2025-05-30

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.