Article: Using Drumbeats to Theorize Meter in Quintuple and Septuple Grooves


Using Drumbeats to Theorize Meter in Quintuple and Septuple Grooves

This article explores how drummers play music in five- and seven-count grooves. The article is published in Music Theory Spectrum.

Dissertation


Unpopular Meters: Irregular Grooves and Drumbeats in the Songs of Tori Amos, Radiohead, and Tool

This is my PhD dissertation (University or Toronto). It's about how listening to the drum kit can help us understand complicated meters in rock music.

Audio samples reffered to in thesis
Chapter 1

Ex. 1.1: Harmonic progression and metric changes in OutKast’s “Hey Ya!” (2003)


Ex. 1.2: Intro and first verse of Tori Amos’s “Spark” (1998)


Ex. 1.5: Breakdown groove in Tool’s “Pushit” (1996)


Ex. 1.7: Comparison of metric annotations of Radiohead’s “Karma Police” (1997)


Ex. 1.10: A common 5/4 backbeat variant in Muse’s “Animals” (2012)


Chapter 2

Ex. 2.1: Second verse and chorus of Taylor Swift’s “I Knew You Were Trouble” (2012)


Ex. 2.2: Second verse and chorus of Miley Cyrus’s “Wrecking Ball” (2013)


Ex. 2.3: End of intro and beginning of first verse of Dream Theater’s “A Nightmare to Remember” (2009)


Ex. 2.4: End of intro and beginning of first verse of Between the Buried and Me’s “Prequel to the Sequel” (2007)


Ex. 2.5: Irregular fill in Soundgarden’s “Pretty Noose” (1996)


Chapter 3

Ex. 3.2: Strong tresillo articulation in the intro of Goo Goo Dolls’s “We Are the Normal” (1993)


Ex. 3.3: Weak tresillo articulation in the first verse of Tori Amos’s “That Guy” (2009)


Ex. 3.4: Retrograde tresillo in James Bay’s “Hold Back the River” (2013)


Ex. 3.6: Subtleties of tresillo-family permutations in three grooves from Tool’s “Parabola” (2001) (A)


Ex. 3.6: Subtleties of tresillo-family permutations in three grooves from Tool’s “Parabola” (2001) (B)


Ex. 3.6: Subtleties of tresillo-family permutations in three grooves from Tool’s “Parabola” (2001) (C)


Ex. 3.7: Virtuosic drum work over a stable guitar part in Tool’s “Ticks & Leeches” (2001)


Ex. 3.8: Variation within a standard triple-meter drumbeat in Tori Amos’s “Fast Horse” (2009)


Ex. 3.9: A unique triple-meter drumbeat in the verse of TTNG’s “Rabbit” (2008)


Ex. 3.10: Projective analysis of an instrumental breakdown in Tool’s “Rosetta Stoned” (2006)


Ex. 3.11: Pulse-retaining metric modulation between 4/4 and 6/16 in Tori Amos’s “Witness” (2005)


Ex. 3.12: Measure-retaining metric modulation between 6/8 and 4/4 in R.E.M.’s “Shiny Happy People” (1991)


Ex. 3.13: Pulse-retaining metric modulation with double-time shift from slow 6/8 to moderate 4/4 in Morrissey’s “Tomorrow” (1992)


Ex. 3.14: Measure-retaining metric modulation from 12/8 to 4/4 in the second chorus of Dream Theater’s “A Nightmare to Remember” (2009)


Ex. 3.15: Metric modulation with a 3:2 ratio between two 4/4 grooves in Tori Amos’s “Hotel” (1998)


Ex. 3.16: Consistent backbeat across various super-metric patternings in the first measures of Pearl Jam’s “The Fixer” (2009)


Ex. 3.17: Recurrent drum fills clarify the super-metric structure of several instrumental passages in Radiohead’s “Black Star” (1995)


Ex. 3.18: Quintuple patterning at multiple hierarchical levels in Gorillaz’s “5/4” (2001)


Ex. 3.19: Triple super-meter with a regular compound cross-rhythm in Tool’s “Stinkfist” (1996)


Ex. 3.20: The standard rock beat challenged by harmonic rhythm and vocal phrasing in Of Monsters and Men’s “Crystals” (2015)


