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X. §111.] 'TEMPERING' AND 'TEMPERAMENT: 205
will contain, on the equal temperament system, the sounds set out below. The vibration-numbers are given true to the nearest integer. When a note is slightly sharper than that so indicated, this is shown by the sign + attached to the vibration-number in question ; when slightly flatter, by the sign —. For the sake of comparison, the perfect intervals of the same scale are written below the tempered ones.
It is clear that the regions of the tempered scale where the tuning is most imperfect are in the neighbourhood of the Thirds and Sixths. E and A are nearly three vibrations per second too sharp. The Fourth and Fifth are less out of tune, in fact only wrong by a fraction of a vibration per second.
111. The intervals of the tempered scale are so nearly equal to those of the perfect scale that, when the notes of the former are sounded successively, it requires a delicate ear to recognise the defective character of the tuning. When, however, more than one note is heard at a time, the case becomes quite different. We saw in Chapter viii. how rigorously accurate the tuning of a consonant interval must be, to secure the greatest smoothness of which it is capable. Such