Subido por Ernesto Cappellori

Rhythmic deviance in the Music of Meshuggah

Rhythmic Deviance in the Music of Meshuggah
guy capuzzo
This paper updates and supplements the published research on Meshuggah, in particular a seminal
2007 article by Jonathan Pieslak. Just as Meshuggah’s music deviates from certain stylistic traits of
heavy metal at the macro level, so too do the technical features of their rhythmic approach deviate
from certain music-theoretical yardsticks at the micro level. Analytic vignettes drawn from six songs
explore the many forms that “rhythmic deviance” takes in this music.
Keywords: popular music analysis, rock music, heavy metal music, rhythm, meter, deviance,
Those who try to make heavy metal their career must master its code, and must be able to create original music that
conforms to the code or expands the code from within
without destroying it.
—Deena Weinstein
guitars’ low registers make the use of metal’s ubiquitous root/
fifth “power chords” impractical, the band almost exclusively
uses single-string riffs, which represents another departure from
stylistic norms.4
Just as Meshuggah’s music deviates from certain stylistic
traits of heavy metal at the macro level, so too do the technical
features of their rhythmic approach deviate from certain
music-theoretical yardsticks at the micro level.5 Their music
makes extensive use of rhythmic devices found in a variety of
vernacular musics, including nearly even rhythms, partially palindromic rhythms, and repeated rhythmic figures that deviate
from alignment with the downbeat.6 What distinguishes
Meshuggah’s use of these devices is the unusual length of the
rhythms combined with wide, dissonant leaps that can foster
the perception of compound melodies. The notion of “musical
deviance” provides a descriptive tool and a narrative device for
discussing these features of Meshuggah’s music. Indeed, the
idea of deviance is crucial to the band’s aesthetic: meshuggah is
the Yiddish word for “crazy” or “insane.”7
[M]etal’s dominant aesthetic valorize[s] sonic power, freedom, and originality.
—Robert Walser1
riginality is essential for a heavy metal band. Since
forming in 1987, the Swedish quintet Meshuggah has
developed and honed what their drummer, Tomas
Haake, describes as “a unique approach to rhythm.”2 This approach, combined with the use of eight-string guitars whose extended ranges reach nearly an octave below that of a traditional
six-string guitar, are the primary ways in which the band’s music
deviates from metal’s stylistic norms.3 Since the eight-string
I am grateful to the colleagues, friends, and anonymous readers who
helped improve this article, which was initially presented at the 2014
meeting of the Society for Music Theory.
1 Weinstein (2000, 21), Walser (2014, 128). Weinstein’s “code” has three
components: sonic, visual, and verbal (2000, 8).
2 Tomas Haake (2008). In this article, a rhythm is a series of note values including rests. Meter is “a regular pattern of strong and weak beats to which
[the listener] relates the actual musical sounds” (Lerdahl and Jackendoff
1983, 12). This definition differs from the influential work of Krebs
(1999, 22), who defines meter as “the union of all layers of motion (i.e.,
series of regularly recurring pulses) active within it.” Group refers to “units
such as motives, themes, phrases, periods, theme-groups, sections, and the
piece itself” (Lerdahl and Jackendoff 1983, 12). In contrast to Lerdahl and
Jackendoff (13), the groups in this article are not hierarchical. Tactus indicates the basic felt pulse. Pulses are grouped into measures, which in turn
are grouped into hypermeasures (I thank an anonymous reader for clarifying
this issue). Rhythmic dissonances “do not normally disrupt the meter
(Krebs’s ‘submetrical dissonances,’ 1999, 30), [and] occur at the tactus
level—in 44 , the quarter-note beat—and below” (Biamonte 2014, ¶ 1.3).
Metric dissonances, which the present article does not study, “disrupt the
bar and the conducting pattern, which is normally quadruple” (Ibid.).
3 The band uses eight-string guitars tuned to F1–B[1–E[2–A[2–D[3–G[3–
B[3–E[4 and five-string basses tuned to B[0–F1–B[1–E[2–A[2. Pieslak
(2007, 243–44) lists some of metal’s most identifiable traits as “the Dorian/
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Aeolian or Phrygian/Locrian modes, the loud, distorted power chord as the
fundamental unit of pitch, and repeated, power-chord driven riffs in 44 time.”
