name	catsharp-sonification
description	Sonify GF(3) color streams via CatSharp scale. Maps Gay.jl colors to pitch classes and plays through sox. No voice synthesis.
version	1.0.0

CatSharp Sonification

Sonify deterministic color streams using the CatSharp scale (Mazzola's Topos of Music).

Galois Chain

seed ⊣ γ ⊣ color ⊣ hue ⊣ pitch ⊣ freq ⊣ tone

Mappings

Hue → Trit (Gay.jl spec)

Hue Range	Trit	Role	Temperature
0-60°, 300-360°	+1	PLUS	warm
60-180°	0	ERGODIC	neutral
180-300°	-1	MINUS	cold

Trit → Waveform

Trit	Waveform	Character
+1	sine	smooth, harmonic
0	triangle	balanced, neutral
-1	square	harsh, digital

Hue → Pitch Class

pitch_class = floor(hue / 30) mod 12

30° per semitone maps the color wheel to the chromatic scale.

CatSharp Pitch → Trit

Pitch Classes	Trit	Structure
{0, 4, 8} (C, E, G#)	+1	Augmented triad
{3, 6, 9} (Eb, F#, A)	0	Diminished subset
Circle of fifths	-1	Fifths stack

Usage

Python (sox required)

import subprocess

def play_color(r, g, b, duration=0.15):
    hue = rgb_to_hue(r, g, b)
    trit = hue_to_trit(hue)
    pc = int(hue / 30) % 12
    freq = 261.63 * (2 ** (pc / 12))  # C4 base
    wave = {1: "sine", 0: "triangle", -1: "square"}[trit]
    subprocess.run(["play", "-q", "-n", "synth", str(duration), 
                    wave, str(freq), "vol", "0.3"])

Babashka

(defn play-trit [trit freq]
  (let [wave (case trit 1 "sine" 0 "triangle" -1 "square")]
    (shell "play" "-q" "-n" "synth" "0.15" wave (str freq) "vol" "0.3")))

Julia (Gay.jl)

using Gay

function sonify_stream(seed, n=12)
    Gay.gay_seed!(seed)
    for _ in 1:n
        c = Gay.next_color()
        hue = Gay.Colors.convert(Gay.HSL, c).h
        pc = mod(round(Int, hue / 30), 12)
        freq = 261.63 * 2^(pc / 12)
        trit = hue < 60 || hue >= 300 ? 1 : hue < 180 ? 0 : -1
        wave = Dict(1 => "sine", 0 => "triangle", -1 => "square")[trit]
        run(`play -q -n synth 0.15 $wave $freq vol 0.3`)
    end
end

GF(3) Conservation

Every tripartite emission sums to 0 mod 3:

MINUS(-1) + ERGODIC(0) + PLUS(+1) = 0

Modelica Formulation

See catsharp.mo for acausal equation-based model.

Dependencies

sox (via flox: flox install sox)
Python 3.x or Julia with Gay.jl
macOS afplay as fallback

Related Skills

gay-mcp: Deterministic color generation
rubato-composer: Mazzola's mathematical music theory
topos-of-music: Full categorical music implementation

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

networkx [○] via bicomodule
- Universal graph hub

Bibliography References

category-theory: 139 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.

catsharp-sonification

Install Skill

SKILL.md