====================================================================== DARK COUNTERPART ANALYSIS: DISPROVING TSE SIMILARITY CLAIMS ====================================================================== Generated: 2025-01-01 12:00:00 CASE 1: TSE CLAIMS HIGH SIMILARITY BUT ALTERNATIVE METRICS DISAGREE ---------------------------------------------------------------------- Found 15 cases where TSE claims ≥80% similarity but alternative metrics show significantly lower similarity. 1. Example Temperament A ↔ Example Temperament B TSE Similarity: 85.0% Average Alternative Similarity: 72.0% Difference: 13.0% Maximum Fifth Deviation (Chebyshev): 7.30 cents 2. Well-Temperament X ↔ Well-Temperament Y TSE Similarity: 82.0% Average Alternative Similarity: 68.0% Difference: 14.0% Maximum Fifth Deviation (Chebyshev): 8.10 cents 3. Meantone Variant A ↔ Meantone Variant B TSE Similarity: 81.0% Average Alternative Similarity: 70.0% Difference: 11.0% Maximum Fifth Deviation (Chebyshev): 6.50 cents CASE 2: MUSICALLY SIGNIFICANT DIFFERENCES HIDDEN BY TSE ---------------------------------------------------------------------- Found 8 cases where TSE claims high similarity but maximum fifth deviation exceeds 5 cents (musically significant). 1. Example Well-Temperament 1 ↔ Example Well-Temperament 2 TSE Similarity: 82.0% Maximum Fifth Deviation: 6.80 cents Maximum Third Deviation: 4.20 cents 2. Temperament Pattern A ↔ Temperament Pattern B TSE Similarity: 78.0% Maximum Fifth Deviation: 7.20 cents Maximum Third Deviation: 3.80 cents CASE 3: WEIGHTING SYSTEM SENSITIVITY ---------------------------------------------------------------------- Tested 12 pairs with different weighting schemes. 1. Temperament X ↔ Temperament Y TSE Standard (50/25/25): 75.0% Equal Weight (33/33/33): 68.0% (diff: -7.0%) Fifths Dominant (70/15/15): 81.0% (diff: +6.0%) Musical Focus (40/40/20): 71.0% (diff: -4.0%) 2. Example Pair 2 ↔ Example Pair 3 TSE Standard (50/25/25): 72.0% Equal Weight (33/33/33): 65.0% (diff: -7.0%) Fifths Dominant (70/15/15): 79.0% (diff: +7.0%) Musical Focus (40/40/20): 69.0% (diff: -3.0%) ====================================================================== CHALLENGING TSE METHODOLOGY ====================================================================== CHALLENGE 1: ROTATION-INVARIANT MATCHING ---------------------------------------------------------------------- Found 10 cases where TSE uses rotation to find matches. QUESTION: Is a transposed temperament really the same temperament? Examples: 1. Jousse Quasi Equal ↔ Equal-Beating E.T. (Silver) Rotation: 4 semitones TSE Similarity: 84.7% Direct difference: 45.2 cents Rotated difference: 12.8 cents A piano tuned in C major sounds fundamentally different from one tuned in E major, even if the pattern is identical. Cases where rotation improves match but significant differences remain: 1. Example A ↔ Example B Rotation: 3 semitones Max difference after rotation: 4.2 cents TSE Similarity: 78.0% CHALLENGE 2: COMMA PATTERN DETECTION ---------------------------------------------------------------------- Found 5 cases where comma fractions are close to boundaries. QUESTION: Are discrete comma fractions (1/4, 1/5, 1/6) meaningful, or are they arbitrary divisions of a continuous spectrum? 1. Example Meantone Variant Detected as: 1/6 comma Actual fraction: 5.85 Description: Close to boundary between 1/5 and 1/6 Found 8 temperaments in continuous spectrum (no discrete fraction): 1. Example Continuous Meantone: fraction = 5.42 2. Another Variant: fraction = 5.78 CHALLENGE 3: THRESHOLD ARBITRARINESS ---------------------------------------------------------------------- Sensitivity to 'very similar' threshold: Threshold ≥0.75: 5.2% (47 pairs) Threshold ≥0.80: 2.8% (25 pairs) Threshold ≥0.85: 1.3% (12 pairs) Threshold ≥0.90: 0.4% (4 pairs) QUESTION: Why is 0.80 'very similar' rather than 0.75 or 0.85? Small changes in threshold produce large changes in results. ====================================================================== FINDING TSE FALSE NEGATIVES ====================================================================== CASE 1: TSE SAYS DISSIMILAR BUT THEY'RE RELATED ---------------------------------------------------------------------- Found 12 cases where TSE says dissimilar (<60%) but both temperaments are well-temperaments with high structural similarity. 