Significantly, Meshuggah uses none of these techniques in the music studied
in this article. Other summaries of heavy metal’s stylistic norms appear in
Walser (1993, 44–51) and Weinstein (2000, 22–27).
Single-string riffs dominate the four albums released between 2002 and
2012 studied here. The band’s earlier and later music makes more frequent use of power chords. This article was completed prior to the 2016
release of Meshuggah’s eighth studio album, The Violent Sleep of Reason.
Osborn (2014, 81–82) makes a similar argument regarding Radiohead.
Near evenness is studied in Tymoczko (2011, 61–63, 123), Toussaint
(2013, 143–50), and Osborn (2014, 7–8). Repeated rhythmic figures that
deviate from alignment with the downbeat are studied in Biamonte (2014,
¶ 7.10) and Cohn (2016, ¶ 6.2–6.4). The importance of maximal evenness to rhythm is established in numerous studies, including Butler (2006,
84), Cohn (2008, 51–52), London (2012, 125–31), Osborn (2014), and
Toussaint (2013, 121–27).
The idea of musical deviance is familiar from disability studies. Lucas
(2016) draws persuasive connections between Meshuggah’s music and
seminal work in music and disability by Straus (2006). A full treatment of
this topic lies beyond the scope of the present article.
music theory spectrum 40 (2018)
example 1. “ Rational Gaze,” Nothing (2002), 0:00–0:15 (after Pieslak 2007, 222)
In a seminal study, Jonathan Pieslak described the essence
of Meshuggah’s approach to rhythm and meter as a fusion of
standard quadruple hypermetrical structures with repeated
rhythmic figures; the duration of each figure does not equally
divide the number of beat subdivisions in the section.8 To begin to explore the role of deviance and near evenness in these
structures, Example 1 presents a transcription of the opening
of “Rational Gaze.”9
I start by describing the metric organization of the passage, which is found in many of the band’s songs. The crash
cymbal projects the tactus level (unit ¼ beat) of the 44 meter
through its steady quarter-note pulse. The snare drum projects the metric level (unit ¼ measure/hyperbeat) through its
attack on beat 3 of each measure. Finally, due to the ubiquity
of this metric framework throughout rock and metal, an experienced listener will likely gather the hyperbeats into hypermeasures at the hypermetric level. Each hypermeasure
contains four measures. The eight-measure unit then repeats
8 Pieslak (2007, 220–23). Other studies of rhythm and meter in
Meshuggah include Hallaråker (2013), Lucas (2016), Metzger (2003),
Smialek (2008), and Rose (2013). Studies of rhythm and meter in metal
include Biamonte (2014, ¶ 8.7), McCandless (2013), and Osborn (2013).
9 The transcription in Ex. 1 closely resembles that of Pieslak (2007, 222). I
have omitted his metric analysis and notated the riff in 44 instead of 25
16 and
16 . All other transcriptions are mine. To avoid excessive ledger lines, I notate the guitar and bass parts in unison. The discussion of Ex. 1 is closely
modeled on that of Pieslak (2007, 220–22).
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example 2. Rhythmic and metric organization (after Biamonte
2014, Ex. 1)
in order to articulate the third and fourth hypermeasures,
thus completing the section level, containing sixteen (or
occasionally twenty-four or thirty-two) measures.10 Example
2 summarizes this metric framework, drawing on work
10 Lerdahl and Jackendoff (1983, 21) and Biamonte (2014, ¶ 1.2) note that
grouping outweighs meter when dealing with units of approximately eight
measures and higher.
rhythmic deviance in the music of meshuggah
example 3. “ Rational Gaze,” nearly even distribution of durations
example 4. “ Rational Gaze,” cyclic representation
in rhythm and meter in rock and metal by Nicole
Let us turn to the rhythmic organization of the passage.
