Physics-first music theory
Physics-first music theory
Music theory rebuilt from physics, for minds that think in equations.
PhizMusic is a foundational music theory framework that derives every concept from physics, mathematics, and neuroscience. Where conventional Western music theory relies on 18th-century terminology and notation conventions that obscure the underlying physics, PhizMusic uses physics-literal vocabulary, transparent mathematical relationships, and psychoacoustic evidence to explain how music works and why it sounds the way it does.
Every culture’s music system is a different engineering solution to the same mathematical constraints. PhizMusic provides the shared physics vocabulary to understand them all.
This wiki is designed for the scientifically-minded learner — someone with a solid understanding of physics, math, and biology who appreciates multicultural music but finds conventional Western music theory incomprehensible. If you’ve ever wondered why a “fifth” is called a “fifth” when it’s actually a 3:2 frequency ratio, this framework is for you.
> 🎯 **Simple version** blocks for quick intuitive understanding.There is no required reading order. Each page is self-contained, with prerequisites listed in its front matter. Start with whatever interests you and follow the links.
Suggested starting points:
The physical foundations that everything else builds on.
| Page | Description |
|---|---|
| Sound Waves | Pressure waves, frequency, amplitude, waveform vs. spectrum |
| The Ear & Cochlea | Biological frequency analyzer, basilar membrane, critical bandwidth |
| Fourier Analysis | Decomposing complex sounds into sine wave components |
| Standing Waves | Resonant modes in strings and pipes, node/antinode patterns |
| Waveform Gallery | Side-by-side comparison of fundamental waveforms and their spectra |
The core musical concepts derived from physics.
| Page | Description |
|---|---|
| Harmonic Series | The natural overtone sequence: f, 2f, 3f, 4f… |
| Frequency Ratios | Comparing pitches by ratio, the cent system |
| Naming System | Step-numbers (0-11) + Dodeka syllables (Do, Ka, Re…) |
| Intervals | Step-intervals and their frequency ratio equivalents |
| Scales | Step-subsets: selecting pitches from the 12 available |
| Chords | Step-combos and ratio-sets: simultaneous pitches |
| Rhythm | Pulse-fraction system: T, onset, duration, cycle |
| Missing Fundamental | Virtual pitch: hearing frequencies that aren’t there |
Deeper understanding, cross-cultural connections, and applied concepts.
| Page | Description |
|---|---|
| Twelve-TET | The equal-temperament compromise and what it sacrifices |
| Consonance & Dissonance | Roughness, harmonic template matching, cultural perception |
| Beating & Roughness | Two-tone interference, beat rate, roughness, and critical bandwidth |
| Pentatonic & Cross-Cultural | The universal 5-note scale and why it appears everywhere |
| Translation Tables | Complete PhizMusic ↔ Western ↔ other systems mapping |
| Notation Layer | Chromatic grid (Dodeka/piano roll) notation approach |
| Chord Progressions | Step-combo sequences, voice-leading, tension and resolution |
| Timbre | Spectral signatures, Sethares’ timbre-tuning coupling |
| Instrument Physics | String, pipe, and membrane acoustics |
| ADSR Envelope | Attack, decay, sustain, release — amplitude over time |
| Digital Audio | Sampling, Nyquist, aliasing, bit depth, room acoustics basics |
| Auditory Masking | Frequency and temporal masking, MP3 compression connection |
| Equal Loudness | Fletcher-Munson curves, frequency-dependent hearing sensitivity |
| Dissonance Curves | Sethares’ timbre-dependent dissonance model, sensory dissonance computation |
| Shepard Tones | Auditory illusion of endlessly ascending/descending pitch |
| Step-7 Cycle | Modular arithmetic of the 7-step-interval, generating all 12 steps |
| Functional Analysis | Step-combo positions within a step-subset, tension and resolution patterns |
| Page | Description |
|---|---|
| Glossary | Canonical definitions of all PhizMusic terms |
| Reference Table | Complete step/syllable/Western/Hz/MIDI mapping |
| Page | Description |
|---|---|
| ROADMAP | Phase 2 vision: interactive tooling, deferred content |
| Page | One-line description |
|---|---|
| ADSR Envelope | Amplitude envelope: attack, decay, sustain, release phases |
| Auditory Masking | How loud sounds render quiet sounds inaudible |
| Beating & Roughness | Physical beating and perceptual roughness across frequency spacing |
| Chords | Simultaneous pitches described as step-combos and ratio-sets |
| Chord Progressions | Sequences of step-combos with voice-leading analysis |
| Consonance & Dissonance | Multi-factorial perception of tonal fusion vs. clash |
| Digital Audio | ADC, sampling rate, Nyquist theorem, aliasing, bit depth |
