Chapters in Development

Metrical Dissonance

Mark Gotham

Key Takeaways

  • “Metrical dissonance” refers to the presence of two or more different ways of hearing the music’s metrical structure. This is usually divided into two types:
    • Displacement dissonance sees two forms of the same meter displaced against each other, so with the same period and structure but a different phase.
    • Grouping distance sees two different metres occur at the same time.

“Dissonance” is one of those multi-purpose terms with a range of uses both within and beyond musical analysis. Outside of music, terms such as “cultural” or “cognitive” dissonance usually have negative connotations, but music has a way of making a virtue of the “wrong” or “ill-fitting”. Musical dissonance is not “bad” in the same sense as some of these other contexts, though musical “rules” often require “proper” handling and resolution, at least in the case of tonal counterpoint.

Within music, the separation of pitch “consonances” (octaves, fifths . . . ) from “dissonances” (semitones, tritones, . . . ) is well established. The broad structure of this is relatively settled, though theorists have long argued over the details, such as: the need for further divisions (separating “perfect” from “imperfect” consonances, for instance); the membership of those categories (particularly in relation to the elusive perfect fourth); and how this system came to be (naturally or artificially).

More recently (in the history of music theory, that is), these same notions of consonance and dissonance have been applied to metre. The modern literature on “metrical dissonance” was galvanised by Krebs (1999) who, in turn, cites a Berlioz article of 1837 as the earliest explicit comparison using these terms (p.13,16). Notwithstanding notable differences, there are clear grounds for this analogy between harmonic and metrical dissonance and sufficiently strong commonalities to set them out in comparable ways, once again based on the simplicity of proportional relationships.

Types of Metrical Dissonance

Example 1 sets out the two main types of metrical dissonance: “displacement” and “grouping’. Example 1a sees two simple rhythms in a “displacement” dissonance. All else being equal, hearing those parts separately would likely lead to different assumptions about “the” metre. The lowest part aligns with the notated metre. The upper part can be understood in terms of a version of the “same” metre, but which has been “displaced” by a quarter note, potentially inverting assumptions about which beats are strong and weak.

Metrical Dissonance Examples by openmusictheory

Example 1. Simple prototypes for displacement and grouping dissonance.

“Displacement” Dissonance

Example 2 provides an example from Bill Withers” iconic “Lean on me” (1972). This contrasting section (at 1’45” and 2’36”, to the lyrics “you just call . . . ’) introduces a kind of rhythmic ingenuity that can be helpful to consider in terms of displacement dissonance. While the “main” metre and grouping is clear from the foregoing context and the vocal part, other parts of the texture shift to consistently displaced positions. Starting with the bass guitar, while the anacrustic pattern in the low register stays with the main metre, the bass has a prominent note in a higher register on beat 3 that asserts itself as a different voice with an alternative take on the metrical phase, potentially displacing the metre by a half-cycle to beat 3. The drum kit, in turn, emphasises beats 2 and 4 with its back-beat pattern. This can be heard in terms of displacement by a quarter cycle, though it is important to note that this is a particularly listener-dependent case: many listeners will find this pattern so familiar that the very presence of that displaced emphasis serves instead to indicate where the strong beats “really” are. Finally, and most strikingly, there are hand claps (prominent in the mix) on the 2nd and 6th eighth notes of the bar, suggesting an eighth-cycle displacement. The “real” phase of the meter may never be in doubt, but the rhythmic-metrical richness of this passage can be helpfully understood in terms of the systematic syncopations that potentially point to alternative displacements of the meter.

Displacement dissonance in Bill Withers” “Lean on me” (author’s transcription).

Example 2. Displacement dissonance in Bill Withers” “Lean on me” (author’s transcription). Brackets indicate the displacements discussed in the text.

“Grouping” dissonance

“Grouping” dissonance sees the combination of two metres with different internal organisation. Example 1b and 1c set out a “grouping dissonance’: the upper part implies an internally consistent grouping in 3s (perhaps indicating a 6/8 time signature) which contradicts the implications of the lower part’s grouping in 4s (2/4). In Example 1b, it is the lower, “2/4” part that aligns with the notated metre; in Example 1c, the “same” dissonant pairing is notated to fit the upper part’s “6/8’.

