The final scale was the triumph of the mathematicians, they gained their ideal. Beyond this, however, nothing was accomplished,—nothing for actual Music. Harmony was not discovered, no great composer arose, certain lyrists and auloi-players we know of, whose deeds excited enthusiasm, but in what kind of display their art consisted no evidence exists, beyond the music to a few hymns, the melodic phrases of which do not commend themselves to us as examples of musical genius or talent. The irresistible charms exercised by the citharists upon the multitudes assembled to hear them, whether they sang by rule or improvised their melodies must be attributable in the main to the character of the singer’s voice, combined with the purport of the words sung. When with the modern knowledge of musical instruments we examine the nature of those which they had in their command, we have every reason to doubt the practical application of those fine distinctions of the pitches of the musical notes insisted upon by their learned theorists. The instruments simply could not give them, the exactness was beyond their staying and playing powers. The strings of a lyre had not the delicate permanence of pitch requisite for such claims, and certainly the flutes could not have rendered intervals so accurate. To set the intervals by bridges on the Kanon or monochords, by patient adjustment to marked divisions, was quite another matter, a mental recreation. The trophy secured in the long march of music the thousand upon thousand years is the simple diatonic scale of five major tones and two semitones,—that is all. Up to the setting in of the Christian era that was the utmost attainment of the human race in the art of music, two formal tetrachords with a disjunct tone between; and if you will think of it this one fact has a mighty significance. What instinct of the race brought out this particular selection and arrangement, what in-dwelling demand of the ear impelled the choice, apparently from earliest impulses, we cannot tell,—there it is—the bed-rock upon which our system of harmony is founded; and the curiosity of the thing is that other races have for ages settled down upon a pentatonic system and still manifest an inborn aversion to harmony. We adjudge tones by means of calculated vibrations, ascertained by mechanism, the Greeks made their determinations by the measuring of strings, the artist is always satisfied by the verdict of the ear. To have established a tetrachord, and after centuries of intellectual strife to have secured a double tetrachord forming merely a simple scale of one octave, and that, the scale of _A minor_, may seem a small matter as a record of human history and of mental achievement. There is a saying of Aristotle which will justify a more inspiriting estimate,—the philosopher wrote,— “The true nature of a thing is whatsoever it becomes when the process of its development is complete.”