Has there ever been a band in the history of rock music more enigmatic than Tool? From their gloomy prog metal sound to their consistent use of long-form song structures to their expansive gaps between album releases to their general desire not to be seen, it difficult to envision a band as ill-suited for stardom as Tool. And while Tool is not likely to ever encounter any crossover success, their limited but beloved canon (only five studio albums over a 30+ year career) has cultivated an ardently devoted following since their emergence in the nineties. Despite receiving only limited airplay on certain modern rock-format radio stations, each of their three most recent studio albums (2019’s Fear Inoculum, 2006’s 10,000 Days, and 2001’s Lateralus) all debuted at number one on the Billboard 200.
For all the reasons Tool is a musical unicorn, the characteristic that probably defines them the most is their use of time signatures and metric organization. In some ways, this puts them in line with mathcore bands of the nineties like Meshuggah and The Dillinger Escape Plan who also embraced a Rush-esque incorporation of unusual time signatures. But while those bands drew more influence from hardcore punk and metal bands, Tool’s approach was less aggressive in favor of a darker, more brooding sound. Although the members of Tool (Maynard James Keenan, vocals; Adam Jones, guitar; Justin Chancellor, bass; Danny Carey, drums) are all virtuosic performers, they never really shred, and their musical skills are on display in how they construct and develop complex musical layerings rather than through verbose soloing. These intricate layers are often assembled through a counterpoint built not just on melodic and rhythmic independence but on a deeper level that factors in meter and causes the listener to actively question how the rhythms are actually being organized.
By using asymmetrical meters, dividing beat and rhythm patterns into unexpected groupings, blurring meter definitions, and juxtaposing multiple meters against themselves simultaneously, Tool have built up their popularity despite all of their unpopular traits. Perhaps no song of theirs better emulates this than the title track from their Lateralus album, and let’s unpack this epic track in order to better understand the different levels on which Tool’s unique approach to meter works.
Form in “Lateralus”
To guide our understanding of the use of meter in “Lateralus,” let us begin with an understanding of its form. At its core, “Lateralus” follows a fairly conventional structure for a rock song in that it consists of a verse/chorus form with two full statements plus an intro and coda (or outro) section. However, at nearly nine-and-a-half minutes, there is obviously quite a bit of expansion happening within that simple framework. The following is a diagram of the song’s form, including section (Capital letters) and subsection (lowercase letters) labels* and time indications:
| Section | Time |
| Intro (A) | 0:00-1:38 |
| a | 0:00 |
| b | 1:14 |
| Verse (B) | 1:38-2:33 |
| c | 1:38 |
| c’ | 2:05 |
| d | 2:18 |
| Chorus (C) | 2:33-2:58 |
| b’ | 2:33 |
| Verse (B’) | 2:58-3:52 |
| c | 2:58 |
| c’’ | 3:13 |
| c’’’ | 3:24 |
| d’ | 3:37 |
| Chorus (C’) | 3:52-4:49 |
| b’’ | 3:52 |
| b’’’ | 4:08 |
| b’’’’ | 4:33 |
| Coda (D) | 4:49-9:24 |
| e | 4:49 |
| f | 7:18 |
| f’ | 8:38 |
* – apostrophes by section labels indicate that the section is similar to the previous section of that same letter with some modifications. b’ = b prime, b’’ = b double prime, and so forth
The track achieves its Mahlerian run-time both through the number of unique ideas presented and the development and repetition of those ideas. Despite having a somewhat standard total of four major sections (intro, verse, chorus, coda/outro), there are at least six distinct subsections within these main sections with their own identifiable themes and riffs. This is certainly more than the average rock song, as typically major sections of rock songs do not contain multiple distinct subsections. The new instrumental section between the verse and chorus (“d,” first heard at 2:18) is analogous to a pre-chorus (though this section would typically have vocals with it), but the fact that both the opening and closing sections have multiple distinct subsections is fairly unusual. The second subsection in the Intro (“b,” 1:14) is essentially an instrumental version of the song’s impending chorus, and while it is not unusual for a song to start with a form of its chorus as an introduction, the fact that this comes more than a minute into the song following a different riff is notable.