Four statements of a riff, each with a duration of twenty-five
sixteenth notes (25 x), precede an extension of the riff whose
11 Biamonte (2014, ¶ 1.2).
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duration is 28 x. In the example, an arrow indicates the onset
of each statement. The sixteenth notes project the subtactus
level; the sixteenth-note unit represents a beat subdivision.
Other than the first statement of the 25 x riff, the 28 x extension is the only statement that begins squarely on a beat (specifically beat 2 of m. 7). I shall refer to the final extended (or
truncated) statement of the riff as the tail. Its purpose is to
music theory spectrum 40 (2018)
example 5. “ Dancers to a Discordant System,” obZen (2008), 0:47–1:20
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rhythmic deviance in the music of meshuggah
example 6. “ Dancers to a Discordant System,” duration palindromes
realign the initial attack of the riff with the downbeat more
quickly than the original unaltered riff would.
Turning to the idea of musical deviance, a number of
departures from the stylistic norms of heavy metal are apparent: the unusually low register, the absence of power chords,
the wide minor ninth leaps, and the use of only two pitches,
all of which depart significantly from blues- and pentatonicbased metal riffs.12 From a music-theoretical perspective,
Example 3 reveals that the rhythmic organization of the riff is
nearly even.
Three pitch cells are present: X ¼ hG[, Fi; Y, the retrograde
of X, hF, G[i; and Z, an embellishment of Y, hF, G[, G[i.
This segmentation takes into consideration durational accents
(each cell has a “short-long” or “short-long-long” profile),
registral accents (the first pitch of each cell leaps a minor ninth
to the second), and the guitarist’s fretting hand (G[ uses a fretting hand finger, while F falls on an open string).13 The duration of the initial X is 6 x, followed by Y ¼ 4 x, Z ¼ 6 x,
X ¼ 4 x, and Z ¼ 5 x. The duration series 6, 4, 6, 4, 5 is a
12 Such riffs are studied by Everett (2008, 160–64) and Biamonte (2010).
13 The riff’s ordered pitch series is nearly palindromic, but the limited pitch
content makes this somewhat trivial, and I am not aware of other (nearly)
palindromic pitch structures in the band’s riffs.
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nearly even distribution of twenty-five elements into five
parts—the maximally even distribution is 5, 5, 5, 5, 5.14 To
summarize the discussion of “Rational Gaze,” Example 4 provides a circular, cyclic representation of its rhythmic and metric
The circumference of the circle contains 128 elements, labeled 0 through 127 mod 128. This represents the 128 sixteenth notes that span the excerpt. The elements are gathered
into fours to prevent clutter. The hexagons labeled 0 and 64
represent hypermeasures. At 12:00, 0 indicates the first sixteenth-note attack, on the downbeat of m. 1. At 6:00, 64 indicates the sixty-fourth sixteenth note, on the downbeat of m. 5.
The repetition of the entire cycle articulates hypermeasures 3
and 4 to complete the section. Ovals indicate the eight hyperbeats, and diamonds indicate the thirty-two beats. Because
each hypermeasure is understood via inclusion relations to also
represent a hyperbeat and a beat, I do not superimpose multiple shapes on a given time point (and likewise for higher
14 The 6, 4, 6, 4, 5 nearly even distribution is also nearly palindromic, but
the latter property inheres in the former, as will become evident in Ex. 6
(21, 20, 19) and Ex. 8 (13, 15, 13, 15, 13, 15, 13, 15, 16). The only nearly
even distribution in this article that is not also nearly palindromic is found
in Ex. 10 (3, 1, 2, 2).
music theory spectrum 40 (2018)
example 7. “ Dancers to a Discordant System,” cyclic representation
metric levels). Rather, the shape representing the highest metric level appears on the circumference. Within the circle, an irregular pentagon in dashed lines indicates the 25 x and 28 x
riff statements; Tn x indicates transposition by n sixteenth
notes. The alignment of the dashed line with units 0 and 100
indicates the alignment of the onset of the riff with the downbeat of m. 1 and beat 2 of m. 7. The remaining statements of
the riff do not begin on a beat, and, thus, the dashed line ends
between units 24
28 , 52 , and 76 . In sum, the diagram represents
both the hypermeter (at the beat, hypermetric, and metric levels) and the riff (at the subtactus level). Listening to the
“Rational Gaze” excerpt while viewing the diagram corroborates and reinforces its representation of rhythm and meter.15
Example 5 offers a second illustration of near evenness and
introduces an instance of duration palindromes. The analysis
15 The circular shape of the diagram brings to mind similar diagrams in
Toussaint (2013) and London (2012).
