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