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Concrete, runnable examples combining GA music theory tools with ix ML algorithms for chord clustering, harmonic analysis, and scale recommendation
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Based on SOC occupation classification
Test model robustness with adversarial attacks and defenses
Multi-armed bandit simulation — epsilon-greedy, UCB1, Thompson sampling
Benchmark and compare ix algorithm performance
Embedded Redis-like cache with TTL, LRU, pub/sub, and RESP protocol
Category theory primitives — monad laws verification, free-forgetful adjunction
Chaos theory analysis — Lyapunov exponents, bifurcation, attractors, fractals
| name | music-ml-demo |
| description | Concrete, runnable examples combining GA music theory tools with ix ML algorithms for chord clustering, harmonic analysis, and scale recommendation |
| disable-model-invocation | true |
Detailed walkthroughs that combine GA's music theory MCP tools with ix's ML algorithms. Each example includes exact tool invocations, expected data formats, and interpretation guidance.
ga_chord, ga_chord_atonal, ga_scale, ga_dsl)ix_kmeans, ix_stats, ix_fft, ix_chaos_lyapunov, ix_supervised)Goal: Cluster common chord voicings by timbral similarity to discover which voicings sound alike regardless of root note.
Call ga_chord for each chord in multiple positions to build a dataset.
Tool: ga_chord
Calls (run these in parallel):
{ "name": "C", "position": 0 } // open C major
{ "name": "C", "position": 5 } // barre C at fret 5
{ "name": "C", "position": 8 } // C at fret 8
{ "name": "Am", "position": 0 } // open A minor
{ "name": "Am", "position": 5 } // barre Am at fret 5
{ "name": "Am", "position": 8 } // Am at fret 8
{ "name": "G", "position": 0 } // open G major
{ "name": "G", "position": 3 } // barre G at fret 3
{ "name": "G", "position": 7 } // G at fret 7
{ "name": "F", "position": 0 } // barre F at fret 1
{ "name": "F", "position": 5 } // F at fret 5
{ "name": "F", "position": 8 } // F at fret 8
Expected output per call:
{
"name": "C",
"position": 0,
"midi_notes": [48, 52, 55, 60, 64],
"intervals": [4, 3, 5, 4],
"register_mean": 55.8,
"span_semitones": 16
}
From each voicing response, construct a feature vector with these dimensions:
| Feature | Description | How to Compute |
|---|---|---|
interval_content (6 values) | Interval class vector (IC1–IC6) | Count interval classes between all note pairs |
register_mean | Average MIDI note value | Mean of midi_notes |
register_spread | Range of MIDI values | Max - min of midi_notes |
voice_leading_density | How close adjacent voices are | Mean of intervals array |
This gives a 9-dimensional feature vector per voicing. Example for open C:
[0, 1, 1, 1, 2, 0, 55.8, 16, 4.0]
Assemble all 12 voicings into a feature matrix (12 rows x 9 columns):
{
"data": [
[0, 1, 1, 1, 2, 0, 55.8, 16, 4.0],
[0, 1, 1, 1, 2, 0, 67.2, 16, 4.0],
[0, 1, 1, 1, 2, 0, 74.4, 16, 4.0],
[1, 1, 0, 1, 2, 0, 53.6, 15, 3.75],
[1, 1, 0, 1, 2, 0, 65.0, 15, 3.75],
[1, 1, 0, 1, 2, 0, 72.8, 15, 3.75],
[0, 1, 1, 1, 2, 0, 54.2, 19, 4.75],
[0, 1, 1, 1, 2, 0, 57.6, 17, 4.25],
[0, 1, 1, 1, 2, 0, 68.0, 17, 4.25],
[1, 1, 1, 0, 2, 0, 56.4, 17, 4.25],
[1, 1, 1, 0, 2, 0, 67.8, 17, 4.25],
[1, 1, 1, 0, 2, 0, 74.0, 17, 4.25]
],
"labels": ["C_0", "C_5", "C_8", "Am_0", "Am_5", "Am_8", "G_0", "G_3", "G_7", "F_0", "F_5", "F_8"]
}
Tool: ix_kmeans
Input:
{
"data": [[0,1,1,1,2,0,55.8,16,4.0], "... (all 12 rows)"],
"k": 3,
"max_iterations": 100,
"seed": 42
}
Expected output:
{
"assignments": [0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2],
"centroids": [
[0.0, 1.0, 1.0, 1.0, 2.0, 0.0, 65.8, 16.0, 4.0],
[1.0, 1.0, 0.0, 1.0, 2.0, 0.0, 63.8, 15.0, 3.75],
[0.33, 1.0, 1.0, 0.33, 2.0, 0.0, 62.3, 17.5, 4.29]
],
"inertia": 234.5,
"iterations": 8
}
Interpretation: The clusters tend to group by interval content (major vs. minor quality) and register spread rather than by root note — voicings with similar harmonic structure cluster together regardless of pitch.
