ON THE

SENSATIONS OF TONE

AS A PHYSIOLOGICAL BASIS FOR THE

THEORY OF MUSIC

HERMANN L. F. HELMHOLTZ, M.D.,

LATE FOREIGN MEMBER OF THE ROYAL SOCIETIES OF LONDON AND EDINBURGH,

PROFESSOR OF PHYSIOLOGY IN THE UNIVERSITY OF HEIDELBERG, AND

PROFESSOR OF PHYSICS IN THE UNIVERSITY OF BERLIN

Translated, thoroughly Revised and Corrected, rendered conformable to the Fourth (and last) German Edition of 1877, with numerous additional Notes and a New additional Appendix bringing down information to 1885 and especially adapted to the use of Musical Students

ALEXANDER J. ELLIS

B.A., F.R.S., F.S.A., F.C.P.S., F.C.P.

TWICE PRESIDENT OF THE PHILOLOGICAL SOCIETY, MEMBER OF THE MATHEMATICAL SOCIETY,

FORMERLY SCHOLAR OF TRINITY COLLEGE, CAMBRIDGE,

AUTHOR OF ‘EARLY ENGLISH PRONUNCIATION’ AND ‘ALGEBRA IDENTIFIED WITH GEOMETRY’

FOURTH EDITION

LONGMANS, GREEN, AND CO.,

39 PATERNOSTER ROW, LONDON

NEW YORK, BOMBAY AND CALCUTTA

1912