unequaltemperament

TSE Dark Proof

PROOF alpha
Mathematical proof and validation of dark counterpart findings. Detailed analysis of where and why pattern detection fails.
TSE Dark Counterpart - Proof & Results

Files Created

Documentation

Python Scripts

Results Files

Socratic Dialog Files

Key Challenges Implemented

1. Weighting System Critique

Tests alternative weightings (33/33/33, 70/15/15, 40/40/20) to show how TSE's 50/25/25 weighting is arbitrary and affects results.

2. Rotation Invariance Question

Challenges assumption that transposed temperaments are equivalent. Shows cases where rotation improves match but significant musical differences remain.

3. Comma Pattern Skepticism

Demonstrates that comma fractions (1/4, 1/5, 1/6) are arbitrary divisions of a continuous spectrum, not meaningful boundaries.

4. Threshold Arbitrariness

Tests sensitivity to "very similar" threshold (0.75, 0.80, 0.85, 0.90) showing large changes in results from small threshold changes.

5. Statistical Significance

Questions whether 2.8% "very similar" rate is significant, analyzes perfect matches for potential data duplication, challenges historical attribution validation.

6. Alternative Metrics

Uses Manhattan distance, Chebyshev distance, cosine similarity, and structural similarity to reveal relationships TSE misses.

7. False Negatives

Finds well-temperament and meantone family relationships that TSE classifies as dissimilar due to focus on exact comma fractions.

Expected Output Structure

JSON Results Format

{ "timestamp": "20250101_120000", "alternative_metrics_analysis": { "tse_high_similarity_but_different": [ { "temp1_name": "Example Temperament 1", "temp2_name": "Example Temperament 2", "tse_similarity": 0.85, "avg_alternative_sim": 0.65, "difference": 0.20, "chebyshev_max_dev": 7.3 } ], "musically_significant_differences": [...], "weighting_comparisons": [...] } }

Text Report Format

====================================================================== DARK COUNTERPART ANALYSIS: DISPROVING TSE SIMILARITY CLAIMS ====================================================================== CASE 1: TSE CLAIMS HIGH SIMILARITY BUT ALTERNATIVE METRICS DISAGREE ---------------------------------------------------------------------- Found X cases where TSE claims ≥80% similarity but alternative metrics show significantly lower similarity. 1. Temperament A ↔ Temperament B TSE Similarity: 85.0% Average Alternative Similarity: 65.0% Difference: 20.0% Maximum Fifth Deviation (Chebyshev): 7.30 cents

Key Findings

Weighting Sensitivity

Found significant differences between TSE's 50/25/25 weighting and alternatives. For example, "1/3 Syntonic ↔ 1/6 Syntonic" shows TSE Standard = 53.7%, but Equal Weight = 14.3% (39.4% difference).

Database Analysis

Processed all 192 temperaments (83 from PianoScope/Fred, 109 from CyberTuner/Chip2) for a total of 18,336 pairwise comparisons.

Historical Attribution

Identified 7 cases where temperaments share historical attribution (e.g., Broadwood, Ellis, D'Alembert, Kirnberger), raising questions about circular reasoning in validation.

Parameterized Weighting System

System Overview

The parameterized weighting system allows running all analysis scripts with different weighting schemes, enabling systematic exploration of how weighting choices affect results.

Predefined Schemes

TSE Standard (50/25/25) - Original TSE weighting
Equal Weight (33/33/33) - No component preference
Fifths Dominant (70/15/15) - Strong emphasis on fifths
Musical Focus (40/40/20) - Balance fifths and thirds
Thirds Emphasis (30/50/20) - Emphasize major thirds
Commas Emphasis (30/20/50) - Emphasize comma patterns

Comparison Capabilities

The comparison script identifies robust relationships (hold across multiple schemes) vs. artifacts (only appear under specific weightings), providing validation of TSE's methodology.

Weighting Scheme Results

Documentation Links