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II. § 31.J INTERVALS. 63
a bass and a treble voice sing the same melody together, the notes of the latter are usually an Octave above those of the former. This interval has the property, shared by no other, that if, starting from any note we choose, we ascend to that an Octave above it, then to that an Octave above the last, and so on, we get a number of notes which sound perfectly smooth and agreeable when heard all together. The same thing holds good if we take the succession of Octaves in descending order from the note fixed on as the starting-point. Hence the whole scale of pitch may be conveniently divided into a series of Octaves taken upwards and downwards from some one sound arbitrarily selected. Narrower intervals situated in any one Octave are repeated in all the others, so that when we have settled those intervals for a single Octave we have settled them for all the rest. Within the limits of each Octave the Major scale presents us with seven notes, or if we include that which forms the starting point of the next cycle, with eight. The fact that the eighth note is the Octave of the first explains the meaning of the word 'Octave,' i.e. 'eighth' (Latin: 'octavus').
The eight notes are those of an ordinary peal of the same number of bells, or of the white keys of the pianoforte between two adjacent C's. We may for