Ex. 3.21: Half-time triple meter in two songs by Tool (A) “The Patient” (2001)


Ex. 3.21: Half-time triple meter in two songs by Tool (B) “Swamp Song” (1993)


Chapter 4

Ex. 4.2: Displaced snare articulations framing fifth-beat continuations in Primus’s “Here Come the Bastards” (1991)


Ex. 4.3: Placement of three continuational snares leading to ambiguity of grouping and hierarchy in Tool’s “Vicarious” (2006)


Ex. 4.4: Three 5/4 grooves with dotted cross-rhythms (A) Vanessa Hudgens, “Last Night” (2008)


Ex. 4.4: Three 5/4 grooves with dotted cross-rhythms (B) Tool, “Rosetta Stoned” (2006)


Ex. 4.4: Three 5/4 grooves with dotted cross-rhythms (C) Akeboshi, “Wind” (2005)


Ex. 4.5: A unique metric structure in Amos’s “Rose Dover” (2014)


Ex. 4.6: Two quintuple-meter grooves in Dream Theater’s “A Nightmare to Remember” (2009) (A)


Ex. 4.6: Two quintuple-meter grooves in Dream Theater’s “A Nightmare to Remember” (2009) (B)


Ex. 4.7: Deferred second continuation in quintuple meter in Tool’s “The Patient” (2001)


Ex. 4.8: Grouping dissonance between the kick-snare pattern and the steady hi-hat in Sting’s “Seven Days” (1993)


Ex. 4.9: A partially underdetermined drumbeat over a metrically irregular guitar ostinato in Dave Matthews Band’s “Seven” (2009)


Ex. 4.10: A repeating five-measure drumbeat pattern in TTNG’s “Rabbit” (2008)


Ex. 4.11: Incipits of each distinct quintuple drumbeat lasting two or more measures in Tool’s “The Grudge” (2001) 1. Intro


Ex. 4.11: Incipits of each distinct quintuple drumbeat lasting two or more measures in Tool’s “The Grudge” (2001) 2. Chorus


Ex. 4.11: Incipits of each distinct quintuple drumbeat lasting two or more measures in Tool’s “The Grudge” (2001) 3. Vamp


Ex. 4.11: Incipits of each distinct quintuple drumbeat lasting two or more measures in Tool’s “The Grudge” (2001) 4. Verse


Ex. 4.11: Incipits of each distinct quintuple drumbeat lasting two or more measures in Tool’s “The Grudge” (2001) 5. Choruses 2 and 3


Ex. 4.11: Incipits of each distinct quintuple drumbeat lasting two or more measures in Tool’s “The Grudge” (2001) 6. Instrumental


Ex. 4.11: Incipits of each distinct quintuple drumbeat lasting two or more measures in Tool’s “The Grudge” (2001) 7. “Admonition”


Ex. 4.11: Incipits of each distinct quintuple drumbeat lasting two or more measures in Tool’s “The Grudge” (2001) 8. Outro


Ex. 4.13: Mid-measure kick-drum anacruses in a 4/4 and a 7/8 groove (A) Stone Temple Pilots’s “Interstate Love Song” (1994)


Ex. 4.13: Mid-measure kick-drum anacruses in a 4/4 and a 7/8 groove (B) Sting’s “St. Augustine in Hell” (1993)


Ex. 4.14: Two 7/16 drumbeats in the introduction of Moe’s “Wind it Up” (2007)


Ex. 4.15: A potential shift from eighth-note to sixteenth-note pulse, supported by the kick drum in Alice in Chains’s “Them Bones” (1992)


Ex. 4.16: Two possible quadruple subdivisions of 7/8 time in Radiohead’s “Paranoid Android” (1997)


Ex. 4.18: A complex septuple pattern containing tresillo ideas in Tool’s “Schism” (2001)


Ex. 4.19: A septuple groove underpinned by the bass in Tool’s “Intension” (2006)


Ex. 4.20: A two-measure (fourteen-beat) metric septuple pattern in TTNG’s “26 is Dancier than 4” (2008)


Ex. 4.21: Ambiguous septuple patterning in the chorus of Ben Folds’s “Bastard” (2005)


Ex. 4.22: A harmonic and bass-line antecedent for “Bastard” in Elton John’s “Goodbye Yellow Brick Road” (1973)