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of “Dancers to a Discordant System” will reveal how pitch and
rhythm series operate within a clear hypermetric environment.
The china cymbal, snare drum, clean guitar octave figures,
and crash cymbal project the hypermeter. Specifically, the
china cymbal projects beats, the snare drum projects hyperbeats, the D]–E octave figure alights on every other hyperbeat
(a “half-hypermeasure”), and the crash cymbal projects hypermeasures through its attacks immediately before m. 5, on the
downbeat of m. 9, and immediately before m. 13.16 The agent
of deviance is the angular guitar/bass riff: the wide, dissonant
intervals and jagged melodic contour suggest the discord
named in the song’s title, as does the quarter-step bend/release
16 Textures similar to that of the oscillating D]/E figure frequently occur in
Meshuggah’s music and appear in the upcoming examples from “The
Paradoxical Spiral” and “Demiurge.” Their purpose is to open up a register
higher than that of the guitar/bass riff and to articulate metric levels above
the tactus. Pieslak (2007, 226–32, especially Ex. 12) studies a similar melody in the Meshuggah song “I.”
rhythmic deviance in the music of meshuggah
example 8. “ Obsidian,” Nothing (2002), 2:57–3:21
indicated by the mordent symbol. As illustrated in Example 6,
each statement of the riff contains three iterations of a fixed
pitch series, X ¼ hA1, B2, F1, C]2, G2, F1, A1, G[2, F1, C]2,
D2, F1, B1, C3, F1i.17
Each iteration of X is set to a different duration series.
The first has a combined duration of 21 e, and its durational series is 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, which
is partially palindromic, as illustrated by the brackets on
the example. The second series has a duration of 20 e. It
contains three alterations to the first series, each indicated
with an underline: 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1,
17 The pitch-class content of the riff can be viewed as an instance of pitch
deviance. The first seven pitch classes, hA, B, F, C], G, F, Ai, form all
but one member of the WT1 whole-tone collection, while the final eight
pitch classes, hG[, F, C], D, F, B, C\, Fi, add members of the WT0 collection (underlined). In general, however, pitch deviance is rare in the
band’s music; most of the riffs employ the OCT2,3 octatonic collection
(an exception will appear in Ex. 10, which uses the chromatic scale segment hE, F, G[, G, A[, Ai). The use of maximally even sets in the pitch
domain (octatonic, whole tone, chromatic) and nearly even sets in the
rhythmic domain invites further study, but a full treatment of this topic is
beyond the scope of the present article.
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which is less palindromic. The third series has a duration
of 19 e. It contains seven alterations to the second series:
1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, which is even less
A quick glance at each durational series reveals that the distribution of its fifteen elements is not nearly even with respect
to its combined duration, since multiple instances of 2 e are
always adjacent, rather than distributed almost as evenly as
possible.18 However, 21, 20, and 19 are nearly even with respect to their sum, 60, since the three numbers are as close as
possible to the maximally even distribution of 60 units into
three parts, 20 þ 20 þ 20. The unique length of each durational series provides contrast to the strict repetitions of the
60 e duration riff. The sum of the three durational series, 60,
also explains why the onset of the riff coincides with the
downbeat every five measures: 60 e / 12 e per measure ¼ five
measures. This places the onset of the riff out of phase with
the quadruple metric levels, superimposing a 5 þ 5 þ 5 þ 1
18 The maximally even distributions are as follows: ME (21, 15) ¼ 1, 1, 2, 1,
2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2; ME (20, 15) ¼ 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2,
1, 1, 2; ME (19, 15) ¼ 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2.
music theory spectrum 40 (2018)
example 9. “ Obsidian,” maximally even (solid line) and nearly even (dashed line) distribution of attacks (2:1 reduction).
grouping atop the 4 þ 4 þ 4 þ 4 meter. On the downbeat of
m. 16, a truncated tail (duration ¼ 12 e) completes the section.
