then there was an alternative arrangement ultimately admitted, making conjunction at _a__{*}, allowing _b_ flat instead of _b_, causing that tetrachord to end on _d_, and placing the tone of disjunction between the _d_ and _e_. Very noticeable this as shewing how popular feeling hankered after the old way of Terpander. This later arrangement of the Greek scale, comprising the two octaves, comes to us from Euclid’s reputed treatise on Music, now attributed to Cleonidas, writing about 120 A.D. Thus was the scale completed. The order of the growth of the scale is shewn by the figures, 1, 2, 3, 4 over the several tetrachords. CHAPTER XXVII. At Alexandria. THE FINAL SETTLEMENT OF THE SCALE. The structure of the Scale so far as was necessary for the development of the Greek modes was comprised in The Disjunct or Greater System Complete; yet at various times the extent of the diatonic scale by degrees was increased, tetrachord was added to tetrachord until in the days of Plato its compass was stated to have been made to comprehend four octaves, a fifth, and a tone. Archytas and Aristoxenus were both of Tarentum, a noted Greek colony in Southern Italy, founded by Sparta about 705 B.C. Archytas was a contemporary of Plato (_b_ 429 _d_ 347). The period was one of artistic luxury, the Parthenon had been completed, and Greece had her golden age of Art, Science, and Philosophy. Here Praxiteles, the great sculptor, second only to Phidias, comes upon the scene, and we may with confidence accept his design of Apollo’s Lyre as a true representation of the instrument as it existed in his day, and, it may be assumed as used in Apollo’s Temple, and by the master-musicians. The date of this sculptor has not been ascertained precisely, Prof. E. A. Gardner gives in a guarded way 400 B.C. Aristoxenus was a musician, the son of a musician, he came at a time when great mathematicians were engaged in battle over fine distinctions in Pythagorean systems, to them of superlative interest and importance. Aristoxenus opposed the Pythagoreans and held that “it was absurd to aim at an artificial accuracy in gratifying the ear beyond its own power of distinction,” a decision very natural, coming from a musician. He was a great writer and theorist, wrote it was said more than four hundred treatises, all of which have been lost except three on “Harmonic Elements,” and this is the oldest musical work at present known.