To the mediaeval musician, religion and science were the twin foundations of his art. But while the influence of religious development can without difficulty be traced in musical history, the influence of scientific development is much more contestable. It may indeed, I think, be said that post-mediaeval music has gone its own way without considering science at all. Theorists of course there have been, and still are, who try to discover scientific foundations for the art of music as we moderns know it: they do their best to correlate mathematical physics with practical composition. But during the past generation these attempts, never very hopeful, have become much less so. It is only too easy to play scientific havoc with the foundations of modern music: but, arbitrary and scientifically indefensible though they may be, they are our inheritance. Music has come to be what it is by methods that will not bear accurate investigation: our tonal systems are mere makeshifts, and no composer can completely express his thoughts in our clumsy notation. I doubt if, throughout all this last generation that has seen such overwhelming scientific advance, music has really been scientifically affected (in the strict sense of the word) in the slightest degree, if we exclude some interesting experiments in sympathetic resonances, primary and secondary, at which some recent composers for the piano have, at present rather tentatively, tried their hands. And whole-tone and duodecuple scales and modern harmony in general are taking us farther and farther away from those natural laws of the vibrating string upon which arm-chair theorists have sought to build a very top-heavy edifice. Of course, the vibrating string ultimately gives--mostly out of tune--all the notes of the chromatic scale, but composers employ them on principles the reverse of mathematical. The growth of music has not been scientific; but growth of some kind is evident enough, though it is none too easy to define it at all adequately. Some might say, with Romain Rolland in his _Musiciens d'autrefois_, that 'the efforts of the centuries have not advanced us a step nearer beauty since the days of St. Gregory and Palestrina'; but this is surely a narrow outlook. Beauty combines the many with the one: and plain-song and the _Missa Papae Marcelli_ show us only a few, a very few, of its manifestations. But artistic progress is, anyhow, very subtle and evasive; and musical progress, in particular, is hardly correctable with any other. Above all, we must recollect that, to us Europeans, music--which, in the only sense worth our present consideration, is an exclusively European product--is incalculably the youngest of the great arts; if we exclude some monophonic conceptions that have still their value for us, it is barely five hundred years old at the most.