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.

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v2.0.0: Metairony & Hydra Flow Grokking

New Modes

Mode	Flag	Description
Metairony	--metairony	The sound of self-reference
Just Intonation	--ji	5-limit tuning ratios
Consonant Only	--consonant	Filter to consonant intervals
PLR Sequences	--plr PLRPLR	Neo-Riemannian transformations
Tool Algebra	--tools exa,babashka,beeper	S-P-O chain sonification
Maximal	--maximal	All modes combined
Champions	--champions	Top 3 GF(3)-conserved seeds

Metairony: Coloring Outside AND Inside the Lines

python3 sonify.py --metairony

Four phases of self-referential sonification:

1. INSIDE THE LINES — Perfect GF(3) conservation

   • finder_search(-1) + oracle_think(0) + create_file(+1) = 0

2. OUTSIDE THE LINES — Deliberate transgression

   • read(-1) + read(-1) + read(-1) = -3 ≡ 0 (the heresy was orthodoxy)

3. METAIRONIC BRIDGE — The joke that knows it's a joke

   • sonify(sonify) — the script sonifying itself

4. SURPRISING BISIMILARITY

   • iBeacon physical consensus ≅ PLR transformations ≅ Gay.jl trit streams

Hydra Flow Grokking: 69 Candidates

Browser-based p5.js visualization of Hydra live-coding synth taxonomy:

open hydra-grok.html

Distance = Information × Agency × Energy

Category	Trit	Functions	Profile
Source	+1 🔴	osc, noise, shape...	High information generation
Geometry	0 🟢	rotate, scale, kaleid...	Transform, conserve
Color	0 🟢	posterize, hue...	Low agency
Blend	-1 🔵	add, mult, diff...	Consume/combine
Modulate	-1 🔵	modulate*, feedback	Highest info (0.9)
External	-1 🔵	initCam, initScreen	Max info input
Synth	+1 🔴	render, out, hush	Max agency

Temperature τ controls clustering:

• Low τ (0.1): Sharp deterministic clusters
• High τ (2.0): Melted stochastic mixing
• τ = 0.69: Nice balance (default)

69 distance metrics cycle through information-theoretic, agency-based, energy-based, GF(3), thermodynamic, and categorical measures.

Yulyia ↔ greentea Bicomodule Bridge

Synthesis from beeper-mcp decision analysis:

Tool Algebra Chain: exa → deepwiki → babashka → beeper
Spectral Gap: λ₂ = 0.32 → tempo = 158.4 BPM
PLR Transitions: Neo-Riemannian as pitch transformations

Bisimulation Indistinguishability:

• Yuliya's tool algebra ≅ --tools sonification mode
• greentea's YOOZ color chains ≅ Gay.jl seed 1069 stream
• iBeacon physical consensus ≅ PLR graph walks

Files Added

File	Description
metairony.html	p5.js + Web Audio metaironic visualization
hydra-grok.html	69-candidate temperature-clustered flow analysis
sonify.py	Extended with --metairony, --ji, --consonant, --plr, --tools

Interaction Exemplar: 2026-01-07

"color outside and inside the lines - the metairony sonify it"

The request to simultaneously transgress AND conserve GF(3) led to:

• Phase 2 plays tritone (devil's interval) for each transgression
• -3 ≡ 0 (mod 3) reveals: even breaking the rules conserves
• The metaironic insight: the difference IS the identity

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Skill Interleavings

Connected Skill	Morphism	GF(3) Role
gay-mcp	seed → color → pitch	Source (+1)
topos-of-music	PLR ↔ pitch class	Transform (0)
hydra-synth	69 functions → clusters	Analysis (-1)
rubato-composer	Mazzola forms	Theory (0)
qri-valence	XY defects → dissonance	Mapping (-1)
bisimulation-game	Entity indistinguishability	Verification (+1)