Chapter 5

Ex. 5.1: A 9:2 cross-rhythm in Radiohead’s “Codex” (2011)


Ex. 5.2: Three stages in the evolution of a half-time 9/4 groove in Tool’s “Jambi” (2006)


Ex. 5.3: A syncopated 9/8 groove in the guitar solo of Soundgarden’s “Black Hole Sun” (1994)


Ex. 5.4: Persistent 9:2 cross-rhythms in Sting’s “Big Lie, Small World” (1999) 1. Intro


Ex. 5.4: Persistent 9:2 cross-rhythms in Sting’s “Big Lie, Small World” (1999) 2. Verse 2


Ex. 5.4: Persistent 9:2 cross-rhythms in Sting’s “Big Lie, Small World” (1999) 3. Verse 3


Ex. 5.5: Three different 11/4 grooves in Tool’s “Right in Two” (2006) 1. Intro


Ex. 5.5: Three different 11/4 grooves in Tool’s “Right in Two” (2006) 2. Chorus


Ex. 5.5: Three different 11/4 grooves in Tool’s “Right in Two” (2006) 3. Instrumental


Ex. 5.5: Three different 11/4 grooves in Tool’s “Right in Two” (2006) 4. End of Instrumental


Ex. 5.6: Subtle variations on a 13/8 structure in an early instrumental in Tool’s “Schism” (2001)


Ex. 5.7A: Toms simultaneously supporting and embellishing a 13/8 structure in the first verse of Tori Amos’s “Carbon” (2002)


Ex. 5.7B: A closer relative of the backbeat in the second verse of Tori Amos’s “Carbon” (2002)


Ex. 5.8: A split irregular pattern in the verse of Soundgarden’s “Spoonman” (1994)


Ex. 5.9: Two formal sections related by split irregular structures in Hail the Sun’s “Eight-Ball, Coroner’s Pocket” (2012) (A)


Ex. 5.9: Two formal sections related by split irregular structures in Hail the Sun’s “Eight-Ball, Coroner’s Pocket” (2012) (B)


Ex. 5.11: A synthesis of half-time groove and split irregularity in Tool’s “The Patient” (2001)


Ex. 5.12: A four-part split pattern in Tori Amos’s “Datura” (1999)


Ex. 5.13: A highly ambiguous split pattern in Tori Amos’s “Police Me” (2009)


Ex. 5.14: Conflicting cues between meter and guitar part in Better than Ezra’s “King of New Orleans” (1996)


Ex. 5.15: Vague metric suggestions in Björk’s “Hollow” (2011)


Ex. 5.16: Transcription of the non-isochronous rhythm in Radiohead’s “Bloom” (2011)


Chapter 6

Ex. 6.1: A short 3/2 groove extended by a 7/16 IMI in Dream Theater’s “Home” (1999)


Ex. 6.2: A modest fill in Tool’s “Prison Sex” (1993)


Ex. 6.3: Drums tacet for two beats in Big Data’s “Dangerous” (feat. Joywave; 2013)


Ex. 6.4: Three choruses with different drumbeats across the same hypermeter in Tori Amos’s “The Beekeeper” (2005) Chorus 1


Ex. 6.4: Three choruses with different drumbeats across the same hypermeter in Tori Amos’s “The Beekeeper” (2005) Chorus 2


Ex. 6.4: Three choruses with different drumbeats across the same hypermeter in Tori Amos’s “The Beekeeper” (2005) Chorus 3


Ex. 6.5: A 3/8 IMI modelled on the second half of a 6/8 groove in Tori Amos’s “Dark Side of the Sun” (2007)


Ex. 6.6: Ambiguity of IMI placement between drums and harmonic rhythm in Tori Amos’s “Flavor” (2009)


Ex. 6.7: Changing drumbeats and tempi in The Struts’s “Could Have Been Me” (2014) (A)


Ex. 6.7: Changing drumbeats and tempi in The Struts’s “Could Have Been Me” (2014) (B)


Ex. 6.8: A structural IMI with unchanging drumbeat in Radiohead’s “All I Need” (2007)


Ex. 6.9: A multi-stage metric transition in Avenged Sevenfold’s “Welcome to the Family” (2010)


Ex. 6.10: A metric shift based on expansion of an earlier rhythmic motive in Tool’s “Undertow” (1993)


