TonalityGUIDE - Tonal music basic theory for Undergraduates
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The cadential six-four is one of many ways of intensifying the sense of closure provided by a perfect cadence by setting up the V of the cadence as the resolution of a tension. The example below first shows an ordinary perfect cadence then the same progression but with a double appoggiatura on the V (marked with a star).

Because the chord marked with a star contains the notes of a C major triad (chord I), some people label it as I6/4 (or IC). Although this is not in the strictest sense wrong, it gives a misleading impression its function. The appoggiatura clearly resolves to V rather than being an independent chord so it is better to label it in away that acknowledges that it is generated by voice-leading more than harmony.

The cadential six-four is so called because of the way the progression is labelled using figured bass (remember: you can always remind yourself about figured bass by clicking on the 'chord identification' link in the toolkit below). The same figure is heard below in the context of a wider progression. It is quite common for two or more ways of intensifying the closure at cadence to be used in this way.