Tool: ix_stats (call once per cluster)
Input (for cluster 0):
{
"data": [55.8, 67.2, 74.4],
"compute": ["mean", "std", "min", "max"]
}
Expected output:
{
"mean": 65.8,
"std": 9.3,
"min": 55.8,
"max": 74.4
}
Cluster labels (assign after inspecting centroids):
Goal: Measure the harmonic complexity and predictability of a chord progression using spectral and chaos analysis.
Analyze the progression: Cmaj7 → Am7 → Dm7 → G7 (a ii-V-I turnaround variant).
Tool: ga_chord_atonal (call for each chord)
Calls:
{ "notes": [0, 4, 7, 11] } // Cmaj7 → pitch classes {0, 4, 7, 11}
{ "notes": [9, 0, 4, 7] } // Am7 → pitch classes {9, 0, 4, 7}
{ "notes": [2, 5, 9, 0] } // Dm7 → pitch classes {2, 5, 9, 0}
{ "notes": [7, 11, 2, 5] } // G7 → pitch classes {7, 11, 2, 5}
Expected output per call:
{
"pitch_classes": [0, 4, 7, 11],
"interval_vector": [2, 1, 1, 1, 1, 0],
"forte_number": "4-20",
"complement": [1, 2, 3, 5, 6, 8, 9, 10]
}
Collect the interval vectors from all four chords:
Cmaj7: [2, 1, 1, 1, 1, 0]
Am7: [2, 1, 1, 1, 1, 0]
Dm7: [2, 1, 1, 1, 1, 0]
G7: [2, 1, 1, 1, 1, 0]
Note: All four chords are of the same set class (4-20), so their interval vectors are identical. This is a hallmark of smooth jazz harmony — same structure, different transposition.
To capture the movement between chords, compute the root motion series as semitone intervals:
C→Am = -3 (or 9)
Am→Dm = 5
Dm→G = 5
G→C = 5
Root motion signal: [9, 5, 5, 5]
Tool: ix_fft
Input:
{
"signal": [9, 5, 5, 5, 9, 5, 5, 5, 9, 5, 5, 5, 9, 5, 5, 5],
"sample_rate": 4
}
We repeat the 4-chord pattern 4 times to give the FFT enough data to detect periodicity.
Expected output:
{
"frequencies": [0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75],
"magnitudes": [96.0, 8.0, 0.0, 0.0, 8.0, 0.0, 0.0, 0.0],
"dominant_frequency": 0.25,
"dominant_magnitude": 8.0
}
Interpretation: The dominant frequency at 0.25 (period = 4 beats) confirms the 4-chord cycle. The relatively low magnitude of the dominant peak vs. DC component (8.0 vs 96.0) indicates a progression that is harmonically stable with mild periodic variation — characteristic of pop/jazz turnarounds.
Tool: ix_chaos_lyapunov
Input:
{
"time_series": [9, 5, 5, 5, 9, 5, 5, 5, 9, 5, 5, 5, 9, 5, 5, 5],
"embedding_dim": 2,
"tau": 1
}
Expected output:
{
"lyapunov_exponent": -0.42,
"is_chaotic": false,
"interpretation": "negative_stable"
}
Interpretation:
| Lyapunov Exponent | Harmonic Character | Example |
|---|---|---|
| < -0.5 | Highly predictable, repetitive | 12-bar blues, I-IV-V |
| -0.5 to 0 | Structured with mild variation | Jazz standards, pop |
| ~0 | Complex, structured unpredictability | Coltrane changes, late Romantic |
| > 0 | Chaotic, atonal | Free jazz, serial music |
Goal: Given a target mood (e.g., "mysterious"), recommend scales by classifying scale interval patterns against mood labels.
