I. On the hindoo division of the octave, with some additions to the theory of the higher orders

Attention has been recently directed to the remarkable division of the octave into 22 intervals, employed by the Hindoos. The paper commences with a slight account of the Hindoo scales as thus derived. It is then remarked that our best way to a real analysis of this music would be to study the system of 22 and compare the results with those actually obtained by Hindoo musicians. The methods which have been employed in the writer’s former paper on the subject are then extended to the higher orders, which have not been before thoroughly discussed. The system of 22 is a system of the second order; and the nature and peculiarities of such systems, and of the system of 22 in particular, are discussed. A classification of systems of the higher orders according to their mode of forming thirds is advanced. If the system be arranged in successive series of fifths, differing by one unit in pitch, then the system is said to be of class x, if the third of any note is in the series units below that which contains the note itself.