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188 MEANING OF VIBRATION-FRACTIONS. [IX. §95.
defined in § 34: any other standard is however equally legitimate, though, in general, less convenient. To illustrate these remarks on a particular case, the
reasoning being equally applicable to other cases, it follows that any fraction greater than unity may denote the number of vibrations and fractions of a vibration made by the higher of two notes forming an interval, while the lower of them is making a single vibration. Similarly, any fraction less than unity may indicate the proportion of a whole vibration performed by the lower note, while the upper is making one complete vibration.
We will next investigate rules for determining the vibration-fractions of the sum and difference of any two intervals whose separate vibration-fractions are known.
95. Suppose that, starting from a given note, we sound a second note, a Fifth above it, and then a third note, a Major Third above the second. What will be the vibration-fraction of the interval formed