The main method of expansion in “Lateralus,” though, is the extension and development of ideas within its form, particularly in the Intro and Coda sections. To start the song, Jones plays a two-bar riff three times and then expands it into a four-bar riff, which he plays a total of seven times. The band crescendos towards the climactic arrival of the Chorus riff at 1:14, but this extensive use of repetition creates a very slow build for its opening.
The Coda section also begins by stating a concise idea and then building gradually through an even more extreme use of repetition. The foundational idea of this section (subsection “e”) is simply four repeating eighth notes played by Chancellor’s bass followed by a quarter rest, and this idea is played, by my calculation, 144 times over the next two-and-a-half minutes of the track, as the other members of the band build around this idea.
Even the Chorus sections of the song utilize repetition in noteworthy ways, particularly with the second Chorus (3:52). This version of the Chorus spans nearly a minute, which is an unusually long duration for a chorus section of a rock song. The second Chorus actually starts with an abbreviated version of the first Chorus (the first one has three vocal phrases, while the second only has two), but then it transitions into an instrumental version of the Chorus with a guitar solo by Jones (4:08). Keenan’s vocals then return, but with a new vocal melody and lyrics from before (4:33).
Tool has certainly mastered the art of building epic songs in the tradition of bands like Led Zeppelin, Pink Floyd, and Rush by subverting common rock song forms to absurd extremes, but the remainder of this chapter will focus on how they manipulate and, at times, juxtapose meters in wildly inventive ways within these sections of “Lateralus.”
Metric Juxtapositions in the Introduction, Chorus of “Lateralus”
There is no part of “Lateralus” that is more metrically stable than the very beginning. The guitar riff that begins the track (Ex. 1) is solidly in the simple quadruple meter of 4/4, and despite some syncopation, there is not any doubt that the music fits into this quadruple meter. As this riff repeats, though, it begins to introduce a bit of uncertainty in regard to its meter. A march-like triplet rhythm emerges in the rhythm section, fading in from silence to eventually drive the song into the next part of the Introduction. The triplet beat divisions imply a compound meter (beats in compound meters divide into three equal parts, and in simple meters, they divide into two equal parts), and they directly conflict with the duple divisions played by the opening guitar riff.
As the song moves into the second part of the Introduction, Tool also pivots into a new meter through a metric modulation, which is a change that occurs between meters at a set mathematic conversion. At this moment, the triplet eighth notes played in the march figure become duple eighth notes in the new meter, which in turn causes the tempo to speed up (the first section clocked in around 112 beats per minute, while this new section is around 180). Furthermore, the meter changes from 4/4 to 3/4, shifting from a quadruple meter to a triple meter. Ironically, even though the song starts by clearly establishing a very conventional simple quadruple meter, this is the only point in the entire song that uses this type of meter on a recurring basis.
What is most fascinating about this new section, though, is not that a metric modulation has occurred, but, rather, that there is a juxtaposition of two potential meters implied against each other. My contention is that the most logical choice of meter here is 3/4, largely because of the way in which Carey plays the beat (Ex. 2). His groove here is built around steady quarter notes on the high hat and bass drum/snare attacks on alternating downbeats of each measure, which strongly implies that quarter notes receive the beat value and that there are three beats (the distance between accented bass/snare attacks) in each measure. However, the rhythmic patterns used by guitar and bass during this section complicate this analysis. Whereas the drum attacks occur generally every beat or every three beats, the guitar and bass attacks occur every one-and-a-half beats, or as a dotted quarter note (Ex. 3). While this still aligns with the 3/4 metric pattern, it fits better with a different meter: 6/8.
