Definitions

# Measure (music)

## Classification of cadences in common practice tonality

In music of the common practice period, cadences are divided into four types according to their harmonic progression: authentic, plagal, half, and deceptive. Typically, phrases end on authentic or half cadences, and the terms plagal and deceptive refer to motion that avoids or follows a phrase-ending cadence. Each cadence can be described using the Roman numeral system of naming chords:

• Authentic (also closed or standard) cadence: V to I. The phrase perfect cadence is sometimes used as a synonym for authentic cadence, but can also have a more precise meaning depending on the chord voicing:
• Perfect authentic cadence (PAC): The chords are in root position; that is, the roots of both chords are in the bass, and the tonic (the same pitch as root of the final chord) is in the highest voice. A PAC is a progression from V to I in major keys, and V to i in minor keys. This is generally the strongest type of cadence.
• Imperfect authentic cadence (IAC), best divided into 3 separate categories:
• 1. Root position IAC: similar to a PAC, but the highest voice is not the tonic ("do" or the root of the tonic chord).
• 2. Inverted IAC: similar to a PAC, but one or both chords must be inverted.
• 3. Leading tone IAC: the V chord is replaced with the viio chord (but the cadence still ends on I).
• Half (or open, or imperfect) cadence: any cadence ending on V, whether preceded by V of V, ii, IV, or I, or any other chord. Because it sounds incomplete or "suspended", half cadence is considered a weak cadence - the weakest cadence, in fact.
• Phrygian half cadence: a half cadence from IV⁶ to V in minor, so named because the motion in the outer voices resembles the structure of the Phrygian mode.
• Plagal cadence: IV to I, also known as the "Amen Cadence" because of its frequent setting to the text "Amen" in hymns.
• Deceptive (or interrupted) cadence: V to any chord other than I (typically ii, vi or VI). This is considered a weak cadence because of the "hanging" (suspended) feel it invokes. One of the most famous examples is in the coda of the Passacaglia and Fugue in C minor%2C BWV 582 by Johann Sebastian Bach: Bach repeats a chord sequence ending with V over and over, leading the listener to expect resolution to I --- only to be thrown off completely with a thunderous fermata on a D flat major chord. Following a pregnant pause, the "real" ending commences.

## Rhythmic classifications

Cadences can also be classified by their rhythmic position. A "masculine cadence" occurs on a strong position, typically the downbeat of a measure. A "feminine cadence" occurs in a metrically weak position, for instance, after a long appoggiatura (see also feminine ending). Masculine cadences are considered stronger and are generally of greater structural significance. Susan McClary has written extensively on the gender characteristics of music in her book Feminine Endings. The Society for Music Theory endorses the terms "metrically accented" and "metrically unaccented cadence" in their Guidelines for Nonsexist Language.

Likewise, cadences can be classified as either transient (a pause, like a comma in a sentence, which implies that the piece will go on after a brief lift in the voice) and terminal (more conclusive, like the full stop or other terminal punctuation, which implies that, at least for the time being, we are done). Most transient cadences are half cadences (which stop momentarily on a dominant chord), though IAC or deceptive cadences are also usually transient, as well as Phrygian cadences. Terminal cadences are usually PAC or sometimes plagal ("Amen") cadences.

Medieval cadences are based upon dyads rather than chords. The first theoretical mention of cadences comes from Guido of Arezzo's description of the occursus in his Micrologus, which is the term he gives to the end of a phrase of two-part polyphony where the two lines converge to a unison.

A clausula is a dyadic or intervallic, rather than chordal or harmonic, cadence. It requires at least two voices in contrary motion. According to Carl Dahlhaus, "as late at the 13th century the half step was experienced as a problematic interval not easily understood, as the irrational remainder between the perfect fourth and the ditone:

$textstyle\left\{\left\{\left\{4 over 3\right\} over left \left(\left\{9 over 8\right\} right \right)^2\right\} = \left\{256 over 243\right\} \right\},!$
In a melodic half step, no "tendency was perceived of the lower tone toward the upper, or of the upper toward the lower. The second tone was not taken to be the 'goal' of the first. Instead, the half step was avoided in clausulas because it lacked clarity as an interval." Beginning in the 13th century cadences begin to require motion in one voice by half step and the other a whole step in contrary motion. In the 14th century, an ornamentation of this with an escape tone became known as the Landini cadence, after the composer who used them prodigiously.