie State University of New York Press ALBANY Page vii Published by State University of New York Press, Albany © 1985 State University of New York All rights reserved Printed in the United States of America No part of this book may be used or reproduced in any manner whatsoever without written permission except in the case of brief quotations embodied in critical articles and reviews.

Hence we may say: a major triad tends to become dominant; a minor triad, subdominant. The oscillation thus produced is, theo- Page 24 retically, perpetual. The original trends can never be completely eliminated; no cadence is ever absolutely closed: A stoppage of tile "perpetual motion" may be effected by changing the mode of the intended last chord, thus introducing a sudden countercurrent: A still more definite cadence is obtained by a combination of such a "counterblow" and an oscillation to the opposite side of the tonic: Passing to the opposite side by a skip, the middle term being omitted, results in the classic cadence: Probing a little further into tonality (tonality: the relationship of tones and chords to a central tone or chord called tonic) we add the dominants of Page 25 the dominants.

For our purposes here, however, the development of one quadrant of the complete planimetric table sufficesthe one, precisely, enclosed in the angle formed by the two primary series. The interpolation may be carried out either by developing the undertones from the horizontal side of the angle, or the overtones from the vertical side. The latter method is somewhat easier. The result is the so-called Pythagorean table. ; Kö1n, 1868-76). In turn, Hans Kayser rediscovered Thimus (who, curiously and sadly enough, had been completely bypassed by musicology) and made the table the object of, and the basis for, intensive research in various fields.

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