Math rock

History and character

Math rock emerged in the late 1980s in the United States and Japan, with roots in 1970s progressive rock (King Crimson's Red and Discipline, Yes, Rush). Slint's Spiderland (1991) is a seminal influence; the pioneers are Polvo, Don Caballero (entirely instrumental), Slint, Bitch Magnet, Bastro and the Japanese band Ruins.

Next came Hella, Battles (a "math rock supergroup" known for irregular meters, tapping and loop pedals), Toe, American Football (tied to emo, where math sounds became a hallmark of the 2000s), and in the 2010s and 2020s Delta Sleep, Covet, Tricot, TTNG, Chon and Polyphia (more virtuosic and closer to prog/fusion). Japan has a very strong scene: Toe, Tricot, The Cabs, Lite, Ling Tosite Sigure, Zazen Boys, Mouse on the Keys.

Characteristics: complex, shifting meters (5/4, 7/8, 11/8, 13/8 instead of 4/4), drums in a leading role with complex, driving rhythms, guitars with tapping and loops, clean, bright tones (in modern math rock) or distorted, angular ones (in the pioneers), vocals treated as just another instrument or absent (many bands are instrumental), and contrapuntal interplay among the instruments.

Scales and keys

Major and Lydian ("twinkly" math rock)

• Major: 1 2 3 4 5 6 7. In E: E F# G# A B C# D#.
• Lydian: 1 2 3 #4 5 6 7. In E: E F# G# A# B C# D#.
• Characteristic note: major 7 and #4 (A#) in maj7#11 and add9 voicings on open strings.
• Lydian chords in E: I E, II F#, iii G#m, #iv° A#dim, V B, vi C#m, vii D#m.
• Use: two-hand tapping arpeggios, bright chords in open tunings (Toe, Chon, Covet).
• Real example: Toe — Goodbye (major with extensions); Covet — Shibuya.

Dorian

• Formula: 1 2 b3 4 5 6 b7. In B: B C# D E F# G# A.
• Use: minor riffs with the major 6, fusion grooves.

Natural minor (Aeolian)

• Formula: 1 2 b3 4 5 b6 b7. In A: A B C D E F G.
• Use: darker, more melancholic math rock (Slint, The Cabs), dissonant riffs.

Pentatonic (major and minor) for tapping

• Major: 1 2 3 5 6; minor: 1 b3 4 5 b7. In E: E F# G# B C# / E G A B D.
• Use: repeated tapping patterns: pentatonics lay out well at two notes per string and don't create awkward half steps.

Chromaticism and intervals (pioneers)

• Don Caballero, Polvo and Hella use dissonant intervals (seconds, tritones), "crooked" tunings and atonal riffs: it's more about rhythm than scale.

How to choose

• Twinkly and bright: major/Lydian with extensions and open strings. Groove: Dorian. Dark and angular: Aeolian or chromaticism. Tapping is best written on pentatonics or extended-chord arpeggios (maj9, m11).

Harmony

Function

Harmony is often rich but static: extended chords (maj7, maj9, m11, add9, sus2, 6/9) played as repeated arpeggios in odd meters, changing slowly; in the pioneers, dissonant and atonal harmony. Cadences are rare: the tension is rhythmic.

Open tunings

• Tunings such as open C, open D, FACGCE (American Football, according to many transcriptions) allow arpeggios with open strings and "bell-like" chords.

Counterpoint

• Guitar 1 (tapping or arpeggio) + guitar 2 (riff or chords) + melodic bass: the harmony arises from the interlocking parts.

Loops

• Loop pedal for layering several figures (Battles, Ian Williams).

Voicing

• Arpeggios on 3–4 strings with open strings, tapping of wide intervals (tenths), slash chords, clusters.

Typical progressions

Rhythm and groove

The heart of the genre: odd, shifting meters (5/4, 7/8, 9/8, 11/8, 13/8), alternations (7/8 + 4/4, 3/4 + 4/4), polyrhythms and phrases that cross the bar line. Typical groupings: 7/8 as 2+2+3 or 3+2+2; 11/8 as 3+3+3+2; 13/8 as 3+3+3+2+2. The feel is precise and "mathematical", but with groove: the drums often play the guitar figures. To program it in FL Studio: set the meter in the Playlist/pattern (e.g. 7/8 = 14 sixteenth-note steps) or use 4/4 patterns with shifted accents.

Drums

Role

The drums are a co-protagonist: they play written figures, accents and unisons with the guitars, with continuous but precise fills. Models: Damon Che (Don Caballero), Zach Hill (Hella), John Stanier (Battles: very high crash, hypnotic grooves), Kashikura Takashi (Toe: ghost notes and jazz fills), Nathan Brown (Chon).

Kick

• Follows the groupings of the meter: in 7/8 (2+2+3) kick on the first and last group (steps 1, 9, 11 of 14).

Snare

• "Displaced" backbeat according to the meter; plenty of ghost notes (velocity 15–40) on all the free sixteenth notes (Toe style).

Hi-hat and ride

• Eighth-note or sixteenth-note hi-hat as a grid; ride and bell to mark the groupings.