Example 7 provides a graphic representation of the “Dancers
to a Discordant System” excerpt.
The diagram contains 192 elements, one for each beat subdivision unit. The elements appear in threes to prevent clutter.
At 12:00, 3:00, 6:00, and 9:00, hexagons represent hypermeasures. Triangles represent half-hypermeasures, ovals represent
hyperbeats, and diamonds represent beats. Finally, the solid
line triangle (with a truncated vertex) represents the duration
of the riff as 60, 60, 60, while the dashed-line irregular decagon represents the 21, 20, 19 duration series and the 12 e tail.
In this way, Example 7 graphically illustrates the interplay of
the deviant riff with the standard meter.
In the previous examples, near evenness and partial palindromes operated at the subtactus level of eight- and sixteenmeasure units, while the drum set projected the tactus and
higher metric levels. The next two examples will study the
roles of near evenness in eight-measure units where the drum
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set does not project levels higher than the tactus.19 Example
8 presents an excerpt from “Obsidian.”
On the bottom staff, attacks of the pitch D1 (made possible
by detuning the F1 string) divide the 128 subtactus units
(n ¼ x) into four statements of 13 þ 15 with a 16 x tail. The
attacks represent a nearly even distribution of 128 units into
nine parts; the maximally even distribution is 14, 14, 14, 14,
15, 14, 14, 14, 15. Example 9 diagrams the maximally and
nearly even distributions on a clockface, shown in a 2:1 reduction for clarity.
The nearly even distribution of the D1 attacks interacts
with the {D3, E[3} attacks shown on the top staff. The internal
arrangement of the 15 x group as 3, 3, 3, 3, 3 is maximally
even and, while not metrical, implies a compound quintuple
organization. By contrast, the internal arrangement of the
13 x group as 3, 3, 3, 1, 3 is not maximally even (2, 3, 2, 3, 3),
instead mimicking the repeated 3 s of the 15 x group with a
19 Pieslak (2007, 223–42) analyzes one such passage in “I.”
rhythmic deviance in the music of meshuggah
example 10. “ The Paradoxical Spiral,” Catch Thirty-Three (2005), 0:00–1:35
“hiccup” created by the 1 x attack. The tail duplicates the
attacks within the 13 x group and tacks on an additional e. at
the conclusion, the latter marked by the bent pitch E[1.
Example 10 presents the opening of “The Paradoxical
Spiral.” By combining rhythmic motion with pitch stasis,
the opening tremolo figure symbolizes the paradox named
in the song’s title. When the drums enter, the pitch content
of the figure varies by semitone. The changes are distributed
nearly evenly across the eight-measure unit: E3 occupies
three measures, F3 one measure, E3 two measures, and F3
two measures. By avoiding a pitch change every two or four
measures, the 3, 1, 2, 2 distribution frustrates a metric interpretation of the passage. The absence of snare drum attacks on
beat 3 of each measure (present in “Rational Gaze,” “Dancers to
a Discordant System,” and upcoming examples) likewise prevents any articulation of meter above the steady quarter-note
pulse on the crash cymbal. The recurring riff divides the thirtytwo beats into groups of 5, 6, 7, 6, and 8 beats respectively, with
the eight-beat group acting as a tail.20 This represents a nearly
even distribution of thirty-two elements into five parts—the
maximally even distribution is 6, 6, 7, 6, 7. Example 11 diagrams the maximally and nearly even distributions on a thirtytwo-element clockface, using solid and dashed lines respectively.
Thus far, I have used cyclic representations to model rhythmic
dissonance created by repeated riffs. A tail eventually alters the
riff in order for it to fit an eight- or sixteen-measure unit. I have
used the metaphor of standard and deviant to describe the interaction of the meter and the riffs. To indulge the metaphor, the
foregoing excerpts suggest that the standard overpowers the deviant, since the tails lengthen or shorten the riffs to fit the hypermeter. By contrast, the final two examples will examine riffs that
lack tails, which permits them to unspool across multiple large
metric units, thus recasting the relation of deviance and standard.
