Find the relation, not the page.
Use the linear course when learning. Use this index when a livecoding or composition question already has a shape: a layer, a time scale, an audible problem or a transformation.
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31 concepts
A changing pressure signal organized by hearing.
measuresound · eventEnvelopeAttack, decay, sustain and release shape one sounding event.
shape · gatesound · signalSpectrumThe frequency content present at one moment.
measure · separatetexture · eventMaskingOne sound makes another harder to hear in shared time or spectrum.
separate · mutetime · beatTempoThe rate of the shared pulse, usually measured in BPM.
scale-timetime · barMeterA repeating hierarchy of stronger and weaker beats.
grouptime · beatSubdivisionEditable positions placed inside a beat.
divide · rotatetime · eventRestIntentional timed silence, not an unassigned editor cell.
rest · mutepitch · signalFrequencyPhysical repetition rate measured in cycles per second.
multiplypitch · systemTuningA mapping from continuous frequency to usable pitch positions.
mappitch · phraseTonal centerThe pitch used as a contextual reference, not a mandatory destination.
transposepitch · systemPitch collectionThe available pitch relationships before hierarchy and grammar.
constrain · maprhythm · beatSyncopationAn attack or accent that contests the currently inferred grouping.
shift · accentrhythm · cyclePhase relationThe relative position of two repeating cycles.
rotate · shiftharmony · eventVoicingThe actual register and spacing of the notes inside a chord.
invert · shiftharmony · eventVoice leadingThe motion of individual voices between sounding structures.
minimize · preserveharmony · phraseContinuation potentialA contextual ranking of several possible next notes or chords.
rank · resolvemelody · phrasePhraseA remembered path of events with roles, boundaries and a direction.
repeat · vary · restmelody · phraseContourThe relative upward, downward and repeated motion of a line.
shift · reflecttexture · sectionTextureThe perceptual result of several musical streams sharing a scene.
layer · separateform · formFormMemory and expectation operating over phrases and sections.
repeat · returnform · sectionTransitionA scoped operation that changes state across a boundary.
ramp · mute · resetsystem · cycleProbabilityA likelihood attached to an event, not a replacement for its position.
choose · constrainsystem · cycleMutationA bounded transformation of state with an identity and return rule.
transform · resetcontext · systemStyle priorA soft ranking of likely meters, roles and gestures—not a law that forbids alternatives.
rank · filtersound · layerInstrumentA sounding source whose register, envelope and spectrum affect whether a layer can perform its role.
choose · separatemelody · cycleArpeggioAn ordered traversal of a pitch structure; the order and rhythm can change while the source structure stays.
permute · fold · rotateform · phrasePhrase shapeA bar-scale rule for repetition, departure, energy, breath and return.
repeat · develop · restsystem · cycleOrca cursorA cyclic position that reads the current cell or relation from a reusable pattern.
advance · wrap · readsystem · eventOrca bangThe event trigger emitted when clock, cursor and condition agree.
test · trigger · outputperspective · systemMusical grammarTuning, hierarchy, motion, rhythm, form and performance practice together.
qualify · studyNotation legend
iposition in a repeating sequenceNnumber of positions in a cycleφrelative phase or cyclic shiftp[i]pitch, hit or event at position ig[i]gate: sounding part of an event slotv[i]velocity or onset energyr[i]intentional rest stateP[i]probability that an assigned event occursμ[i]signed microtiming offsetmodwrap a value around a cycle boundaryarg minchoose the candidate with the smallest measured costLCMfirst shared return point of independent cyclesDetailed lookup
Style grammar, not genre law
Builder uses style as a prior: it recommends familiar meters and approaches first, while keeping compatible alternatives available. A style name never proves that one rhythm, scale or instrument is mandatory.
Open
Open / exploratory
Keep every meter and pitch collection available.
- Starts with
- 2 / 4 · 3 / 4 · 4 / 4 · 5 / 4 · 6 / 8 · 7 / 8 · 9 / 8 · 12 / 8
- Pulse
- chosen explicitly
- Density
- unconstrained
- Articulation
- unconstrained
- Harmony
- unconstrained
- Form
- test one relation at a time
Electronic & process
Techno frame
Loop-led motion; 4/4 is the curated starting frame, not a genre law.