In some ways, 3/4 and 6/8 are very similar meters. Both have a total of six eighth notes in them, but the way that those eighth notes are divided is different, and as a result, they have different numbers and placements of beats. 3/4 is a simple triple meter in which its six eighth notes are grouped into three beats of two divisions:
On the other hand, the six eighth notes in a measure of 6/8 are grouped into two beats of three divisions:
When these three eighth notes are combined into one beat, they form a dotted quarter note. And this is where the rhythmic alignment of the dotted quarter-based guitar and bass parts conflicts with the quarter-based drum groove. If you focus on the guitar part and you tapped your foot along to the beat, your foot would tap twice every measure. But if you focused on the drum part, your foot would tap three times in the same amount of time.
This same instrumental texture returns for the song’s Chorus (2:33) but adds Keenan’s vocal melody to it, and the vocal melody exacerbates this juxtaposition even further (Ex. 4). Unlike the more punctuated guitar and bass parts, Keenan’s vocals sustain dotted quarter durations for much of its phrase, and this added connectivity heightens the feeling of each dotted quarter note acting as a downbeat. The space between many of the attacks in the guitar part lend it to a bit more of a syncopated feel in 3/4, but when these attacks are connected in the vocal line, they feel more like contiguous beats. The steady drum groove keeps the music rooted in the simple triple meter, though, and this metric juxtaposition is made even more prominent.
There is one other notable aspect of the use of meter found in the Introduction and Chorus sections, and it has to do with the grouping of measures and the manipulation of downbeats in the latter half of the phrase. The entire phrase consists of 24 beats (assuming the simple triple meter of 3/4), which strongly implies an eight-measure phrase. This is, in fact, how the music unfolds; however, the way in which Tool achieves these eight measures is very unexpected. An eight-measure phrase implies a bifurcation of two four-measure subphrases, but the first inflection point in the phrase occurs after its third measure, not its fourth (made clearest by the fill into a cymbal crash on the downbeat of the fourth measure in Carey’s drum part – Ex. 2). The next inflection point occurs after another three measures (the sixth of the whole phrase), but the beat of emphasis is what would be beat 3 of the sixth measure rather than beat 1 of the seventh measure. Because of this, the sixth measure makes more sense as a measure of 2/4 in order to place this beat of emphasis on beat 1 of a bar rather than beat 3. The phrase then concludes with a third subsegment consisting of 7 beats. The beats of emphasis within this subgrouping are the first and fourth beats, which means that the final two bars of the phrase would be 3/4 and 4/4. Taken altogether, the metric pattern of this phrase would be:
3 – 3 – 3 – 3 – 3 – 2 – 3 – 4
Add it up, and you get 24 beats, but because Tool is manipulating where they are putting their downbeats, they take a very roundabout way to get there. This metric pattern is further confirmed by Keenan’s vocal phrasing, so at least that aspect of it doesn’t make matters any more complicated than they already are.
Metric Juxtapositions in the Verse of “Lateralus”
The Verse section (1:38) continues the same propulsive beat that concludes the Introduction, but the meter abruptly changes to 5/4. As an asymmetrical meter, 5/4 uses neither the duple nor triple meters being juxtaposed in subsection “b,” but in a way, it is also both duple and triple simultaneously. Tool’s use of 5/4 in the Verse conforms to a 3+2 beat grouping, which is made explicit largely through the rhythmic movement in the drum (Ex. 5, 1:38) and bass (Ex. 6, 1:51) parts.
It thus alternates between a triple and duple meter within its five-beat measures. Even though this section is significantly different from anything from the Introduction, I do see a rhythmic linking between the two in their shared use of dotted quarter notes to blur the meter. In subsection “b,” dotted quarters are used to superimpose a compound 6/8 meter against the track’s simple 3/4, while in the Verse (subsection “c”), Carey’s drums accent the first two dotted quarters of each bar in a way that allows the meter to stretch from 4/4 (what the meter would likely be if he played two quarter notes instead of two dotted quarter notes) to 5/4. Chancellor’s bass also implements these dotted quarters as a variation on his bass riff during the second Verse (3:11), which strengthens this linkage of dotted quarter notes across multiple sections.
