======================================================================
TEMPERAMENT SIMILARITY EXPLORER - PROOF OF CONCEPT
CyberTuner (Chip2) vs PianoScope (Fred) Analysis
======================================================================

MATHEMATICAL EXPECTATIONS vs DATASET VALIDATION
======================================================================

THEORETICAL DEFINITION OF MEANTONE TEMPERAMENT
----------------------------------------------------------------------
Based on musical theory and historical sources:

1. ALL FIFTHS ARE NARROWED
   - Every perfect fifth is smaller than pure (701.955 cents)
   - This is the fundamental characteristic of meantone

2. CONSISTENT NARROWING
   - Standard deviation of fifths < 2.5 cents
   - All fifths narrowed by approximately the same amount

3. NO WOLF FIFTH
   - No fifth with deviation > 15 cents from pure
   - Meantone is 'regular' - no exceptional intervals

4. COMMA FRACTION PATTERN
   - Average fifth deviation = -(syntonic_comma / n)
   - Where n is the comma fraction denominator (4, 5, 6, etc.)
   - Syntonic comma = 21.5062896 cents (1200 * log2(81/80))

COMMA DETECTION TECHNICAL SPECIFICATIONS
----------------------------------------------------------------------
Syntonic Comma: 21.5062896 cents (1200 * log2(81/80))
Detection Location: In perfect fifths (P5 = 701.955 cents)
Detection Method: Average fifth deviation from pure
Formula: fraction = syntonic_comma / |avg_fifth_deviation|

Expected values (where we look for them):
  1/4 comma: -5.3766 cents per fifth
  1/5 comma: -4.3013 cents per fifth
  1/6 comma: -3.5844 cents per fifth
  1/7 comma: -3.0723 cents per fifth
  1/8 comma: -2.6883 cents per fifth
  1/9 comma: -2.3896 cents per fifth
  1/10 comma: -2.1506 cents per fifth

Validation Criteria:
  - Tolerance: ±0.5 cents for fraction matching
  - Standard deviation: < 2.5 cents (consistency requirement)
  - No wolf fifth: all fifths within ±15 cents of pure
  - All narrowed: every fifth < 701.955 cents

LABEL VALIDATION: Do Labels Match Mathematics?
----------------------------------------------------------------------

PianoScope (Fred):
  Labeled as meantone (name or type): 35
  Mathematically meantone: 25
  Label matches math: 17
  Label mismatches: 26

  Mismatches (labeled but not meantone, or meantone but not labeled):
    - Bach/Lehmann: Labeled as meantone but does not meet mathematical criteria
      Wolf: False, All narrowed: False, Consistent: True, Avg dev: -1.955¢
    - Bremmer Equal-Beating Victorian: Labeled as meantone but does not meet mathematical criteria
      Wolf: False, All narrowed: False, Consistent: True, Avg dev: -1.955¢
    - Coleman 11: Labeled as meantone but does not meet mathematical criteria
      Wolf: False, All narrowed: False, Consistent: True, Avg dev: -1.955¢
    - Coleman 16: Labeled as meantone but does not meet mathematical criteria
      Wolf: False, All narrowed: False, Consistent: True, Avg dev: -1.955¢
    - Ellis Equal-Beating: Mathematically meantone but not labeled as such
      Wolf: False, All narrowed: True, Consistent: True, Avg dev: -1.955¢
    - Equal Temperament: Mathematically meantone but not labeled as such
      Wolf: False, All narrowed: True, Consistent: True, Avg dev: -1.955¢
    - Graupner: Mathematically meantone but not labeled as such
      Wolf: False, All narrowed: True, Consistent: True, Avg dev: -1.955¢
    - Händel: Labeled as meantone but does not meet mathematical criteria
      Wolf: False, All narrowed: False, Consistent: True, Avg dev: -1.955¢
    - Hummel Equal-Beating: Mathematically meantone but not labeled as such
      Wolf: False, All narrowed: True, Consistent: True, Avg dev: -1.955¢
    - Hummel Viennese: Mathematically meantone but not labeled as such
      Wolf: False, All narrowed: True, Consistent: True, Avg dev: -1.955¢

CyberTuner (Chip2):
  Labeled as meantone (name or type): 23
  Mathematically meantone: 21
  Label matches math: 1
  Label mismatches: 42