The analysis of “Do Not Look Down,” whose opening
appears in Example 12, will illustrate the interaction of the riff
with the song’s formal boundaries, tracking the fluctuating relationship of deviance and standard along the way.
The song begins in a state of metric uncertainty.21 The
opening riff presents four statements of an attack/rest series:
e e e e e e e e e e e (duration ¼ 17 e). In terms
20 The high degree of repetition can make it difficult to determine where the riff
begins and ends. In my interpretation, each statement of the riff begins with
the eighth notes hG2, A[1, A[2i and ends with the held G1 or hG1, G[1i.
21 I use the term “metric uncertainty” instead of the more common “metric
ambiguity” following London (2012, 99–100), who defines metric ambiguity as a clash of two meters.
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music theory spectrum 40 (2018)
example 11. “ The Paradoxical Spiral,” maximally even (solid line) and nearly even (dashed line) distribution
of pitch, all four statements begin identically, but the final six
pitches differ in the second and fourth statements. Each statement uses six members of the OCT2,3 octatonic collection
(G], A, B, D, D], F]), and no other pitch classes. I shall refer
to the ordered presentation of the four statements as Riff A
(duration ¼ 68 e). Later in the song, the same attack/rest series is used with a riff whose ordered pitch content differs
from that of Riff A, but is still restricted to the OCT2,3 octatonic collection. I shall refer to this later riff as “Riff B.”
The unusual duration of the attack/rest series combines
with a paucity of additional cues to make a metric interpretation difficult. As such, I have not included a meter signature in
the transcription. By contrast, the rhythmic profile of the series
is unambiguous. The bass drum projects a steady eighth-note
pulse; the snare drum hits create accents that suggest a
7 e þ 10 e grouping; and the china cymbal announces the
start of each 17 e series. Notably, the invocation of maximal
evenness both supports and complicates the 7 e þ 10 e grouping. As indicated by “ME (7, 3),” the 7 e grouping is
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supported by the maximally even distribution of the three
attacks (G]1–A1–G]1) that precede the second snare drum hit.
However, the distribution of the eight remaining attacks is
neither maximally nor nearly even (ME [10, 8] ¼ 1, 1, 1, 2, 1,
1, 1, 2). Below the staff, I indicate a second potential grouping
for the 17 e series. ME (11, 5) indicates the maximally even
distribution of the five attacks preceding the closing eighthnote run, and ME (6, 6) indicates the (trivial) maximally even
distribution of the closing eighth notes. The 11 e grouping, as
well as the maximally even distribution of its five elements, adhere to Justin London’s characterization of an eleven-beat
non-isochronous meter.22 As such, the listener may metrically
interpret the riff as one measure of 11
8 (eleven pulses, five
attacks) followed by one measure of 68 (six pulses, six attacks).
The next section of the song sets aside the metric uncertainty
by placing Riff A in a clear 44 metric context. Example 13 provides a transcription.
22 London (2012, 166–68).
rhythmic deviance in the music of meshuggah
example 12. “ Do Not Look Down,” Koloss (2012), 0:00–0:24
The drums now project 44 at the tactus level (cymbal crashes
on every quarter note) and metric level (snare drum attacks on
beat 3 of each measure). As indicated by the circles on the guitar/bass staff, each onset of the 17 e series shifts ahead by 1 e,
since 17 mod 8 ¼ 1.23
23 McCandless (2013, ¶ 25) studies a similar passage in the Dream Theater
song “Sacrificed Sons.”
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The appearance of Riff A in a new, clear metric context
prompts questions about the song’s overall form. Looking
ahead, it is safe to predict that the tactus and metric levels introduced in Example 13 will continue to structure the song,
given their presence in “Rational Gaze,” “Dancers to a
Discordant System,” and much of Meshuggah’s music.
Looking back, the clarity of the 44 meter in Example 13
prompts a retrospective hearing of the opening measures; it is
music theory spectrum 40 (2018)
Start 8-measure unit; end second statement of Riff A
Continue 8-measure unit; begin third statement of Riff A
example 13. “ Do Not Look Down,” 0:24–0:35
example 14. “ Do Not Look Down,” 0:00–1:48, formal diagram
as if the song has been in 44 from the very beginning. For this
reason, I label the initial measure of Example 13 as m. 17.