Despite the switch to an asymmetrical meter, the overall use of meter in the Verse is probably more stable than it was during the Introduction and Chorus sections. All of the instruments conform to the same 3+2 beat groupings up until the transition into the Chorus (2:30). Here, they break away from 5/4 with a riff consisting of four eighth notes that recalls both the guitar’s rhythm in the Verse and the march-like triplets from the very beginning. This rhythm allows the band to pivot back to a triple meter – they play three measures of the riff repeating in 3/4 followed by a shortened version of it played in 2/4, which then launches into the Chorus. Even in these measures, though, the band is in agreement as to what the meter is, even if the meter itself is changing.
The one element during the Verse that blurs the collective sense of meter away from 5/4 occurs with Keenan’s vocals. Keenan sings only quarter notes during the Verse, which means he only ever enunciates syllables on downbeats (no dotted rhythms). Below is a transcription of Keenan’s vocals during the first Verse, with accents added on syllables that he emphasizes in his delivery (Ex. 7):
Because Keenan’s pitches fall on downbeats, it fits within 5/4 without much issue, but at the very least his melody does not conform to the same metric pattern of 3+2 established by the instruments. His melody is perhaps ametric and just simply exists as a steady flow of notes that could fit into any meter, but it is notable that his emphasized attacks tend to imply groupings of either three or two. This is similar to what the instruments are doing, but whereas their groupings always follow the same 3+2 pattern, Keenan’s are essentially random. The beat groupings for Keenan’s first phrase are as follows (starting from his first entrance in beat 2 of the first measure):
3 – 3 – 3* – 3 – 2* – 3 – 3 – 2 – 3 – 2 – 2 – 5 – 2 – 3
* – these groupings are consecutive beats of rest
His second phrase in the first Verse uses the following beat groupings:
2 – 3 – 3 – 3 – 2 – 2* – 3 – 3 – 2 – 3* – 2 – 2 – 3 – 2 – 3 – 2*
Many of these points of emphasis do not line up with the established meter of the instruments, and while there are some similarities when comparing the beat groupings of his two phrases, it seems that this is largely a random succession of groupings. Actually, random is probably not the best way of describing this sequence, as it is undoubtedly determined by the syllabic alignment of Keenan’s lyrics. Because he is just following the shape of the syllables, and in doing so, he is effectively ignoring the meter outlined by the music, Keenan’s approach to text setting is very organic and speech-like. It also creates another type of metric juxtaposition that connects well to Tool’s overarching use of this technique throughout the track.
Metric Juxtapositions in the Coda of “Lateralus”
Although the second Verse and Chorus sections are not identical (there is actually much more variation between these second occurrences compared to their initial appearances relative to the vast majority of rock songs), they present minimal new techniques specific to this discussion of metric juxtaposition, so let us skip ahead to the Coda section (4:49), which is the chocolatey prog center of this musical Tootsie Pop. This expansive section kicks off with a very simple and sparse idea: four repeating eighth notes on the tonic pitch of “D” followed by a quarter rest (Ex. 8).
This repeating rhythm serves as the foundation off which this entire subsection (“e,” which lasts nearly two-and-a-half minutes) is built, but it is not a new idea within the track. This is the same rhythm as the marching triplets that fade in during the Intro as well as the guitar’s rhythm when it enters during the Verse (“c’,” 2:05). What is most notable about this rhythm in this isolated context is its metric malleability. Because it is just a string of eighth notes, it could function in both the simple triple meter of 3/4 (two two-eighth note groupings followed by a third beat of rest) or the compound duple meter of 6/8 (one three-eighth note grouping followed by a short downbeat attack on the second beat). The previous instances of this motif only exacerbate this metric dilemma – in its former use, the eighth notes follow the 3+1 grouping when they are presented as triplets, while in its latter use, the eighth notes use the simple meter 2+2 grouping (albeit in a 5 meter). Since the section of the song that immediately precedes the Coda is pretty clearly in a simple meter with its steady use of plodding quarter notes, I tend to hear this bass part in 3/4, although I also believe its context is left intentionally ambiguous.
