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IV. § 47.]            THEORY OF QUALITY.                        93
ing the same fundamental tone, are given in the fol­lowing enumeration:—
Two at a time :
(1, 2), (1, 3), (1, 4), (1, 5), (1, 6).
Total 5.
Three at a time :
(1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6), (l, 3, 4), (1, 3, 5), (1, 3, 6), (1, 4, 5), (1, 4, 6), (l, 5, 6).
Total 10.
Four at a time :
(1, 2, 3, 4), (1, 2, 3, 5), (1, 2, 3, 6), (1, 2, 4, 5), (1, 2, 4, 6), (1, 2, 5, 6), (1, 3, 4, 5), (1, 3, 4, 6), (1, 3, 5, 6), (1, 4, 5, 6).
Total 10.
Five at a time :
(1, 2, 3, 4, 5), (1, 2, 3, 4, 6), (1, 2, 3, 5, 6), (1, 2, 4, 5, 6), (1, 3, 4, 5, 6).
Total 5.
Six at a time : (1, 2, 3, 4, 5, 6).
Total 1.
The whole number of groups is 31, or if we allow the fundamental-tone (1) to count by itself as a sound of separate quality, 32. Let us next examine how many clangs of different quality can be obtained from a single combination of three fixed partial-tones by variations of intensity only, supposing that each
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