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sevenths, &c. taken one or more octaves higher; and even the most remote distances, extending through all the octaves, make no difference in this respect. Even the tenth is nothing but a third taken an octave higher.
5thly. The ninth is also, in truth, but a second taken an octave higher; but, in thorough-bass, it is used in a different manner in both forms; and it is therefore named sometimes in the one way, sometimes in the other.
6thly. All intervals are computed and sought for from the lower note upwards,—that is, in the direction from the bass towards the treble,—and never in the reverse way, or from the upper note downwards. Their inversions will be explained afterwards.
7thly. The above scheme of intervals I have written on C as a root, and therefore in the key of C major; and, as I proceed, I shall also give all the subsequent examples in one key only, generally that of C major or A minor.
It is, however, of the greatest importance that you should transpose all these examples into all the other keys, and that too in writing; for which purpose, your having learned to copy music will be very useful. It is to be remembered here, that all the examples in a major key can only be transposed into major keys; and, similarly, all the examples in minor, only into minor keys. Thus, as the preced-
