2025-05-09

non-additive sound synthesis and processing overview

this document surveys synthesis and processing methods beyond pure additive techniques, organized by category.

subtractive synthesis

builds timbres by filtering and shaping rich oscillator outputs rather than summing sines alone.

  • core idea: start with harmonically rich waveforms, then sculpt their spectra with filters
  • common oscillators:

    • square

      • alternates between two levels
      • contains only odd harmonics
      • can be viewed as a two-state stochastic trajectory
    • triangle

      • linear ramps up and down
      • odd-only harmonics, softer timbre than square
    • sawtooth

      • sharp ramp with abrupt reset
      • full harmonic series (even + odd)
      • especially suited to emulating bowed-string spectra
      • beware aliasing if harmonics exceed nyquist
    • pulse/rectangle

      • like square, but with variable duty cycle (peak vs. trough duration)
  • sine wave (as a special case)

    • pure single-frequency tone, no harmonics

    • retains shape under linear superposition

    • common implementations: direct sin() calls, lookup tables, polynomial approximations

frequency modulation (fm) synthesis

creates complex timbres by modulating one oscillator’s frequency with another at audio rates.

  • timbre generation: sidebands emerge from carrier–modulator interactions
  • advantages: compact parameter set, rich spectra from simple algorithms

noise generation

provides broadband or textured content, often as input to filters.

  • white noise: random samples across full spectrum
  • colored noise: filter white noise to emphasize or attenuate bands (pink, brown, etc.)
  • alternative methods: summing many random-phase sines, or using fm with stochastic inputs

time-based effects & basic DSP

  • delay: replay samples after a set time, with optional feedback for echoes
  • reverberation: simulate room acoustics via networks of short delays or convolution with impulse responses
  • basic signal operations:

    • addition/subtraction: mix or difference signals (e.g. chorus, phase cancellation)

    • multiplication/division: envelope shaping, gating, or normalization

    • convolution: spectral filtering and reverb when using impulse responses

granular processing

splits audio into short "grains" and reassembles them for creative time and texture manipulation.

  • grain operations: randomize, repeat, remove, or reorder grains
  • time-stretching: lengthen or shorten without changing pitch by adjusting grain overlap
  • rhythmic effects: treat grains like tiny delays for glitch or stutter textures
  • parameters: grain size, density, overlap, envelope shape

additional techniques

  • amplitude modulation: low-rate tremolo or high-rate ring modulation for sidebands
  • waveshapng: apply non-linear transfer functions or lookup tables to distort timbre
  • sample-based vs. formula synthesis:

    • analysis-resynthesis uses extracted parameters from recordings
    • pure synthesis builds sounds from algorithmic models
  • hybrid freedom: even when sampling, full access to sine-based configurations allows perfect reconstruction beyond what FFT-based analysis can achieve

sequencer model comparison

traditional sequencers often map as follows:

  • track: holds samples, oscillators, or grouped instruments
  • beat grid: quantized onset timing
  • riffs/patterns: build from tracks for repeated motifs
  • songs: assemble riffs into full arrangements
  • routing: send tracks through effect channels for processing

this high-level model parallels the event-based, hierarchical approach used in advanced synthesis frameworks.