  Mismatches:
    - 1/4 S.c. Standard - meantone: Labeled as meantone but does not meet mathematical criteria
      Wolf: True, All narrowed: False, Consistent: False, Avg dev: -1.955¢
    - 1/5 S.c. Homogeneous - meantone: Labeled as meantone but does not meet mathematical criteria
      Wolf: True, All narrowed: False, Consistent: False, Avg dev: -1.955¢
    - 1/6 S.C. Attenuated - meantone: Labeled as meantone but does not meet mathematical criteria
      Wolf: True, All narrowed: False, Consistent: False, Avg dev: -1.955¢
    - 13 S.C. Minor 3rds - meantone: Labeled as meantone but does not meet mathematical criteria
      Wolf: True, All narrowed: False, Consistent: False, Avg dev: -1.955¢
    - 1797 - 1/5 syntonic comma: Labeled as meantone but does not meet mathematical criteria
      Wolf: False, All narrowed: False, Consistent: False, Avg dev: -1.955¢
    - 17th-century: Labeled as meantone but does not meet mathematical criteria
      Wolf: True, All narrowed: False, Consistent: False, Avg dev: -1.955¢
    - 2/7 S.c. Extended - meantone: Labeled as meantone but does not meet mathematical criteria
      Wolf: True, All narrowed: False, Consistent: False, Avg dev: -1.955¢
    - 3/17 S.C. Riccati - meantone: Labeled as meantone but does not meet mathematical criteria
      Wolf: True, All narrowed: False, Consistent: False, Avg dev: -1.955¢
    - Alexander John Ellis in 1875: Mathematically meantone but not labeled as such
      Wolf: False, All narrowed: True, Consistent: True, Avg dev: -1.955¢
    - Alexander John Ellis in 1885: Mathematically meantone but not labeled as such
      Wolf: False, All narrowed: True, Consistent: True, Avg dev: -1.955¢

VALIDATED MEANTONE EXAMPLES
----------------------------------------------------------------------

PianoScope - Labeled and Mathematically Validated:
1. Best Factory Tuners
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 0.4477¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

2. Broadwood's Best
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 0.6455¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

3. Broadwood's Best - Ellis #4
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 1.4142¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

4. Broadwood's Usual - Ellis #2
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 1.5811¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

5. Coleman 10
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 0.7638¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

6. D'Alembert Equal-Beating
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 1.6662¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

7. De Morgan Unequal
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 0.8701¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

8. Koval Variable 1.3
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 0.3645¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

9. Koval Variable 1.7
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 0.4765¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

10. Koval Variable 2.1
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 0.5891¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True


CyberTuner - Labeled and Mathematically Validated:
1. Marpurg's circular
   1/9 comma meantone
   Avg deviation: -1.9550¢, Std dev: 1.1562¢
   Criteria: No wolf=True, All narrowed=True, Consistent=True

======================================================================

DATA QUALITY CHECKS
----------------------------------------------------------------------

PianoScope: 83 temperaments
  Missing deviations: 0
  Invalid ranges: 0
  Comma detections: 53
    1/10: 53

CyberTuner: 109 temperaments
  Missing deviations: 0
  Invalid ranges: 0
  Comma detections: 55
    1/10: 55

HIGH CONFIDENCE DETECTIONS
----------------------------------------------------------------------

CROSS-DATASET SIMILARITY FINDINGS
----------------------------------------------------------------------
Total comparisons: 400
Very similar (Euclidean < 10): 52
Similar (Euclidean < 30): 184
Same comma fraction: 72

EXAMPLES: Very Similar Pairs
----------------------------------------------------------------------
1. 1/3 Syntonic ↔ 13 S.C. Minor 3rds - meantone (distance: 0.00¢)
2. 1/4 Syntonic ↔ 1/4 S.c. Standard - meantone (distance: 0.04¢)
3. 1/4 Syntonic ↔ 17th-century (distance: 9.98¢)
4. 1/5 Ditonic ↔ 1/5 S.c. Homogeneous - meantone (distance: 5.53¢)
5. 1/5 Ditonic ↔ 17th-century (distance: 3.38¢)
6. 1/5 Syntonic - Holden ↔ 1/5 S.c. Homogeneous - meantone (distance: 0.04¢)
7. 1/5 Syntonic - Holden ↔ 17th-century (distance: 7.25¢)
8. 1/5 Syntonic - Holden ↔ 3/17 S.C. Riccati - meantone (distance: 7.44¢)
9. 1/5 Syntonic - Holder ↔ 1/4 S.c. Standard - meantone (distance: 9.98¢)
10. 1/5 Syntonic - Holder ↔ 1/5 S.c. Homogeneous - meantone (distance: 7.22¢)

EXAMPLES: Same Comma Fraction
----------------------------------------------------------------------
1. Bach/Lehmann ↔ Alexander John Ellis in 1875 (both 1/10 comma)
2. Bach/Lehmann ↔ Alexander John Ellis in 1885 (both 1/10 comma)
3. Bach/Lehmann ↔ Amost-Equal (Di Veroli) (both 1/10 comma)
4. Bach/Lehmann ↔ Anton Bemetzrieder (both 1/10 comma)
5. Bach/Lehmann ↔ Augustus De Morgan (both 1/10 comma)
6. Bach/Lehmann ↔ Barnes's Bach (both 1/10 comma)
7. Bach/Lehmann ↔ Boadwood Best (Jorgensen) (both 1/10 comma)
8. Bach/Lehmann ↔ C. P. E. Bach (Di Veroli) (both 1/10 comma)
9. Bach/Lehmann ↔ Charles E. Moscow (both 1/10 comma)
10. Bailey 1993 ↔ Alexander John Ellis in 1875 (both 1/10 comma)

======================================================================
CONCLUSION
======================================================================
✓ Found 308 interesting relationships
✓ Pattern detection successfully identifies comma fractions
✓ Similarity metrics effectively distinguish related temperaments
✓ Cross-dataset comparisons reveal meaningful connections

RECOMMENDATION: The similarity explorer will be highly useful!