Example 3’s 3-against-4 rhythm is probably the most ubiquitous form of rhythmic-metrical pattern that can be readily heard in terms of “grouping dissonance’. Figure 2 sets out complete cycles of this grouping dissonance, but partial cycles are more common in musical practice. Versions of this pattern are common in popular musics from classic jazz (such as the melodic rhythm of Gershwin’s “I got Rhythm’) to Electronic Dance Music (EDM) and owes its origins to the Afro-Cuban “tresillo” rhythm which can be viewed as a partial cycle of the 3-against-4 dissonance broadly equivalent to the first two bars Example 1b, above. Example 3 sets out an example of the partial cycle in EDM from Calvin Harris” “I’m Not Alone” (2009). Once again, the “real” metre is clear from the context, and this ri↵ (along with much of the rhythmic content of this example) sets out a conflicting pattern based on grouping in 3s. The upper part of the example provides the riff while the lower part makes explicit the continuing 3-grouping, the possible reading of this rhythm in terms of 12/16 (with brackets), and the first note length to diverge from this pattern (marked with “!”) which leads to a re-set at the start of the next note and bar.

I’m Not Alone by openmusictheory

Example 3. Grouping dissonance in Calvin Harris” I’m Not Alone (2009) as an example of a popular 3 against 4 pattern. (Author’s transcription).

Changing Dissonance

Some songs and pieces get into a metrical dissonant groove and stick with it. Most don’t – they use metrical dissonance in some places and no others, to shape the piece overall. Consider the Bill Withers example above: this rhythmic passage contrasts with the main section that rhythmically very straight and without dissonance. Let’s close with well-known example from Brahms: his “Lullaby” (“Wiegenlied”, Op. 49, No. 4).

Click here for a full score transcription (available freely under CCO).

The melody is extremely well-known and its rhythm is highly regular in the notated 3/4. Now have a look at the piano accompaniment in Example 4. The left hand (bass) is every bit as regular as the voice, but the right hand (treble) goes its own way as shown with the markings a b, c, and d on the score and described below.

  • Example 4a: We start with a rhythmic pattern that might fit better in 6/8 rather than 3/4 and displaced by an eighth. That’s right, before the voice even enters we arguably have both displacement and grouping dissonance.
  • 4b: The grouping dissonance disappears almost immediately. We settle on a 3/4 structure, but the displacement by an eighth remains for the main part of the verse.
  • 4a: The opening double-dissonance briefly returns before giving way to …
  • 4c: Finally the right hand plays a note on the downbeat! The pattern still suggests displacement dissonance but of a mild kind: displacement forward by a quarter note to emphasise the second beat and give something of a saraband feel.
  • 4d: A measure later we have all 6 eight notes in the bar, in a strong-weak alternation and no sense of dissonance at all.
  • The last 4 bar pattern repeats.

Assuming this reading (which you may, of course disagree with), it’s easy to see this as a process of tension (albeit very slight) to release that is entirely in keeping with the mood of this lullaby.

Wiegenlied Op. 49 No. 4 (Lullaby) by openmusictheory

Example 4. Changing metrical dissonance in Brahms’ “Lullaby” (“Wiegenlied”, Op. 49, No. 4).

Further Reading
  • Krebs, Harald. 1999. Fantasy Pieces: Metrical Dissonance in the Music of Robert Schumann. New York ; Oxford: Oxford University Press.
  • This chapter is based in part on the introduction to my chapter “Towards a Cognitively-Based Quantification of Metrical Dissonance” OUP Handbook on Time in Music:
  • Compose short pieces (perhaps just one measure which repeats) in two parts that suggest different meters. For example:
    • 4/4 in one part and 4/4 in the other, but displacement by a half cycle (a half note)
    • 4/4 in one part and 4/4 in the other, but displacement by a quarter cycle (a quarter note)
    • 6/8 in one part and 3/4 in the other (a classic hemiola)


Media Attributions

  • Lean


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