music, which approaches the richness of an orchestra. But this suggestive remark is quite an exception. The extant musical tracts are wholly theoretical, and are concerned with the scientific basis of music, not its application to practice. And the first problem to which they applied themselves, which they solved, and have handed down to us, their heirs in art, is the determination of the proper scale or scales in which music should be composed. This was no easy thing to do, and if you take the trouble to hear the music of any people who have not adopted the Greek solution, or one like it, you will at once perceive the difference. I well remember persuading, with great difficulty, a band of gipsies, in Hungary, to play for me not the music of the Hungarians, for which they are so celebrated, but some of their own Oriental stuff, which they play among themselves in private. I found it wholly unintelligible on account of the scale, which seemed to have thirteen or fourteen notes within the octave. All this the Greeks had contemplated, and in some of their early scales they used quarter-tones and intervals strange and disagreeable to us. But, after much hesitation, they fixed upon the diatonic scale, which became the basis of their music, and in due time of ours. The varieties of this scale which they used were far greater than ours. We are contented with the variation of major and minor, and repeat the same intervals in the same order with a mere difference of pitch, very slightly modified by the temperament of our tuning. The Greeks thought the position of the two semitones far more important, and considered that the quality of the scale, quite apart from pitch, was produced by the variety in the placing of these intervals. But I must repeat that our extant treatises are so absolutely scientific and not practical that it would be impossible to attempt an analysis of them in a popular lecture. The discovery of the scientific basis of concord or harmony and its difference from discord had been made very early by the Pythagoreans, and I have often thought that their famous theory that numerical relations were the key of the universe was much stimulated and fortified by finding that octaves, fifths, and fourths, which are recognised by the ear as concords, can be produced by stopping a vibrating string at the points dividing it into portions represented by 1:2, 2:3, and 3:4. They did not acknowledge our favorite major ⅓ as a concord, the proportion being more complex, _viz._ 4:5 or 5:6; and indeed if the major ⅓ on our instruments be tuned to its full height of two full tones, it sounds sharp and very disagreeable. In this as in most detail we can follow and understand the Greek theory. When Aristotle tells us that the middle note of the scale is that to which the melody always returns, he is evidently speaking of the unaccompanied melody, and there are scores of our melodies that move up and down round this keynote,