Looking at the octaves which on our key-board, as on the Greek scale, exhibit the several species, we cannot but be struck with the peculiar relation in which they stand to the Keys. In the tables given above the keys stand in the order of their pitch, from the Mixo-lydian down to the Hypo-dorian: the species of the same names follow the reverse order, from _b-b_ upwards to _a-a_. This, it is obvious, cannot be an accidental coincidence. The two uses of this famous series of names cannot have originated independently. Either the naming of the species was founded on that of the keys, or the converse relation obtained between them. Which of these two uses, then, was the original and which the derived one? Those who hold that the species were the basis of the ancient Modes or [Greek: harmoniai] must regard the keys as derivative. Now Aristoxenus tells us, in one of the passages just quoted, that the seven species had long been recognised by theorists. If the scheme of keys was founded upon the seven species, it would at once have been complete, both in the number of the keys and in the determination of the intervals between them. But Aristoxenus also tells us that down to his time there were only six keys,--one of them not yet generally recognised,--and that their relative pitch was not settled. Evidently then the keys, which were scales in practical use, were still incomplete when the species of the Octave had been worked out in the theory of music. If on the other hand we regard the names Dorian, &c. as originally applied to keys, we have only to suppose that these names were extended to the species after the number of seven keys had been completed. This supposition is borne out by the fact that Aristoxenus, who mentions the seven species as well known, does not give them names, or connect them with the keys. This step was apparently taken by some follower of Aristoxenus, who wished to connect the species of the older theorists with the system of keys which Aristoxenus had perfected.