# tuning
defines how pitches are mapped to actual frequencies. supports tempered grids to ratio-based or freely defined arrays.

## introduction
`tuning` belongs to the pitch layer and acts after `tonal`, `atonal`, or `generative` forms have produced a stream of pitch indices.
its task is purely translational: given an integer or fractional index n, return a frequency f(n).
no spectral shaping, modulation, or temperament drift occurs here; every output is deterministic and sample-accurate.

## overview
each form translates a pitch index to frequency using a unique model:

### 0. `equal_division`
 behavior: divides an octave into q* equal steps; linear in cents
 analogy:* a well-tuned digital synth
 parameters:*
  * `a`: quantized divisions per octave (5 to 24)
  * `b`: global transpose from −600 to +600 cents

### 1. `just_intonation`
 behavior:* maps indices to low-integer ratios within a chosen prime-limit
 analogy:* a choir tuning pure fifths and thirds
 parameters:*
  * `a`: prime-limit morphing (3-limit to 11-limit)
  * `b`: root ratio (1/1 to 9/8)

### 2. `harmonic_series`
 behavior:* interprets index as harmonic number of a fundamental
 analogy:* touching a string at nodal points
 parameters:*
  * `a`: starting harmonic number (1 to 32)
  * `b`: stride (1 to 4) - selects every nth harmonic

### 3. `table_lookup`
 behavior:* fetches from a user-supplied list (1–128 entries), wraps linearly
 analogy:* twisting a radio dial across fixed stations
 parameters:*
  * `a`: fractional position into the table (wraps around)
  * `b`: per-note detune from −100 to +100 cents

## parameter behavior summary
each form maps `a` and `b` to perceptually relevant controls:
 *equal\_division**
  * `a`: number of equal steps per octave (integer)
  * `b`: global detuning in cents
 *just\_intonation**
  * `a`: complexity of allowed ratios (lower primes to higher)
  * `b`: selects base ratio within the harmonic series
 *harmonic\_series**
  * `a`: first harmonic number used as index base
  * `b`: harmonic spacing step (stride)
 *table\_lookup**
  * `a`: fractional index into user-provided table
  * `b`: local detuning in cents

## why these were chosen
 minimal and complete coverage:* the selected forms span the full space of tuning logic:
  * equal temperament families
  * rational tuning systems
  * spectral/harmonic frameworks
  * arbitrary or culturally specific scales
 orthogonality:* no form can express the function of another without external data or parameters.
 parametric clarity:* each form uses exactly two parameters to traverse a useful and distinct perceptual space.
 deterministic sound structure:* all tunings yield exact, precomputed frequencies-compatible with the system's goals.

## what is not included
 historical temperaments (e.g., meantone, well):* can be approximated via `equaldivision` or encoded in `tablelookup`.
 dynamic or adaptive tunings:* require context-sensitive logic, which is outside this system's design scope.
 continuous glissandi or curves:* considered upstream, at the pitch-generation level, not within tuning translation.

## conclusion
these four forms give the system a complete and flexible pitch-to-frequency translation layer.
they honor the commitment to irreducibility, determinism, and two-parameter expressivity while leaving space for future inclusion of non-octave or non-logarithmic tunings under the same structural principles.