- Starts with
- 4 / 4
- Pulse
- stable cyclic anchor
- Density
- layered, gradually changed
- Articulation
- short attacks against sustained fields
- Harmony
- slow relative to pulse
- Form
- subtraction, ramps and returns
House pulse
Four-beat grounding, offbeat lift and syncopated harmonic punctuation.
- Starts with
- 4 / 4
- Pulse
- four-beat ground
- Density
- open offbeats
- Articulation
- clipped stabs and lifted hats
- Harmony
- regular punctuation
- Form
- layer exchange around a stable pulse
Dub techno space
Sparse chord clouds, delayed answers and a patient low anchor.
- Starts with
- 4 / 4
- Pulse
- patient low anchor
- Density
- sparse with long tails
- Articulation
- soft attack, extended decay
- Harmony
- very slow
- Form
- space, feedback and gradual filtering
Broken beat
Displaced attacks and gaps; the curated pack starts in 4/4 while odd cycles remain compatible.
- Starts with
- 4 / 4
- Pulse
- implied through displacement
- Density
- irregular gaps and clusters
- Articulation
- contrasting accents
- Harmony
- independent of drum grid
- Form
- cut, rotate and re-align
Drum & bass motion
Fast two-step pressure with rolling bass and clear half-time landmarks.
- Starts with
- 4 / 4
- Pulse
- fast grid with half-time landmarks
- Density
- busy highs, protected lows
- Articulation
- sharp transients and rolling gates
- Harmony
- slow or pedal-based
- Form
- pressure arcs and drop boundaries
Garage shuffle
Skipped attacks, swung subdivisions and clipped chord answers in a curated 4/4 frame.
- Starts with
- 4 / 4
- Pulse
- shuffled or skipped duple grid
- Density
- syncopated gaps
- Articulation
- clipped answers
- Harmony
- short recurring stabs
- Form
- variation through swing and omission
Electro machine-funk
Syncopated drum-machine grids, angular bass and call–response cells.
- Starts with
- 2 / 4 · 4 / 4
- Pulse
- machine grid with syncopation
- Density
- compact interlocking cells
- Articulation
- dry, accented attacks
- Harmony
- cell-based
- Form
- call, answer and register shifts
Acid sequence
Short repeating pitch cells whose accents, gates and register do the development.
- Starts with
- 4 / 4
- Pulse
- steady repeated grid
- Density
- dense small pitch cell
- Articulation
- accent and gate are primary
- Harmony
- pedal or slow root motion
- Form
- filter, accent and register development
Minimal process
Small cells transformed by phase, rotation, subtraction and gradual change; 4/4 is the complete starter pack.
- Starts with
- 4 / 4
- Pulse
- repeating cell or independent clocks
- Density
- few elements, gradual mutation
- Articulation
- consistent enough to expose process
- Harmony
- static or slowly permuted
- Form
- rotation, phase and subtraction
Ambient field
Long spans, sparse events and weak metric pressure; the starter pack uses a neutral 4/4 clock.
- Starts with
- 4 / 4
- Pulse
- weak or hidden
- Density
- sparse with overlap
- Articulation
- slow attack and long release
- Harmony
- very slow
- Form
- continuous spectral and density arcs
Generative cycles
Asymmetric cycles and controlled phase drift; 5/4 is the complete starter system.
- Starts with
- 5 / 4
- Pulse
- multiple bounded clocks
- Density
- rule-controlled
- Articulation
- parameterised
- Harmony
- derived from independent cycles
- Form
- convergence, mutation and reset
Classical composition
Waltz / three-beat
One strong pulse followed by two lighter positions.
- Starts with
- 3 / 4
- Pulse
- one strong plus two light beats
- Density
- breathing three-beat phrases
- Articulation
- first-beat anchor, lighter continuation
- Harmony
- often one change per bar
- Form
- periodic phrases and returns
Baroque counterpoint & dance
Independent lines, repeating basses and dance-derived pulse.
- Starts with
- 3 / 4 · 4 / 4 · 6 / 8
- Pulse
- dance grouping or steady tactus
- Density
- several independent active voices
- Articulation
- speech-like motifs and patterned sequences
- Harmony
- regular but driven by voice motion
- Form
- sequence, imitation, cadence and return
Classical phrase
Balanced antecedent–consequent phrases with explicit cadence hierarchy.
