non-additive sound synthesis and processing overview

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

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

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

• 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

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

• 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

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.