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

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 3. Variations on an Arithmetic Theme

Concepts: generic arithmetic, coercion, symbolic, numeric

GF(3) Balanced Triad

catsharp-sonification (○) + SDF.Ch3 (○) + [balancer] (○) = 0

Skill Trit: 0 (ERGODIC - coordination)

Secondary Chapters

• Ch1: Flexibility through Abstraction
• Ch8: Degeneracy
• Ch10: Adventure Game Example

Connection Pattern

Generic arithmetic crosses type boundaries. This skill handles heterogeneous data.

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) |