- Starts with
- 3 / 4 · 4 / 4
- Pulse
- regular phrase-supporting metre
- Density
- clear foreground over restrained support
- Articulation
- contrasting motifs and clean boundaries
- Harmony
- goal-directed and phrase-scaled
- Form
- question, answer, cadence and development
Romantic arc
Long melodic tension, flexible pacing and expanding register.
- Starts with
- 3 / 4 · 4 / 4 · 6 / 8
- Pulse
- stable frame with expressive surface displacement
- Density
- swells from intimate to saturated
- Articulation
- legato lines and weighted arrivals
- Harmony
- elastic, intensified near goals
- Form
- long arc, postponement and climactic return
Colour & planing
Timbral harmony, parallel motion and weakened functional gravity.
- Starts with
- 3 / 4 · 4 / 4 · 6 / 8
- Pulse
- fluid or gently repeating
- Density
- layered resonance with transparent gaps
- Articulation
- soft attacks and pedal-like overlap
- Harmony
- colour-led rather than cadence-led
- Form
- register, texture and harmonic-colour transformation
Jazz & blues
Jazz swing
Triplet-inflected pulse, walking support and interactive phrasing.
- Starts with
- 4 / 4
- Pulse
- swing subdivision over a steady beat
- Density
- interactive gaps and overlapping responses
- Articulation
- accented offbeats and varied note length
- Harmony
- regular changes with substitutions possible
- Form
- head, solos, exchanges and return
Blues cycle
Call–response phrases over a repeating harmonic frame.
- Starts with
- 4 / 4 · 12 / 8
- Pulse
- straight or shuffled four-beat frame
- Density
- phrases answered by space
- Articulation
- bent or accented target tones approximated here
- Harmony
- cyclic I–IV–V region movement
- Form
- repeated chorus with varied calls and turnarounds
Modal jazz field
Long harmonic areas that foreground motif, register and rhythmic development; the full starter band is in 4/4.
- Starts with
- 4 / 4
- Pulse
- steady or asymmetric groove
- Density
- space for motivic dialogue
- Articulation
- phrase-dependent, often sharply profiled
- Harmony
- slow modal fields
- Form
- motif expansion over long harmonic spans
European folk & dance sketches
Navigation group, not a claim that these traditions form one musical system.
Irish reel & jig sketch
Continuous melodic motion over reel or compound-dance grouping.
- Starts with
- 4 / 4 · 6 / 8 · 9 / 8
- Pulse
- reel duple or jig compound grouping
- Density
- continuous line with brief breathing points
- Articulation
- dance accents and compact ornaments
- Harmony
- support follows phrase landmarks
- Form
- repeated strains with internal variation
Balkan aksak sketch
Unequal short–short–long groupings encoded on additive metres.
- Starts with
- 7 / 8 · 9 / 8
- Pulse
- additive unequal groups
- Density
- repeating dance cell with interlocking parts
- Articulation
- group-start accents
- Harmony
- often slower than the asymmetric pulse
- Form
- repeated cycle, variation and sectional lift
Flamenco compás sketch
Twelve-position accent cycles represented as a programmable grid.
- Starts with
- 12 / 8
- Pulse
- cyclic accent positions, not a single downbeat hierarchy
- Density
- palmas-like interlock around marked accents
- Articulation
- dry attacks and forceful phrase closures
- Harmony
- supports compás and vocal/instrumental phrase
- Form
- cycles, llamadas and explicit closures
Klezmer dance sketch
Dance pulse with ornament-ready melodic turns and responsive accompaniment.
- Starts with
- 2 / 4 · 4 / 4
- Pulse
- clear dance grouping
- Density
- foreground melody over punctuated support
- Articulation
- short ornaments and expressive attacks approximated here
- Harmony
- phrase-led accompaniment
- Form
- strain repetition, variation and accelerative lift
Slavic dance sketch
Additive or regular dance cycles with drone support and sharply profiled melodic turns.
- Starts with
- 2 / 4 · 7 / 8
- Pulse
- dance cycle with marked group starts
- Density
- foreground line over compact support
- Articulation
- accented turns and repeated cells
- Harmony
- drone or phrase-level movement
- Form
- strain repetition, variation and lift
Central European dance sketch
Clear dance metre, periodic bass–chord support and repeated strains.