The second layer to emerge within the Coda is Carey’s hi hat, which enters with a succession of sixteenth and eighth note attacks at 4:57 (Ex. 9).
Carey’s rhythm follows a steady pattern consisting of two sixteenth notes followed by four eighth notes, and this pattern continues without deviation until 5:38 in the track. What is fascinating about this rhythm is that it implies neither a simple triple nor compound duple meter. In fact, the most logical meter for this motif is one that has not been used at all to this point in the track: 5/8. Since the first two sixteenth notes are equivalent to one eighth note, the pattern is five eighth notes long, and these implied downbeats are heightened with the extra emphasis Carey uses on the first sixteenth note that restarts the sequence. And since these two rhythmic motifs (bass and hi hat) exist simultaneously without any attempts to conform to the other, Tool establishes a very blatant polymetric texture with these first two gestures.
But wait, there’s more! Jones’ guitar is the third musical character to enter the Coda at 5:05, and it begins with a series of sustained, wide interval pairs that establish an eight-measure phrase length for this section (Ex. 10).
Unlike the previous two motifs, this one gradually evolves throughout this section, and each time it recurs, it adds a bit more rhythmic and melodic motion. Even in its least rhythmically active initial version, this idea very clearly asserts the compound duple meter of 6/8 through its use of dotted quarter notes. In this context, the bass motif perhaps sounds more like a 6/8 idea, but even if it is definitely in 6/8, the 5/8 hi hat part maintains the metric dissonance of this section.
As the guitar pattern evolves, its rhythmic additions continue to reinforce a 6/8 meter, although they do so using syncopation. For example, the first rhythmic addition occurs at 5:18 in a measure that would feature a quarter note “G” moving to a sustained note “A” that starts on the third eighth note of the bar (Ex. 11), and the following addition at 5:27 adds a “C” on the sixth eighth note followed by another “A” on the third eighth note of the following measure (Ex. 12). While in a vacuum these rhythms perhaps make more sense in 3/4 (the first addition would simply be written as a quarter note and then a half note, for example), the steady use of dotted quarter notes leading up to these inflections essentially prohibits feeling them in that simple triple meter. Instead, the note changes on the third and sixth eighth notes of each measure feel like anticipations of their following downbeats (the first and fourth eighth notes would be emphasized in 6/8). With these three instrumental gestures – none of which is very complicated on its own – Tool have established three separate meters that exist simultaneously.
One other fascinating aspect of this guitar riff is its connection to the opening guitar riff of the entire song, which is made clearest when the Coda riff reaches its maximum level of rhythmic activity with the phrase that begins at 5:30 (Ex. 13). This pitch pattern – D-A-G-A-C-A-G-A-G-D – is identical to that of the opening guitar riff. And although they are played in two different meters, their rhythms are very similar, particularly in their use of syncopation. The main difference between their rhythms is in how the final four pitches are played. At the beginning (simple quadruple), all four of these notes are played as equal beat divisions, while during the Coda (compound duple for the guitar part), they are played with a long-short lilt. Along with the bass motif that starts the Coda, Tool have repurposed both of the defining musical gestures from the Intro here in the Coda, but they have done so while changing the meters for both of them.
Tool actually adds in one additional meter juxtaposition within this first subsection in the Coda, and it happens when Carey changes his drum pattern at 5:38 (Ex. 14).
His hi hat continues but does so using steady eighth notes and omitting the staggered sixteenth notes. To this, he adds bass drum and snare parts. The bass drum plays four eighth notes (in a pattern that recalls the bass part’s rhythm in the Coda), and then, after two beats (four eighth notes) of rest, he adds a single snare downbeat attack. This is immediately followed on the next downbeat with a restarting of the bass drum attacks, thus establishing this new looping idea. In total, this pattern spans five beats (ten eighth notes), which means that Carey’s drum part switches from implying 5/8 to 5/4. This recalls the use of 5/4 during the Verse, although the use of rhythms between these sections is very different. As was the case with the solely hi hat part before this, Carey’s ostinato repeats independently of the guitar/bass parts to perpetuate the metric juxtaposition.
