Plagal and authentic cadences both conclude on a root-position triad and use a penultimate bass pitch a perfect fifth away from tonic. However, this dualistic symmetry fails to account for some marked features of the plagal cadence. To explain these differences, this presentation employs “stochastic counterpoint,” which is defined against the more familiar “deterministic counterpoint.” As an example of the latter, some theorists recognize the authentic bass conclusion of ^5-^1 as the optimal harmonization of the pair of stepwise upper voices ending on ^7-^1 and ^2-^1. Of the seven major scale degrees, only the bass pitch of ^5 is consonant with both ^2 and ^7 above it, while also avoiding (anti)parallel octaves with one of the upper voices as all three voices close on ^1. A stochastic derivation of the authentic-cadential ^5-^1 modifies this method by recognizing the bass’s ^5-^1 as the one well-formed harmonization of either ^2 or ^7 before ^1 at a treble line’s end. Although stochastic and deterministic approaches lead to identical results in this case, a stochastic approach is easily generalizable to other cases, such as longer treble lines and treble lines that end on something besides ^1. In one case, of the 258 bass endings of 2-4 scale-degree successions that end on ^1, only two of them offer classically idiomatic counterpoint with the majority of eighteen stepwise treble lines of 3-5 notes that end on ^1, and both of these bass endings end ^4-^5-^1. In another case, a classically common bass line of ^3-^4-^5-^1 well complements ten stepwise treble approaches to ^1. The same stochastic approach to the four two-note stepwise treble endings on ^3 or ^5 recognizes the plagal bass’s ^4-^1 as the one well-formed harmonization of any of these four treble endings. However, given the more diffuse treble options, an antepenultimate bass scale degree as preferred as ^4 is for authentic cadences does not emerge for plagal cadences. Moreover, less conclusive treble endings on ^3 or ^5 instead of ^1 become a Romantic hallmark; a theory of stochastic counterpoint holds that the nineteenth-century plagal bass rendered this melodic open-endedness into schematized harmony.

Temperley (2011) describes three different cadential roles for the IV chord in rock music, but the plagal half cadence (PHC, henceforth) is not one of them: he says “IV rarely occurs in half-cadential contexts” and closes the matter there. I will demonstrate that IV chords are, in fact, commonly used as endpoints of half cadences. Pop/rock music is the natural arena for PHCs since this is where IV overtook V as the second most commonly used chord after I (de Clercq and Temperley 2011). And Nobile’s (2016) redefinition of harmonic function in rock based on syntax—rather than chord type—shows that IV chords (within a given context) can perform the same roles we traditionally expect from V chords. Theorists have varying ideas of what “cadence” means in pop/rock music, so amalgamating core elements from Temperley (2011), Nobile (2020), Stephenson (2002), Burstein (2014), and de Clercq (2025), I have compiled the following closure factors that can contribute to a sense of cadence: caesura, form, harmony, melody, theme, rhythm, hypermeter, texture, and lyrics. I show how these closure factors can be used (in any combination) to diagnose PHCs in pop/rock songs spanning across forty years, and I show how PHCs differ from chord loops ending on IV. I will close by demonstrating the ubiquity of PHCs with an example from a hugely popular 1990s television show in which the inter-scene music (performed by rock band) ended equally often on V, bVII, and IV chords. By using these as equivalent half-cadential endpoints, the show creators tacitly equated HCs and PHCs, trusting that audiences would hear a similar sense of half-closure in both—and they could count on this because the pop/rock PHC was already firmly implanted in America’s ear.

Robert Glasper’s neo-soul-inspired music employs chromatic progressions that challenge analytical models grounded in tonic-dominant teleology. Ben Baker’s (2019) cyclic model describes Glasper’s progressions through alternating M/m3rd cycles in a compelling alternative to functional analysis, but it largely ignores questions of local chord ordering and expressive meaning. Joseph Straus’s (1982) concept of the tonal axis in Stravinsky’s music is similar since it emphasizes tonal organization mediated through root movement spelling out a major or minor seventh chord. Straus (2013) later expands this to reconceive tonal centricity as distributed across referential collections as open 5ths rather than anchored to a single tonic. While each approach gives us potential insight into Glasper’s harmonic organization, neither alone account for the local relational logic between chord groupings.

My talk addresses these gaps through an analysis of Robert Glasper’s song “Trust” (2013), Rather than framing the harmonies as placed through random orderings on an ic3/4 cycle, a failed tonic–dominant system, or a purely non-tonal construction, I combine Baker’s and Straus’ methodologies to argue the harmonies of “Trust” are best understood as a network of isolated plagal progressions articulated through movements along dual third cycles and mediated by overlapping fifths to stabilize perception. This hybrid approach allows for chord pairs to function as localized plagal gestures, and incorporates perceptual cues like harmonic rhythm and metric placement to justify these hearings. I further correlate harmony with lyrics to show how this aligns with changes in lyrical stance from vulnerability to affirmation. In this way, plagality emerges as both structural and expressive mechanism through which harmonic disruption and affective meaning are negotiated.