- Starts with
- 2 / 4 · 3 / 4
- Pulse
- regular paired or triple dance grouping
- Density
- melody over periodic support
- Articulation
- clear group accents
- Harmony
- regular phrase-supporting changes
- Form
- repeated strains and cadential turns
Celtic air & dance sketch
Modal or pentatonic contour shaped as either a breathing air or repeated dance strain.
- Starts with
- 4 / 4 · 6 / 8
- Pulse
- free-breathing or compound dance grouping
- Density
- single leading line with drone or sparse support
- Articulation
- ornament-ready phrase accents
- Harmony
- drone or slow support
- Form
- air-like arc or repeated strains
Nordic folk sketch
Modal melody, drones and asymmetric phrase weight without claiming one regional practice.
- Starts with
- 3 / 4 · 4 / 4
- Pulse
- dance-derived or gently asymmetric
- Density
- open intervals and spare counterline
- Articulation
- bow-like phrase weight approximated by gates
- Harmony
- drone-centred or slowly changing
- Form
- repeated tune with registral variation
African & diasporic cycle sketches
Generic cyclic starting points; named regional practices require specific sources.
West African timeline sketch
A reference timeline with cross-rhythmic parts on a shared cycle.
- Starts with
- 6 / 8 · 12 / 8
- Pulse
- multiple felt groupings over one cycle
- Density
- interlocking attacks with stable role separation
- Articulation
- distinct timbres clarify rhythmic identity
- Harmony
- optional and subordinate to cycle
- Form
- entry, substitution, call–response and density change
Reggae & dub space sketch
Offbeat support, sparse low foundation and delay-ready gaps.
- Starts with
- 4 / 4
- Pulse
- four-beat frame with offbeat harmonic marks
- Density
- protected low end and deliberate gaps
- Articulation
- short chops against long tails
- Harmony
- slow repeating cycle
- Form
- dropout, echo space and return
Southern African interlock sketch
A generic cyclic interlock for call–response and layered entry, not a named regional genre.
- Starts with
- 4 / 4 · 12 / 8
- Pulse
- shared cycle with several perceived groupings
- Density
- interlocking attacks with distinct registers
- Articulation
- timbre separates rhythmic functions
- Harmony
- optional repeated field
- Form
- entry, response, substitution and density arc
Latin American song & dance sketches
Operational entry points, not complete regional performance practices.
Bossa nova sketch
Even pulse, syncopated accompaniment and understated dynamics.
- Starts with
- 2 / 4 · 4 / 4
- Pulse
- even duple grid with recurring syncopation
- Density
- interlocking but dynamically restrained
- Articulation
- short bass against sustained harmony
- Harmony
- regular, often two or more events per bar
- Form
- song phrase with recurring accompaniment cell
Afro-Cuban clave sketch
Interlocking layers organized around a repeating reference timeline.
- Starts with
- 4 / 4 · 6 / 8
- Pulse
- clave-oriented cyclic reference
- Density
- independent parts occupy complementary slots
- Articulation
- dry attacks with role-specific accents
- Harmony
- repeating montuno-like area or song changes
- Form
- layer entry, breaks and call–response
Samba ensemble sketch
Layered duple cycle with distinct low, middle and high rhythmic functions.
- Starts with
- 2 / 4
- Pulse
- continuous duple cycle with layered syncopation
- Density
- high but role-separated
- Articulation
- short attacks with differentiated accents
- Harmony
- song-scaled over persistent percussion
- Form
- groove, break, call and return
Tango phrase sketch
Marked duple gesture, syncopation and dramatic phrase-level suspension.
- Starts with
- 2 / 4 · 4 / 4
- Pulse
- marked duple with displaced attacks
- Density
- contrasting tutti and sparse answers
- Articulation
- short weighty attacks and held tension
- Harmony
- goal-directed phrase motion
- Form
- gesture, suspension, arrival and return
Cumbia cycle sketch
Steady duple dance frame with syncopated low cell and repeating melodic answers.