Tool: ga_scale (call for each scale)
Calls:
{ "name": "major", "root": "C" }
{ "name": "natural_minor", "root": "C" }
{ "name": "harmonic_minor", "root": "C" }
{ "name": "melodic_minor", "root": "C" }
{ "name": "dorian", "root": "C" }
{ "name": "phrygian", "root": "C" }
{ "name": "lydian", "root": "C" }
{ "name": "mixolydian", "root": "C" }
{ "name": "locrian", "root": "C" }
{ "name": "whole_tone", "root": "C" }
{ "name": "diminished", "root": "C" }
{ "name": "pentatonic_major", "root": "C" }
{ "name": "pentatonic_minor", "root": "C" }
{ "name": "blues", "root": "C" }
Expected output per call:
{
"name": "harmonic_minor",
"root": "C",
"intervals": [2, 1, 2, 2, 1, 3, 1],
"notes": ["C", "D", "Eb", "F", "G", "Ab", "B"],
"degree_count": 7
}
For each scale, extract a feature vector from its interval pattern:
| Feature | Description |
|---|---|
semitone_count | Number of semitone (1) intervals |
whole_tone_count | Number of whole-tone (2) intervals |
aug_second_count | Number of augmented-second (3) intervals |
degree_count | Number of notes in the scale |
interval_variance | Variance of interval sizes |
max_interval | Largest interval in the scale |
symmetry | 1 if palindromic interval pattern, 0 otherwise |
Feature matrix (14 rows x 7 columns):
{
"data": [
[0, 5, 0, 7, 0.24, 2, 1],
[2, 3, 0, 7, 0.24, 2, 1],
[2, 2, 1, 7, 0.57, 3, 0],
[1, 4, 0, 7, 0.24, 2, 0],
[1, 4, 0, 7, 0.24, 2, 0],
[2, 3, 0, 7, 0.24, 2, 0],
[0, 5, 0, 7, 0.24, 2, 0],
[1, 4, 0, 7, 0.24, 2, 0],
[2, 3, 0, 7, 0.24, 2, 0],
[0, 6, 0, 6, 0.00, 2, 1],
[4, 0, 0, 8, 0.25, 2, 1],
[0, 2, 0, 5, 0.96, 3, 0],
[0, 1, 1, 5, 1.36, 3, 0],
[0, 1, 1, 6, 1.14, 3, 0]
],
"labels": [
"major", "natural_minor", "harmonic_minor", "melodic_minor",
"dorian", "phrygian", "lydian", "mixolydian", "locrian",
"whole_tone", "diminished",
"pentatonic_major", "pentatonic_minor", "blues"
]
}
Assign mood labels to the training data based on established music theory associations:
{
"mood_labels": [
"bright", "sad", "mysterious", "jazzy",
"groovy", "dark", "dreamy", "relaxed",
"tense", "ethereal", "tense",
"bright", "bluesy", "bluesy"
]
}
Tool: ix_supervised
Input:
{
"task": "classify",
"algorithm": "knn",
"k": 3,
"features": [
[0,5,0,7,0.24,2,1], [2,3,0,7,0.24,2,1], [2,2,1,7,0.57,3,0],
[1,4,0,7,0.24,2,0], [1,4,0,7,0.24,2,0], [2,3,0,7,0.24,2,0],
[0,5,0,7,0.24,2,0], [1,4,0,7,0.24,2,0], [2,3,0,7,0.24,2,0],
[0,6,0,6,0.00,2,1], [4,0,0,8,0.25,2,1],
[0,2,0,5,0.96,3,0], [0,1,1,5,1.36,3,0], [0,1,1,6,1.14,3,0]
],
"labels": [
"bright", "sad", "mysterious", "jazzy",
"groovy", "dark", "dreamy", "relaxed",
"tense", "ethereal", "tense",
"bright", "bluesy", "bluesy"
],
"seed": 42
}
Expected output:
{
"model_trained": true,
"accuracy": 0.71,
"confusion_matrix": { "... (omitted for brevity)" },
"feature_importance": [0.12, 0.08, 0.25, 0.18, 0.22, 0.10, 0.05]
}
Key insight: aug_second_count (feature 3) and interval_variance (feature 5) are the strongest predictors of mood — scales with augmented seconds tend toward "mysterious"/"dark", while low variance correlates with "bright"/"relaxed".
To find scales that match "mysterious":
Tool: ix_supervised
Input:
{
"task": "predict",
"query_features": [
[2, 2, 1, 7, 0.57, 3, 0],
[2, 3, 0, 7, 0.24, 2, 0],
[0, 6, 0, 6, 0.00, 2, 1]
],
"target_mood": "mysterious"
}
Expected output:
{
"predictions": ["mysterious", "dark", "ethereal"],
"distances_to_target": [0.0, 0.33, 0.67],
"recommendations": [
{ "scale": "harmonic_minor", "mood": "mysterious", "confidence": 0.95 },
{ "scale": "phrygian", "mood": "dark", "confidence": 0.72, "note": "closest neighbor to mysterious" },
{ "scale": "whole_tone", "mood": "ethereal", "confidence": 0.58, "note": "alternative ethereal option" }
]
}
Recommendation summary: For a "mysterious" mood, use harmonic minor (highest confidence). If you want to shade toward darkness, try phrygian. For a more floating/ambiguous mystery, try whole tone.
These three examples can be chained in a single session:
This gives a complete workflow: voicing selection, progression analysis, and melodic palette — all driven by data rather than convention.