# 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.