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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

sound · signalSound

A changing pressure signal organized by hearing.

measure
sound · eventEnvelope

Attack, decay, sustain and release shape one sounding event.

shape · gate
sound · signalSpectrum

The frequency content present at one moment.

measure · separate
texture · eventMasking

One sound makes another harder to hear in shared time or spectrum.

separate · mute
time · beatTempo

The rate of the shared pulse, usually measured in BPM.

scale-time
time · barMeter

A repeating hierarchy of stronger and weaker beats.

group
time · beatSubdivision

Editable positions placed inside a beat.

divide · rotate
time · eventRest

Intentional timed silence, not an unassigned editor cell.

rest · mute
pitch · signalFrequency

Physical repetition rate measured in cycles per second.

multiply
pitch · systemTuning

A mapping from continuous frequency to usable pitch positions.

map
pitch · phraseTonal center

The pitch used as a contextual reference, not a mandatory destination.

transpose
pitch · systemPitch collection

The available pitch relationships before hierarchy and grammar.

constrain · map
rhythm · beatSyncopation

An attack or accent that contests the currently inferred grouping.

shift · accent
rhythm · cyclePhase relation

The relative position of two repeating cycles.

rotate · shift
harmony · eventVoicing

The actual register and spacing of the notes inside a chord.

invert · shift
harmony · eventVoice leading

The motion of individual voices between sounding structures.

minimize · preserve
harmony · phraseContinuation potential

A contextual ranking of several possible next notes or chords.

rank · resolve
melody · phrasePhrase

A remembered path of events with roles, boundaries and a direction.

repeat · vary · rest
melody · phraseContour

The relative upward, downward and repeated motion of a line.

shift · reflect
texture · sectionTexture

The perceptual result of several musical streams sharing a scene.

layer · separate
form · formForm

Memory and expectation operating over phrases and sections.

repeat · return
form · sectionTransition

A scoped operation that changes state across a boundary.

ramp · mute · reset
system · cycleProbability

A likelihood attached to an event, not a replacement for its position.

choose · constrain
system · cycleMutation

A bounded transformation of state with an identity and return rule.

transform · reset
context · systemStyle prior

A soft ranking of likely meters, roles and gestures—not a law that forbids alternatives.

rank · filter
sound · layerInstrument

A sounding source whose register, envelope and spectrum affect whether a layer can perform its role.

choose · separate
melody · cycleArpeggio

An ordered traversal of a pitch structure; the order and rhythm can change while the source structure stays.

permute · fold · rotate
form · phrasePhrase shape

A bar-scale rule for repetition, departure, energy, breath and return.

repeat · develop · rest
system · cycleOrca cursor

A cyclic position that reads the current cell or relation from a reusable pattern.

advance · wrap · read
system · eventOrca bang

The event trigger emitted when clock, cursor and condition agree.

test · trigger · output
perspective · systemMusical grammar

Tuning, hierarchy, motion, rhythm, form and performance practice together.

qualify · study

Notation legend

iposition in a repeating sequence
Nnumber of positions in a cycle
φrelative phase or cyclic shift
p[i]pitch, hit or event at position i
g[i]gate: sounding part of an event slot
v[i]velocity or onset energy
r[i]intentional rest state
P[i]probability that an assigned event occurs
μ[i]signed microtiming offset
modwrap a value around a cycle boundary
arg minchoose the candidate with the smallest measured cost
LCMfirst shared return point of independent cycles

Detailed 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

unconstrained

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

soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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

soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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

soft prior

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
soft prior

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
soft prior

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.

soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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.

soft prior

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
soft prior

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
soft prior

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.

soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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
soft prior

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.

soft prior

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
soft prior

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
soft prior

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.

soft prior

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
soft prior

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
soft prior

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.
Tradition-specific evidence

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.