As such, mm. 17 and 18 play complementary roles. Measure
17 starts an eight-measure unit and ends the second statement of
Riff A. Measure 18 continues the eight-measure unit and begins a
third statement of Riff A. The result is that no tail has confined
Riff A to an eight- or sixteen-measure unit. In terms of musical
deviance, the deviant riff and standard meter are on equal footing for the first time (or, might the deviant riff overpower the
standard meter?). To answer this question, Example 14 traces
the path of Riffs A and B in later sections of the song.
The upper portion of the diagram, labeled “standard,” indicates the meter projected by the snare drum, cymbal, vocals
(not shown), and alternations of Riffs A and B. Seventy-two
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measures divide into three twenty-four-measure units. The
first unit is an instrumental introduction, while the second and
third units contain vocals. In sum, this portion of the diagram
contains 576 e.24
The lower portion of the diagram, labeled “deviant riff,”
brackets eight statements of Riff A or B; each statement occupies 8.5 measures. There follows a half-statement of Riff A
that occupies 4.25 measures. In all, this portion of the diagram
contains 578 e, equivalent to 72 measures of 44 plus two eighth
notes. Why is the final statement of Riff A cut in half?
24 The reader is reminded that units of this size are products of grouping,
not meter. The onset of the riff realigns with the downbeat in mm. 35,
52, and 69, but these moments are not rhetorically marked in any way.
rhythmic deviance in the music of meshuggah
3 24-measure units (hexagons), 72 hyperbeats (ovals), riff (dashed line)
example 15. “ Do Not Look Down,” cyclic representation
In m. 73, a new section begins (a guitar solo). The final two
eighth notes of the halved Riff A “spill over” into this section.
The halved Riff A does not function as a tail, since it neither
realigns the onset of Riff A with the downbeat nor confines
the riff to a particular section of the song. Rather, 578 e is the
smallest number of statements of Riffs A and B that runs the
riff through seventy-two measures, continues beyond the
seventy-two measures without shortening the 17 e series, and
ends the riff as quickly as possible in the new section. This
accounts for the 2 e discrepancy between the standard and deviant portions of the formal diagram. In descriptive terms,
the absence of a tail once again enables the deviant riff to override the sectional boundaries of the song, as first seen in
Example 13. Example 15 summarizes this information with a
cyclic representation.
Because each measure contains eight eighth notes, the
seventy-two measures of 44 are labeled with the integers 0
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through 576. Hexagons on the circumference and the solid line
triangle inside the circle indicate the three twenty-four-measure
units. Ovals indicate hyperbeats, and the dashed line irregular
nonagon traces the path of the deviant riff. The arrowhead issuing from the final dashed line indicates the two eighth
notes that exceed the seventy-two measures represented by
the space.
How does the deviance/standard narrative play out in the
rest of the song? The guitar solo (m. 73) and each subsequent
section contain sixteen or thirty-two measures, save for a twomeasure “coda.” The sixteen- and thirty-two-measure sections
come as no surprise, in light of the metric frameworks in
Examples 1 and 5. What is perhaps surprising is that each
subsequent riff remains within its section; there is no more
trespassing. In all, three sectional boundaries are violated
(intro ! verse one; verse one ! verse two; verse two ! guitar
solo), while six are not. The deviant riff and standard meter
music theory spectrum 40 (2018)
example 16. “ Demiurge,” Koloss (2012), 4:11–4:56
may have been on equal footing in the first seventy-two measures of the song, or perhaps the riff had the upper hand.
However, since all subsequent sections confine the durations
of their riffs, the song’s deviance/standard conflict ends with a
victory for the standard hypermeter.
In “Do Not Look Down,” large-scale rhythmic deviance in
the opening sections of the song yielded to an alignment of
rhythm and meter in the closing sections. The final musical
example features the opposite sort of arrangement, in which
large-scale rhythmic deviance first appears in the final section
of the song. The analysis of “Demiurge” will track the progress
and resolution of the deviance. Example 16 presents the opening sixteen measures of the section.