| Dissonance Curves | Sethares’ sensory dissonance model for arbitrary timbres |
| The Ear & Cochlea | Biological frequency decomposition via basilar membrane |
| Equal Loudness | Fletcher-Munson curves and frequency-dependent hearing |
| Fourier Analysis | Decomposing waveforms into component sine waves |
| Frequency Ratios | Pitch comparison by ratio, the cent measurement system |
| Functional Analysis | Step-combo positions within a step-subset, tension and resolution |
| Glossary | Canonical PhizMusic vocabulary definitions |
| Harmonic Series | Integer-multiple overtone sequence from vibrating objects |
| Instrument Physics | Acoustics of strings, pipes, and membranes |
| Intervals | Step-intervals between pitches with ratio equivalents |
| Missing Fundamental | Perceiving pitch from harmonic pattern without the fundamental |
| Naming System | Step-numbers (0-11) + octave, Dodeka syllables |
| Notation Layer | Chromatic grid notation based on Dodeka and piano roll |
| Pentatonic & Cross-Cultural | The 5-note scale across world music traditions |
| Reference Table | Complete pitch mapping: octave × step → syllable → Hz |
| Rhythm | Pulse-fraction system for temporal organization |
| ROADMAP | Future plans: interactive tools, deferred content topics |
| Scales | Step-subsets: selecting from the 12 chromatic pitches |
| Shepard Tones | Auditory illusion of endlessly ascending/descending pitch |
| Standing Waves | Resonant modes in strings and pipes, nodes and antinodes |
| Step-7 Cycle | Modular arithmetic of the 7-step-interval, generating all 12 steps |
| Timbre | Spectral fingerprint of a sound, timbre-tuning coupling |
| Translation Tables | Bidirectional PhizMusic ↔ Western ↔ other systems |
| Twelve-TET | Equal temperament: the engineering compromise |
| Waveform Gallery | Side-by-side waveform and spectrum comparison |
Formulas are written in inline code blocks for portability:
f = 440 × 2^((n - 69) / 12) where n = MIDI note numberc = 1200 × log₂(f₂/f₁)fₙ = n × f₁ for integer nFuture versions may render these using KaTeX for proper mathematical typesetting.
The syllable system used throughout this wiki — Do, Ka, Re, Xo, Mi, Fa, Hu, So, Bi, La, Ve, Si — is adapted from the Dodeka Music system by Jacques-Daniel Rochat. Each of the 12 chromatic steps gets one unique syllable, with no sharps or flats needed. See Naming System for full details.
Use the canonical template at wiki/_template.md when creating or revising concept pages.
Contribution checklist:
title, tier, scope-boundary (plus aliases/tags/prerequisites/related)> 🎯 **Simple version** block## Translation Table and ## Connections section where applicable<!-- INTERACTIVE: ... --> placeholders only as future-facing notes (no embedded scripts in markdown)# Structural
wiki/README.md — this file (index hub)
wiki/_template.md — page template for contributors
wiki/glossary.md — canonical vocabulary reference
wiki/reference-table.md — complete pitch mapping table
# Tier 1 — Physics Primitives
wiki/sound-waves.md — pressure waves, frequency, amplitude
wiki/ear-cochlea.md — biological frequency analyzer
wiki/fourier-analysis.md — waveform ↔ spectrum decomposition
wiki/standing-waves.md — resonant modes, nodes, antinodes
wiki/waveform-gallery.md — fundamental waveform + spectrum comparison
# Tier 1 — Music Primitives
wiki/harmonic-series.md — the overtone sequence
wiki/frequency-ratios.md — pitch ratios and cents
wiki/naming-system.md — step-numbers + Dodeka syllables
wiki/intervals.md — step-intervals and ratio equivalents
wiki/scales.md — step-subsets
wiki/chords.md — step-combos and ratio-sets
wiki/rhythm.md — pulse-fraction temporal system
wiki/missing-fundamental.md — virtual pitch perception
# Tier 2 — Essential Context
wiki/twelve-tet.md — equal temperament compromise
wiki/consonance-dissonance.md — perceptual fusion mechanisms
wiki/beating-roughness.md — interference beating, roughness, and CB transitions
wiki/pentatonic-cross-cultural.md — universal 5-note scale
wiki/translation-tables.md — PhizMusic ↔ Western ↔ others
wiki/notation-layer.md — chromatic grid notation
wiki/chord-progressions.md — step-combo sequences
wiki/timbre.md — spectral signatures
wiki/instrument-physics.md — string, pipe, membrane acoustics
wiki/adsr-envelope.md — amplitude envelope
wiki/digital-audio.md — sampling, Nyquist, aliasing
wiki/auditory-masking.md — frequency/temporal masking
wiki/equal-loudness.md — Fletcher-Munson curves
wiki/dissonance-curves.md — Sethares sensory dissonance model
wiki/shepard-tones.md — endlessly ascending/descending pitch illusion
wiki/step-7-cycle.md — modular arithmetic of the 7-step-interval
wiki/functional-analysis.md — step-combo positions, tension and resolution
# Future
wiki/ROADMAP.md — Phase 2 interactive tooling vision