preceding, is called crvvqixiiarov (synemmenon). Thefourth, which is disjoined, called 81 e&vypevov (diezeug-menon). The fifth, which is the highest, the Greekscall* virepfSoXatov (hyperbolseon). The natural conso-nances, which the Greeks call o-vfjujjwviai (symphonise),are six in number; diatessaron (fourth), diapente (fifth),diapasbn (octave), diapason with diatessaron (eleventh),diapason with diapente (twelfth), and disdiapason (fif-teenth). These names are given them from the numberof tones which the voice passes through in going tothem, counting that on which the voice begins as one;thus, moving through them to the fourth sound is calleddiatessaron; to the fifth, diapente, to the eighth dia-pason, to the eleventh diapason with diatessaron, to thetwelfth diapason with diapente, to the fifteenth disdia-pason. For between two intervals, either in a melodysung by a voice, or played on a stringed instrument,neither with the third, sixth nor seventh can there heconsonances, but only, as above shewn, with the diates-saron and diapente up to the disdiapason do natural con-sonances arise, and those are produced by an union ofthose sounds which the Greeks call cfcdoyyoL (phthongi).

CHAPTER V.

OF THE VASES USED IN THE THEATRE.

On the foregoing principles, the brazen vases are to bemade with mathematical proportions, depending on thesize of the theatre. They are so formed, as whenstruck, to have sounds, whose intervals are a fourth,fifth, and so on consecutively to a fifteenth. Then, betweenthe seats of the theatre, cavities having been prepared,they are disposed therein in musical order, but so as notto touch the wall in any part, but to have a clear space