A MODE, in ancient music, was equivalent to a Key, in the modern. And it is expressly said that the tones or modes differ from each other in nothing else but the being situated in a higher or lower pitch of the voice or instrument ; which is but saying that the modes differed from each other only by transposition. Aristoxenus admitted of but thirteen modes, though subsequent musicians allowed of fifteen ; and this is the number of which Alypius has given us a diagram in all the three genera. These are placed by every musical writer, anterior to Ptolemy, at the distance of half a tone from each other. And as it is generally agreed that the lowest of the Greek modes, which was called Hypodorian, had its proslambanomenos, or lowest sound, in that part of the modern scale which is expressed by A upon the first space in the base, the following table will convey an idea to the musical reader of the comparative situation of the rest. It was with reason that Aristoxenus refused admission to the two last of the fifteen modes, which are only octaves of the second and third, as the thirteenth is of the first.