198 HAND-BOOK OF ACOUSTICS.
sounded by voices at different pitches below middle C, first on such vowel sounds as "a" in father, "i" in pine, and afterwards on " oo " in cool. The diminution in roughness in the latter case is very striking. The chief cause of the charm of soft singing, doubtless lies in the fact, that the upper dissonating partials of Thirds, Sixths, &c, become so faint, as to be practically nonexistent.
Intervals between Compound Tones consisting of the odd partials only,—such tones, for example, as are produced by the narrow stopped pipes of the organ and by the clarionet—may be more briefly noticed. Fig. SI shows the ordinary consonant intervals between such tones, fully drawn out on the plan of fig. 80. The first thing that strikes us on looking at the figure, is the improvement noticeable in each interval; most of the dissonances of fig. 80 having vanished. The reader will be surprised, doubtless, by the apparent inferiority of the Fifth to most of the other intervals—to the Thirds—for example ; but we must point out that it is for the most part only apparent. For we have already seen, that the Fifth is a perfectly smooth interval above middle 0; consequently the Thirds can only be superior to the Fifth below that limit: and we have shown above that the Thirds rapidly deteriorate as they sink in pitch from that point, in consequence of their fundamentals approaching the Beating Distance.
Another interesting case is that of Intervals between Compound Tones, one of which consists of only odd, and the other of the full scale of partials; such intervals as would be produced, for example, by a Clarinet sounding one tone and a Oboe the other. There will be two cases according as the lower tone is sounded on the former, or the latter instrument. Fig. 82 shows the ordinary consonant intervals, drawn out after the manner of the two preceding figures. Each interval is given twice: in those marked Ob CI the lower tone of the interval is supposed to be sounded by the Oboe, while in those marked CI Ob the Clarinet produces the lower tone.
It is evident at once, that it is not a matter of indifference, to which instrument the lower tone is assigned. The Fifth and Major Third are decidedly better when the lower tone is given to the the Clarinet; while the Fourth, Major Sixth, and Minor Sixth are smoother, when the Oboe takes the lower tone.
From the foregoing, it is quite clear that no hard and fast line can be drawn between Consonance and Dissonance; for as we have seen, every interval, between ordinarily constituted Compound