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HARMONIOUSNESS OF CONSONANT INTERVALS. 199
Tones, except the Octave, becomes a dissonance when taken sufficiently low in pitch. Furthermore, when the intervals of fig. 80 are taken in the same region of the musical scale, there is an uniform gradation of roughness, or diminution of smoothness in passing from the Perfect Fifth on the left, to the diminished Fifth on the right, which is usually looked upon as a dissonance. Again, with similar Compound Tones, and in the same region of pitch, some so-called dissonances are not inferior to intervals universally termed consonant. Compare for example,
Hitherto, we have only considered Intervals not greater than an Octave, and in musical theory, no great distinction is drawn, between an interval, and its increase by an Octave. In reality, however, the addition of an Octave to an Interval, between Compound Tones, does exercise a great influence on its relative smoothness. Fig. 83 shows, on the same plan as before the Twelfth, Eleventh, Tenths, and Thirteenths.
The first point to be noted about these intervals is that the addition of an Octave to a Fifth, makes the Interval a perfect one ; the addition of the Compound Tone (s) to the Compound Tone (d|) supplying no new partial tone to the latter. A Twelfth is therefore decidedly superior to a Fifth. On the other hand by comparing the Eleventh of fig. 83 with the Fourth of fig. 80 it will be seen that the former is the worse of the two: for though the