Ex. 6.11: A short metric pivot with a strongly interruptive gesture in Tool’s “Schism” (2001)


Ex. 6.12: A mid-phrase metric pivot as a means of phrase expansion in Dream Theater’s “A Nightmare to Remember” (2009)


Ex. 6.13: Two metric pivots complicate metric and formal structure in Tori Amos’s “Spark” (1998)


Ex. 6.14: A complex metric surface, obscuring the location of an isolated metric irregularity in Tool’s “Rosetta Stoned” (2006)


Ex. 6.15: Large-scale (A,B)(A,C) structure and relevant details of an instrumental in Dream Theater’s “Metropolis Part 1: The Miracle and the Sleeper” (1992)


Ex. 6.16: Inconsistent irregularity in the second verse of Tori Amos’s “Fast Horse” (2009)


Ex. 6.17: Inconsistent irregularity in the outro of Tori Amos’s “Professional Widow” (1996)


Ex. 6.18: Inconsistent irregularity in the verse and prechorus of Tori Amos’s “Barons of Suburbia” (2005)


Ex. 6.19: Inconsistent irregularity with consistent internal logic in the intro of Radiohead’s “Sail to the Moon (Brush the Cobwebs out of the Sky)” (2003)


Ex. 6.20: Metric inconsistency through several adjacent formal sections in Radiohead’s “Sail to the Moon (Brush the Cobwebs out of the Sky)” (2003)


Chapter 7

Ex. 7.1: Double tresillo and split irregular structures in the intro of Tool’s “Schism” (2001)


Ex. 7.2: Isomorphism between a vocal rhythm in the verse of Tool’s “Schism” (2001) and the bell part of the basic pattern


Ex. 7.3: Rhythmic dissonance between a (regular) dotted cross-rhythm and split irregular meter in the first verse of Tool’s “Schism” (2001)


Ex. 7.4: Subdivisional ambiguity in the first bridge of Tool’s “Schism” (2001)


Ex. 7.5: Drum fill IMI initiating the septuple-meter extension of a tredecuple post-verse in Tool’s “Schism” (2001)


Ex. 7.6: Breakdown cycle with cardinality of twenty-seven in Tool’s “Schism” (2001)


Ex. 7.7: Various Platonic-trochaic successions in the build-up and second bridge of Tool’s “Schism” (2001)


Ex. 7.8: Frequent metric changes and displacement of downbeats in the final instrumental of Tool’s “Schism” (2001)


Ex. 7.9: Pairing of tresillo and backbeat elements in the virtuosic instrumental outro of Tool’s “Schism” (2001)


Ex. 7.10: Consistent drumbeat pattern in Radiohead’s “Decks Dark” (2016)


Ex. 7.11: Unique super-metric irregularity in the first verse of Radiohead’s “Decks Dark” (2016)


Ex. 7.12: Drum fills in the second verse of Radiohead’s “Decks Dark” (2016)


Ex. 7.13: Two initially inconsistent passages resolving into cyclical grooves in Tori Amos’s “Icicle” (1994) (A)


Ex. 7.13: Two initially inconsistent passages resolving into cyclical grooves in Tori Amos’s “Icicle” (1994) (B)


Ex. 7.14: First-verse phrases with unambiguous compound meter in Tori Amos’s “Icicle” (1994)


Ex. 7.15: Sources of metric ambiguity in the first phrase of the first verse of Tori Amos’s “Icicle” (1994)


Ex. 7.16: Hypothetical drumbeats for the first phrase of the first verse of Tori Amos’s “Icicle” (1994) (A) 6/8


Ex. 7.16: Hypothetical drumbeats for the first phrase of the first verse of Tori Amos’s “Icicle” (1994) (B) 9/8


Ex. 7.16: Hypothetical drumbeats for the first phrase of the first verse of Tori Amos’s “Icicle” (1994) (C) 9/8 with Hi-hats


Ex. 7.16: Hypothetical drumbeats for the first phrase of the first verse of Tori Amos’s “Icicle” (1994) (D) 10/8 with Hi-hats


Article: Rock Modulation and Narrative


Rock Modulation and Narrative

My first published article summarizes research from my masters thesis (University of Toronto). In this article, I explore the connection between key changes and narrative in rock music.