A closer examination of this modified drum part reveals that there is actually a trace of the previous 5/8 meter within the new 5/4 pattern. Even though the hi hat rhythm moves away from the pair of sixteenth notes every fifth beat division, Carey does still maintain the same grouping of five eighth notes by way of his use of open and closed hi hat strikes (drummers use a foot pedal to either open the hi hat cymbals, which creates more of a ringing sound, or close them, which creates a tighter sound). The pattern he uses has one open strike (o), one closed (+), one open, and two closed, which makes for a 2+3 pattern in which the ringing open strikes provide a bit more emphasis. This hat pattern ends up lining up with the 5/4 pattern implied by the bass drum and snare figures, but because the bass/snare pattern spans five quarter notes, the five eighth note groupings of the hat are played at a 2:1 ratio. As a result, there are in fact four (!) meters being played simultaneously at this point in the track.
It should be noted that Keenan’s vocals add another layer to the texture, although to my ear his rhythms do not add anything different from the existing meters implied by the instrumental parts. Keenan’s rhythms mostly conform to the 6/8 implied by Jones’ guitar, but his use of sustain does detract from the rhythmic and metric precision of his part.
As the “e” subsection of the Coda continues, the band gradually works towards a more unified sound by removing some of its metric dissonance. Around 6:12, the bass transitions to a more sustained gesture. Then at 6:20, Carey’s drum groove finally relents at 6:20 when it breaks away from its five-beat hemiola, favoring a more driving pattern that clearly outlines a simple triple 3/4 meter (bass and snare drum emphasis of downbeats of each measure fit it firmly in its triple meter). The 6/8 guitar riffs continues for a bit, but at 6:38, it also switches to a more sustained power chord idea (and then a sustained prog solo), which makes the track sound pretty clearly in 3/4 for the first time in a while.
The guitar solo then builds into the final new subsection of the track at 7:18 (“f”), which kicks off with a crunchy dotted quarter-based guitar riff that recalls the guitar’s rhythm from the Intro and Chorus sections. However, after four measures of this riff playing by itself, the bass and drums kick back in at 7:22 with a new heavy groove that strongly implies a half-time feel. The groove still sounds like it is in a triple meter, but the half notes now sound like the beat rhythms rather than the quarter notes. Once again, Carey’s use of bass and snare drum attacks guide the listener’s understanding of the meter, and these heavier, more spacious attacks present yet another distinct metric juxtaposition. Every two measures of the original 3/4 meter now sound like they are superimposed over one larger measure of 3/4.
However, as with the previous Coda subsection, this new part adds yet another layer to its metric casserole in the form of Keenan’s vocal melody when it returns at 7:31. As he does in the Chorus, Keenan sings with a series of sustained dotted quarter attacks that once again imply a compound duple 6/8 meter. This rhythm is similar to what Jones’ guitar is playing, but because Keenan’s vocals utilize consistent sustain, they bring out the lilting quality of 6/8 a bit more. The connection between the vocal parts for this closing part of the song and the Chorus is also notable. Rhythmically, they are very similar, and they also share a decent amount of melodic overlap. The drastically different instrumental parts, particularly with the half-time implication in the drums in subsection “f,” makes these vocal parts sound distinct from one another, but they are still consciously connected to each other.
Conclusion:
“Lateralus” is such an intricately constructed masterpiece in many regards. Despite the relatively large amount of distinct motifs and themes, the music is incredibly efficient and interconnected, with ideas like the marching triplets from the Intro and the sustained dotted quarter notes from the vocal melody in the Chorus returning multiple times, often undergoing a modification when they do. The true genius of its construction, though, occurs with their incorporation and manipulation of several meters. Meters are used in unexpected ways through a variety of techniques, including metric modulation (Intro), downbeat displacement (end of the Verse), and especially metric juxtaposition (Chorus and Coda). As Keenan sings during the Chorus, over analyzing separates the body from the mind, but when Tool has melted our minds so thoroughly, it might be time to invest in a replacement, anyway.