- Starts with
- 4 / 4
- Pulse
- steady duple dance cycle
- Density
- interlocking repeated roles
- Articulation
- short percussive attacks
- Harmony
- slow repeating field
- Form
- cyclic groove with call–response variation
Andean pentatonic sketch
A qualified pentatonic contour over drone or restrained cyclic support.
- Starts with
- 2 / 4 · 4 / 4
- Pulse
- song or dance grouping chosen explicitly
- Density
- clear contour over spare support
- Articulation
- phrase-shaped attacks and breaths
- Harmony
- drone or slow movement
- Form
- motif repetition, registral answer and return
West & South Asian sketches
Qualified pitch inventories and cycles—not complete maqam, makam, raga or tala practice.
Maqam-informed 12-TET sketch
A qualified pitch inventory with drone, phrase and cadence experiments.
- Starts with
- 4 / 4 · 6 / 8
- Pulse
- free phrase or explicit cyclic accompaniment
- Density
- one leading line over sparse support
- Articulation
- ornament and intonation remain performance-dependent
- Harmony
- drone or slowly changing support
- Form
- phrase exploration and return to a focal degree
Turkish aksak 12-TET sketch
Unequal rhythmic groups paired with a qualified makam-like pitch projection.
- Starts with
- 7 / 8 · 9 / 8
- Pulse
- short and long additive units
- Density
- dance cell under a foreground phrase
- Articulation
- group accents with ornament-ready melody
- Harmony
- drone or slow supporting motion
- Form
- cyclic usul-like grouping and phrase return
Raga–tala 12-TET sketch
A qualified pitch inventory developed against an explicit repeating time cycle.
- Starts with
- 7 / 8 · 9 / 8 · 12 / 8
- Pulse
- marked and unmarked regions of a repeating cycle
- Density
- motif expansion over drone and pulse
- Articulation
- ornament, intonation and hierarchy remain outside this grid model
- Harmony
- drone-centred rather than chord-progressive
- Form
- return to cycle boundary through progressive elaboration
East & Southeast Asian sketches
Tempered keyboard projections; tuning, hierarchy and performance practice remain source-specific.
Japanese ma & pentatonic sketch
Sparse attacks and qualified pentatonic pitch inventories shaped by interval and silence.
- Starts with
- 4 / 4 · 5 / 4
- Pulse
- weak or selectively marked
- Density
- silence treated as structural material
- Articulation
- isolated attacks with audible decay
- Harmony
- drone, dyad or slowly changing field
- Form
- gesture, resonance, silence and return
Chinese pentatonic sketch
A qualified pentatonic inventory developed through contour, register and ornament-ready gaps.
- Starts with
- 2 / 4 · 4 / 4
- Pulse
- explicit song or dance grouping
- Density
- clear melodic foreground with spare support
- Articulation
- phrase accents and ornaments remain style-specific
- Harmony
- drone, heterophony or restrained support
- Form
- motif variation and registral return
Gamelan colotomic sketch
Nested cycle boundaries and rough keyboard pitch projections for structural experimentation.
- Starts with
- 4 / 4 · 6 / 8
- Pulse
- nested boundary markers over a shared cycle
- Density
- interlocking register layers
- Articulation
- short resonant attacks
- Harmony
- cyclic pitch field rather than imported functional harmony
- Form
- large-cycle return through nested punctuation
Editorial sources
The book translates mechanisms into operational models rather than claiming one complete theory of music. These works define important parts of its mathematical, perceptual and compositional background.
- Musimathics, volumes 1–2 — Gareth Loy. Mathematical foundations of sound, tuning, rhythm and digital music.
- A Geometry of Music — Dmitri Tymoczko. Geometric models of chords and voice leading.
- The Geometry of Musical Rhythm — Godfried T. Toussaint. Cyclic rhythm, distance and distribution.
- Tuning, Timbre, Spectrum, Scale — William A. Sethares. Relations among tuning systems and spectra.
- Auditory Scene Analysis — Albert S. Bregman. Perceptual grouping and auditory streams.
- Sweet Anticipation — David Huron. Expectation, memory and musical response.
- An Introduction to the Psychology of Hearing — Brian C. J. Moore. Psychoacoustic mechanisms and limits.
Collection names in this project are orientation labels. Intonation, hierarchy, phrase grammar, rhythm, ornament and performance practice require musicians, teachers and primary or specialist sources from the named tradition.