HANDBOOK OF ACOUSTICS - online book

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HARMONIOUSNESS OF CONSONANT INTERVALS. 203
The consonant intervals less than an Octave vary in smoothness according to the constitution or quality of their constituent Com­pound Tones, and according to their position in the scale of pitch. Helmholtz's arrangement for average qualities of tone is,
(1)    Fifth,
(2)    Fourth, Major Third, Major Sixth,
(3)    Minor Third,
(4)    Minor Sixth.
For other consonant intervals greater than an Octave, Helmholtz's rule applies, viz :—
Those intervals in which the smaller of the two numbers expressing the ratios of the vibration numbers, is even, are improved by having the upper tone raised an Octave, and vice versa ; thus,