Similar to “Do Not Look Down,” the riff uses five members
of the OCT2,3 octatonic collection (D, E[, F, G[, A[) and no
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other notes. As in the prior examples, instruments belonging
to the drum set establish the metric standard: the crash cymbal
projects beats while the snare drum projects hyperbeats. The
duration of the deviant riff is 102 x, and recurrences of the
highest pitch A[2 create smaller groupings with durations of
21 x, 27 x, 24 x, and 30 x. Repetitions of the x e figure create trivial maximal evenness within each grouping and project
Harald Krebs’s grouping dissonance G4/3.25 Each statement
of the 102 x riff spans 102/16 ¼ 6.375 measures of 44 . Each iteration begins six sixteenth notes later than the previous one,
since 102 mod 16 ¼ 6. The onset of the 102 x riff will realign
with the downbeat in m. 51, because the least common multiple of 102 and 16 is 816, and 816
16 ¼ 51.
25 Krebs (1999, 31–33).
rhythmic deviance in the music of meshuggah
example 16. (Continued)
Immediately after the first eight-measure unit, a highregister electronically processed melody enters, which completes
the OCT2,3 octatonic collection (it introduces A\, B, C and
duplicates A[) and, more importantly, reinforces the 44 meter.
At the metric level, the melody begins on the downbeat, and
each subsequent attack falls on a beat. At the hypermetric level,
the melody enters on a strong beat and repeats every four measures. In all, eight statements of the four-measure melody create
a thirty-two-measure unit. The complete organization of the
section is thus eight measures (riff only) þ thirty-two measures
(riff and melody). This falls short of the fifty-one measures
needed for the onset of the 102 x riff to realign with the downbeat. What then becomes of the riff at the end of the song?
The outcome is not produced by rhythmic or metric means,
but instead by a simple recording studio effect—a fadeout.
During the sixth and seventh iterations of the melody, the volume of the guitar, bass, and drums gradually decreases while
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the volume of the melody remains constant. The eighth and
final iteration of the melody is heard alone. In this way, the
deviant riff gives way to the standard hypermeter. Example 17
models this process.
Because each measure contains sixteen sixteenth notes, the
forty measures of 44 are labeled with the integers 0 through
640. Hexagons connected by solid lines indicate four-measure
units projected by the melody; an asterisk indicates that the
first four-measure unit is not articulated since the melody
enters at m. 5 (unit 64). Ovals indicate hyperbeats projected by
the snare drum, and dashed lines indicate statements of the
102 x deviant riff, which cease at m. 36 (unit 576), the point
at which the guitar, bass, and drums are no longer audible.
The analyses in this article take a preliminary step toward a
deeper understanding of Meshuggah’s “unique approach to
rhythm,” as described by Haake at the start of this article. They
also support the thesis that the band’s music deviates from certain
music theory spectrum 40 (2018)
10 4-measure units (solid line, hexagons), 40 hyperbeats (ovals), riff (dashed line)
* = not articulated
example 17. “ Demiurge,” cyclic representation
conventions of heavy metal at a broad stylistic level (through the
use of eight-string guitars and single-note riffs) and from certain
music-theoretical benchmarks at the level of rhythmic/metric
structure (through lengthy rhythmic figures that employ wide interval leaps and involve near evenness, partial palindromes, and
the misalignment of grouping and meter). Together, the stylistic
and theoretical deviations begin to explain how the band “creates
original music that expands the genre’s code from within without
destroying it,” as per Weinstein. Since Meshuggah’s influence
has been widespread, having spawned an entire metal subgenre
called “djent,” the methodology adopted here should apply to future work on similar artists.26
26 “Djent” is an onomatopoeic word used to describe low register, distorted,
palm-muted guitar riffs, as well as the bands that use such riffs. On this
and other subgenres of metal, see Kegan (2015).
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Music Theory Spectrum, Vol. 40, Issue 1, pp. 121–37, ISSN 0195-6167,
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electronic ISSN 1533-8339. V
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DOI: 10.1093/mts/mty005
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