DOUBLE OCTAVE, in music, an interval composed of fifteen notes in diatonic progression; and which, for that reason, is called a fifteenth. "It is (says Rousséau) an interval composed of two octaves, called by the Greeks disdiapason."
It deserves, however, to be remarked, that in intervals less distant and compounded, as in the third, the fifth, the
Doublet. the simple octave, &c. the lowest and highest extremes are included in the number from whence the interval takes its name. But, in the double octave, when termed a fifteenth, the simple number of which it is composed gives the name. This is by no means analogical, and may occasion some confusion. We should rather choose, therefore, to run any hazard which might occur from uniformly including all the terms of which the component intervals consist, and call the double octave a sixteenth, according to the general analogy. See INTERVAL.