CONTRAPUNK

Contrapunk Learning Project

Wavetable Synthesis

From first principles and instrument history to contextual timbre

3 of 34 chapters published · Part I in progress

3 of 34

Part 1 · Chapters 1–9

How Synthesis Problems Created DSP Concepts

3 of 9 published
  1. 01 · Published

    Electrical Tone and the Harmonic Idea

    Harmonics, additive synthesis, spectra, and the Telharmonium.

  2. 02 · Published

    Making Electronic Oscillation Performable

    LC oscillation, heterodyning, gesture, and articulation.

  3. 03 · Published

    When the Studio Became the Instrument

    Fixed sound, tape editing, signal chains, modulation, and stored control.

  4. 04 · Planned

    Voltage Control and Modular Thinking

    Control and audio rate, envelopes, LFOs, patch graphs, and subtractive synthesis.

  5. 05 · Planned

    Sound from Numbers

    Sampling, PCM, Nyquist, quantization, buffers, and computational signal graphs.

  6. 06 · Planned

    The Stored-Waveform Oscillator

    Table lookup, phase accumulation, frequency increment, and wrap.

  7. 07 · Planned

    Reading Between Stored Samples

    Periodic interpolation, guard samples, reconstruction error, memory, and CPU.

  8. 08 · Planned

    Fourier Analysis Becomes a Construction Tool

    Fourier series, transforms, leakage, windows, and spectral construction.

  9. 09 · Planned

    Why Early Digital Oscillators Sounded Digital

    Aliasing, fold maps, discontinuities, quantization, and measurement.

Part 2 · Chapters 10–15

The Historical Birth of Dynamic Wavetables

0 of 6 published
  1. 10 · Planned

    The Problem of the Static Digital Tone

    Exact repetition and competing methods for evolving timbre.

  2. 11 · Planned

    Wolfgang Palm's Second Dimension

    Frame stacks, table position, scanning, transitions, and hybrid filtering.

  3. 12 · Planned

    Character or Defect?

    Phase mismatch, interpolation artifacts, aliasing, and deliberate historical grit.

  4. 13 · Planned

    Different Ways to Move Through Digital Sound

    FM, sampling, vector synthesis, and wave sequencing compared.

  5. 14 · Planned

    Waldorf and the Continuing Hybrid Architecture

    Bank identity, hybrid filters, interpolation, normalization, and compatibility.

  6. 15 · Planned

    From Hardware Tables to Visual Software Editors

    Editors, sample conversion, phase alignment, spectral morphing, and modern expectations.

Part 3 · Chapters 16–25

Rebuilding the Modern Instrument

0 of 10 published
  1. 16 · Planned

    Correct Single-Cycle Frames

    Analytic and drawn frames, endpoint convention, DC removal, phase, and normalization.

  2. 17 · Planned

    Recorded Sound into Periodic Frames

    Period estimation, cycle extraction, resampling, detrending, and provenance.

  3. 18 · Planned

    Aligning Frames

    Circular correlation, phase unwrap, polarity, ambiguity, and perceptual locks.

  4. 19 · Planned

    From Crossfade to Spectral Morph

    Time, complex, and magnitude-phase interpolation with cancellation checks.

  5. 20 · Planned

    Band-Limited Banks

    Harmonic ceilings, mip levels, FFT truncation, selection, and transition crossfades.

  6. 21 · Planned

    Other Historical Answers to Aliasing

    BLIT, BLEP, polyBLEP, DPW, oversampling, and integrated tables.

  7. 22 · Planned

    Scanning and Spectral Transformation

    Modulated scanning, phase distortion, sync, FM, formants, and warping.

  8. 23 · Planned

    Polyphonic Instruments

    Voice ownership, envelopes, sustain, stealing, de-click, and panic.

  9. 24 · Planned

    MIDI, MPE, and Expressive Control

    Per-note state, pitch bend, pressure, smoothing, and stable mappings.

  10. 25 · Planned

    The Real-Time Software Instrument

    Audio boundaries, immutable assets, bounded queues, safety, and state migration.

Part 4 · Chapters 26–28

Wavetable Synthesis as Musical Practice

0 of 3 published
  1. 26 · Planned

    Hearing Historical Wavetable Aesthetics

    Analyze scans, pads, bells, basses, formants, and spectral warps.

  2. 27 · Planned

    Tuning, Roughness, Harmonicity, and Masking

    Beating, critical bands, temperament, fusion, masking, and separation.

  3. 28 · Planned

    Timbral Orchestration and Counterpoint

    Parallel, contrary, oblique, imitative, cadential, and suspended timbral motion.

Part 5 · Chapters 29–34

Current Research and Contrapunk's Question

0 of 6 published
  1. 29 · Planned

    From Timbre Spaces to Perceptual Wavetable Maps

    Descriptors, psychophysical scaling, graph paths, and uniformity tests.

  2. 30 · Planned

    Partial Voice Leading

    Assignment, phase-aware interpolation, transport, and harmonic constraints.

  3. 31 · Planned

    Timbre as Phrase and Performance

    Relative-event mapping, articulation, phrase shaping, and motif memory.

  4. 32 · Planned

    Neural and Semantic Wavetables

    Differentiable dictionaries, semantic models, licenses, and offline baking.

  5. 33 · Planned

    Contextual and Contrapuntal Timbre

    Musical context compiled into bounded deterministic per-voice targets.

  6. 34 · Planned

    Reproducible Research Dossier

    Fair baselines, listening tests, resource costs, and ship or defer decisions.

Wavetable Synthesis

How to Use This Draft

This volume contains Part I, Chapters 1 through 3.

Each section starts with a sound, song, number, diagram, or Rust example. It then derives the model from observable facts and shows why the idea became necessary.

EXAMPLE → OBSERVE → ASK → MODEL → DERIVE → CHECK
→ LISTEN → CODE IN RUST → APPLY MUSICALLY

Files used by the listening labs

Keep the PDF beside its assets directory. Four listening files are included:

All were generated deterministically by included Python or Rust source. They contain no third-party recording. The public-domain melodies are newly synthesized monophonic teaching renditions; no modern engraving or arrangement is reproduced.

Hearing safety

Begin at a low monitoring level. The examples are level-controlled but not calibrated to your room, headphones, interface, or hearing. Do not raise the volume merely to expose a subtle difference, and stop if a sound becomes uncomfortable.

Mathematical conventions

Every numbered formula has an adjacent deterministic plot. Each plot states its exact parameter values. assets/manifests/formula-visuals.json maps formulas to plots and source code.

Evidence and images

Every reproduced image has source-page public-domain or Creative Commons metadata. assets/manifests/images.json records the source, creator, institution, licence, access date, alterations, descriptions, bibliography key, and jurisdiction caveats. This is evidence, not legal clearance. Recheck the 1927 theremin photograph before external commercial publication. Generated figures and diagrams retain their source.

Accessibility boundary

The PDF is searchable and bookmarked. Every figure has an adjacent long description. The PDF is not tagged PDF/PDF-UA, so use the bundled semantic HTML with assistive technology. Final publication still requires tagged-PDF generation and validation.