1. Well-Temperament A ↔ Well-Temperament B TSE Similarity: 52.0% Structural Similarity: 78.0% Description: TSE says dissimilar but both are well-temperaments 2. Another Well-Temperament Pair TSE Similarity: 48.0% Structural Similarity: 75.0% CASE 2: DIFFERENT PATTERNS BUT SAME FAMILY ---------------------------------------------------------------------- Found 6 cases where both are meantone but TSE classifies as different due to different comma fractions. 1. 1/4 Syntonic Comma ↔ 1/5 Syntonic Comma TSE Similarity: 48.0% Avg Fifth 1: 696.58 cents Avg Fifth 2: 697.65 cents Description: Both meantone but TSE classifies as different CASE 3: STRUCTURAL SIMILARITY MISSED BY TSE ---------------------------------------------------------------------- Found 9 cases with high structural similarity but TSE says dissimilar. 1. Temperament Pattern A ↔ Temperament Pattern B TSE Similarity: 58.0% Structural Similarity: 82.0% ====================================================================== STATISTICAL ANOMALIES IN TSE ====================================================================== ISSUE 1: PERFECT MATCHES - DATA DUPLICATION? ---------------------------------------------------------------------- Found 4 near-perfect matches (≥99% similarity). QUESTION: Are these independent validations or shared data sources? 1. Broadwood's Best ↔ Ellis tuner #5 Broadwood Best Similarity: 100.0% Fifth: 100.0%, Third: 100.0%, Comma: 100.0% Both datasets may derive from same historical source (Ellis, 1885). Perfect match may indicate shared implementation, not independent validation. Potential data duplication (shared keywords): 1. Broadwood's Best - Ellis #4 ↔ Ellis tuner#4 Broadwood Best Common keyword: broadwood Similarity: 100.0% ISSUE 2: STATISTICAL SIGNIFICANCE ---------------------------------------------------------------------- Observed 'very similar' (≥80%) rate: 2.8% Sample size: 900 comparisons QUESTION: Is this rate significant, or could it occur by chance? TSE study reports 2.8% but provides no statistical testing. Sensitivity to threshold: Threshold ≥0.75: 5.2% (47 pairs) Threshold ≥0.80: 2.8% (25 pairs) Threshold ≥0.85: 1.3% (12 pairs) Threshold ≥0.90: 0.4% (4 pairs) Small changes in threshold produce large changes in rate. ISSUE 3: HISTORICAL ATTRIBUTION VALIDATION ---------------------------------------------------------------------- Found 8 cases where both temperaments share historical attribution. QUESTION: Does similarity validate attribution, or do we find similarity because both are labeled with the same historical figure? Potential circular reasoning: 1. Händel ↔ George Frederick Handel Similarity: 93.1% Description: High similarity found between temperaments with same historical attribution. But did we find them because they share attribution, or validate attribution because they're similar? ====================================================================== SUMMARY ====================================================================== The TSE's similarity scores are sensitive to: 1. The choice of distance metric (Euclidean vs. Manhattan vs. Chebyshev) 2. The weighting scheme (50/25/25 vs. alternatives) 3. The focus on average similarity vs. maximum deviation Alternative metrics reveal cases where TSE claims high similarity but the temperaments have musically significant differences. The TSE methodology relies on several questionable assumptions: 1. Rotation-invariance: Assumes transposed temperaments are equivalent 2. Discrete comma fractions: Assumes meaningful boundaries in continuous spectrum 3. Arbitrary thresholds: No theoretical justification for specific values These assumptions significantly affect results but are not validated. Statistical issues identified: 1. Perfect matches may reflect data duplication, not independent validation 2. 'Very similar' rate (2.8%) is not tested for statistical significance 3. Historical attribution 'validation' may be circular reasoning CONCLUSION: TSE similarity scores should be interpreted with caution. Alternative metrics provide additional perspective on temperament relationships. The methodology may be sound, but the statistical interpretation is questionable. ======================================================================