Interaction

• Unisons with tapping and arpeggios; the drums must make the start of each cycle clear (crash or strong kick).

Sections

• Each section can change meter: intro in 7/8, verse in 5/4, chorus in 4/4 for contrast.

Fills

• Frequent, musical, often in odd groupings (quintuplets, septuplets), flams and linear fills.

Sounds

• Natural kit, bright, sensitive snare, bright cymbals (crashes mounted high like Stanier's); sometimes drum machines and loops.

Typical mistakes

• Odd meters without clear accents; ghost notes that are too loud; rigid quantization that kills the groove.

Bass

Sound

Clean, defined bass, often with a pick or fingerstyle; sometimes tapping on the bass too.

Role

• Melodic lines in counterpoint with the guitars, odd-meter ostinatos, unisons with the kick.

Examples

• Don Caballero — Fire Back About Your New Baby's Sex; Toe — Goodbye; TTNG — Cat Fantastic.

Harmonic instruments

Guitars

• Clean, bright tones (Fender Telecaster, Jazzmaster, 7-string guitars in modern math; Fender Twin, Roland JC-120 amps) with light compressor, delay and reverb; in the pioneers, distorted, angular tones.
• Techniques: two-hand tapping, arpeggios in open tunings, loop pedal, harmonics.
• Layering: two guitars with different roles L60–80/R60–80 (tapping on one side, chords/riffs on the other), loops in the center.

Keyboards

• Synths and samplers (Battles), electric piano (Mouse on the Keys uses two keyboards and drums).

Voicing

• Extended arpeggios, tenths in tapping, slash chords, open strings.

Melody and vocals

Vocals

• Often absent; when present, an instrument among others, less prominent (Tricot: female vocals in Japanese over odd meters; TTNG: soft vocals; Battles: vocals treated with pitch shift).

Instrumental melody

• Handled by the tapping, trumpet (American Football), glockenspiel or synth; short, repeated phrases that shift against the bar.

Effects

• Short reverb, delay, pitch shift (Battles).

Instruments

• Two electric guitars (tapping, loop pedal).
• Electric bass.
• Acoustic drums.
• Vocals (optional).
• Synth, samplers, trumpet, glockenspiel (optional).

Drum patterns

Synths and sounds

• Stage-73 V — Rhodes: Extended chords and jazz arpeggios in keyboard-based math rock (Mouse on the Keys).
• Prophet-5 V — Synth lead and loops: Battles-style synth lines and loops: square with little filtering, short sequences.
• Piano V — Piano: Arpeggios in odd meters, open voicings.
• DX7 V — FM bells and mallets: Bell and mallet sounds to double the tapping.

Song structure

Form (3:00–6:00)

The form is often sectional (A–B–C–A) rather than verse–chorus.

Mixing and mastering

Sonic goal

Absolute clarity of every note and every hit: the complex figures must be legible. Clean, bright sound with lively transients. References: Toe — For Long Tomorrow (2009), Battles — Mirrored (2007), Chon — Grow (2015), Covet — Effloresce (2018).

Kick

• EQ: HP 35 Hz; +2 dB at 60 Hz; −3 dB at 350 Hz; +3 dB at 3–4 kHz. Light compression (3 dB).

Snare

• EQ: +2 dB at 200 Hz; +3 dB at 5–6 kHz; compression 3–4 dB; parallel to bring out the ghost notes; short room.

Hi-hat and cymbals

• HP 400 Hz; dynamics preserved; realistic stereo overheads.

Bass

• EQ: HP 40 Hz; +2 dB at 90 Hz; −2 dB at 250 Hz; +2 dB at 1 kHz; compression 4–5 dB.

Guitars

• Two parts L60–80/R60–80; HP 120–150 Hz; +2 dB at 3–5 kHz; compression 3–5 dB (evens out the tapping); short delay and light reverb (plate 0.8–1.2 s).
• Avoid chorus and long reverbs that "smear" fast notes.

Vocals

• Standard chain (HP 100 Hz, 1176 4 dB, LA-2A 2 dB, de-esser), level like an instrument, short plate.

FX

• Short plate, synced delay (watch out for odd meters: set the delay in milliseconds calculated on the eighth note).

Buses and groups

• Guitar bus with light compression; lightly compressed mix.

Sidechain

• No.

Master

• Target: −11/−9 LUFS integrated; true peak −1 dBTP; preserve the transients.

Common mistakes

• Long reverbs; too much compression that flattens the ghost notes; guitars overlapping in the same band.

Reference tracks for the mix

• Don Caballero — Fire Back About Your New Baby's Sex (2000); Battles — Atlas (2007); Toe — Goodbye (2009); TTNG — Cat Fantastic (2008); Tricot — Pool (2013); Chon — Story (2015).

Reference listening

• Slint — Breadcrumb Trail (1991)
• Don Caballero — Fire Back About Your New Baby's Sex (2000)
• Hella — Biblical Violence (2002)
• Battles — Atlas (2007)
• TTNG — Cat Fantastic (2008)
• Toe — Goodbye (2009)
• Tricot — Pool (2013)
• Chon — Story (2015)
• Covet — Shibuya (2018)