as he left the _diatonic octave scale_, so it remains, practically the same in the teachings of the theorists since: some scholiasts have thought that preferably the minor tone should be placed between A and B, transferring the major tone between G and A. This distinguished astronomer and mathematician Ptolemy, like Pythagoras, was the child of his time, given to much fanciful speculation and mysticism, finding music analogies in the virtues, and the sciences, in the parts of the human soul, and in the zodiac. He wrote largely, and completed the foundations upon which European music had been constructed, yet he had no conception of the structure that would be raised by coming generations. The Greeks had in their scale the elements of harmony yet they fell short of the realization, and it must ever be a wonder that, intellectual as they were, they missed it. Evolution was the destined way,—but it is so slow—so slow. Except to the chosen few these questions of the scales fail to maintain their interest, however fascinating such studies of the calculation of theoretical niceties of numbers and ratios undoubtedly are to some minds, gifted with an aptitude for figures, yet with the general body of musicians a broad survey tells that old formalisms in study are fast becoming obsolete. The advance of the System of Equal Temperament in these later years throughout the two worlds will render necessary a reconcilement between theory and practice, now widely at variance. Historically the settlement of scale had its importance, although it came too late in time to be for the Greeks an effective force in their national music. The glory of Greece was fast departing, century after century in the course we have looked upon during our survey, empires had risen, empires had fallen, and in the disrupted state of social conditions, chaos often came, the Greek race itself was worn down and ultimately became absorbed amongst strangers, conquering races, and in the end we have to speak of her Art as Greco-Roman. Out of all these world changes we have isolated Music. To apprehend aright the slow march along the path of progress, we should now and then lift our thoughts to take account of the atmosphere and glance at the environment.