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Definition: harmonic analysis from Musical Terms, Symbols and Theory: An Illustrated Dictionary

the study of chords and harmony in composition, including the labeling of chords by degree (tonic, dominant, subdominant, etc.) and by inversion. See also chord; interval; inversion.

Summary Article: harmonic analysis
From The Hutchinson Unabridged Encyclopedia with Atlas and Weather Guide

Method of describing the chords and progressions used mainly in music of the 18th and 19th centuries. The principles rest on the identification of a chord by its root and by the position of the root within the scale. Thus, a root-position chord on the tonic is designated as I, its first inversion as Ib (or, using the parlance of thorough bass, I6) and its second inversion as Ic (or I6/4); further elaborations of the system are all based on figured bass notation. Within diatonic music with straightforward harmonies, the main chords are I, IV, and V; II and VI are also common, but III and VII are used more rarely. First inversions are important and used frequently except in structural cadences. Second inversions of triads are normally considered discords and can be used only in particular circumstances.

A further refinement of this system is ‘functional harmony’, first devised by Heinrich Riemann in his Vereinfachte Harmonielehre (1893). Here every chord was described as part of a tonic (I), dominant (V) or subdominant (IV) function. This system, still little practised outside Germany, makes the entire chordal vocabulary of the classical and romantic eras more comprehensible as a logical system; but at the same time many details need to be glossed over and this leads to the use of ‘reduction’ graphs which describe certain chords as passing chords within a broader progression. Hierarchical reductions of this kind led to the analytical techniques of Heinrich Schenker and his followers.

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