Collier's New Encyclopedia

A complete general encyclopedia of 1921 — the world as it was understood just after the Great War, from Aachen to Zwingli, across twelve volumes and six thousand pages.

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Inversion

the chemical change or sugar is boiled with a dilute acid.

Inversion may also take place in the INVERTEBRATA presence of ferments, or by prolonged boiling with water.

In geology, the overturning or folding over of strata by igneous agency, so that the order of their succession seems reversed.

In mathematics, the operation of changing the order of the terms, so that the antecedent shall take the place of the consequent and the reverse, in both couplets. Thus, from the proportion a : b :: c: d, we have, by inversion, b: a ::d:c.

In music, the transposition of certain phrases, having a common root. (1) The inversion of a chord is effected by making one of the inner notes act as a bass note, and by this means as many inversions can be made as there are actual notes in the chord, not counting the root. In such inversions the harmony remains the same, though the order of component parts is changed. (2) Intervals are inverted by making that which was the upper note the lower, and the reverse. The inversion of an interval within the octave may readily be found in the difference between the figure 9 and the interval known; then an interval of a second becomes a seventh by inversion, etc. (3) The inversion of a subject is produced by inverting the intervals of which it consists.

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