unequaltemperament

Fred-Seeded Top-X Temperaments

Hundreds of named temperaments reduce to a handful of structural families — "seven names become three patterns" (Sturm). We bucket by fifth-deviation fingerprint, seeded from Fred's PianoScope selections. Full methodology · Sturm: Practical Application

Input temperaments: 192 · Structural buckets: 156 · Fred seed buckets: 10 · Displaying top: 50

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Scoring math

Each temperament's 12 fifths are expressed as deviations from pure (701.955 cents), quantized to 0.1-cent steps, and rotation-canonicalized. Identical signatures form a bucket. Scoring rewards popularity, cross-source agreement, and proximity to Fred's practical choices.

Base score (prominence)
\(s_{base}=n\cdot(1+0.5(c-1))\cdot h\)
n = bucket size, c = coverage (sources/2), h = cohesion = 1/(1+RMS)
Fred pattern fit
\(f=\frac14\left(f_{dist}+f_{span}+f_{abs}+f_{levels}\right)\)
each sub-score = 1/(1+|difference from Fred seeds|)
Fred ratio
\(r=\frac{\#\,\text{PianoScope}}{\#\,\text{members}}\)
fraction of bucket from Fred's practical selections
Final score
\(s=s_{base}\cdot(0.60+0.40f)\cdot(0.75+0.25r)\)
Fred fit boosts up to 40%, Fred presence up to 25%

Top 50 representatives

1. Vallotti
PianoScope · bucket 6 · Fred 2 · score 2.1621 · id 6161
[-3.9, -3.9, -3.9, -3.9, -3.9, -3.9, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0]
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2. Hummel Viennese
PianoScope · bucket 5 · Fred 5 · score 2.1015 · id 6128
[-2.6, -1.8, -2.3, -1.6, -2.1, -1.4, -1.9, -2.5, -1.7, -2.2, -1.5, -2.0]
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3. Broadwood's Best - Ellis #4
PianoScope · bucket 2 · Fred 1 · score 1.4452 · id 6146
[-5.0, -4.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -2.0, -2.0, -4.0]
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4. Broadwood's Usual - Ellis #2
PianoScope · bucket 2 · Fred 1 · score 1.4452 · id 6145
[-5.0, -5.0, -4.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -2.0]
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5. 1/6 Syntonic - Silbermann
PianoScope · bucket 2 · Fred 1 · score 1.4227 · id 6182
[-3.6, -3.6, -3.6, -3.6, -3.6, -3.6, -3.6, -3.6, -3.6, -3.6, -3.6, +16.0]
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6. Kirnberger III
PianoScope · bucket 2 · Fred 1 · score 1.3977 · id 6163
[-5.4, -5.4, -5.4, -5.4, +0.0, +0.0, -2.0, +0.0, +0.0, +0.0, +0.0, +0.0]
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7. Broadwood's Best
PianoScope · bucket 2 · Fred 1 · score 1.3770 · id 6117
[-3.0, -3.0, -2.0, -1.0, -2.0, -2.5, -2.5, -2.0, -2.0, -1.0, -1.5, -1.5]
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8. Moore - Representative Victorian
PianoScope · bucket 2 · Fred 1 · score 1.3599 · id 6154
[-3.5, -3.5, -3.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.5]
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9. Neidhard Dorf
PianoScope · bucket 2 · Fred 1 · score 1.3542 · id 6172
[-5.9, -5.9, +0.0, -2.0, +0.0, -2.0, +0.0, +0.0, -2.0, +0.0, -2.0, -3.9]
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10. Kirnberger Equal-Beating
PianoScope · bucket 2 · Fred 1 · score 1.3269 · id 6165
[-10.8, +0.0, +0.0, -2.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, -10.7]
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11. 2/7 Syntonic
PianoScope · bucket 2 · Fred 1 · score 1.3199 · id 6186
[-6.1, -6.1, -6.1, -6.1, -6.1, -6.1, -6.1, -6.1, -6.1, -6.1, -6.1, +44.1]
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12. 1/3 Syntonic
PianoScope · bucket 2 · Fred 1 · score 1.3122 · id 6174
[-7.2, -7.2, -7.2, -7.2, -7.2, -7.2, -7.2, -7.2, -7.2, -7.2, -7.2, +55.4]
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13. Young
PianoScope · bucket 2 · Fred 1 · score 1.3024 · id 6156
[-4.0, -4.0, -4.0, -4.0, -1.8, -1.8, +0.0, +0.0, +0.0, +0.0, -1.8, -1.8]
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14. Veroli Almost-Equal
PianoScope · bucket 2 · Fred 1 · score 1.3019 · id 6141
[-2.2, -2.2, -2.2, -2.2, -2.2, -2.2, -2.2, -2.2, -1.4, -1.4, -1.4, -1.4]
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15. Preston Theoretical
PianoScope · bucket 2 · Fred 1 · score 1.2909 · id 6159
[-2.8, -2.8, -2.8, -2.8, -2.8, -2.8, -2.8, -2.8, -2.8, -2.8, -2.8, +7.4]
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16. Rousseau Theoretical
PianoScope · bucket 2 · Fred 1 · score 1.2687 · id 6166
[-3.0, -3.0, -3.0, -3.0, -3.0, -0.5, -0.5, -0.5, -1.0, -1.5, -2.0, -2.5]
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17. Stanhope Equal-Beating
PianoScope · bucket 2 · Fred 1 · score 1.2619 · id 6143
[-10.2, -6.8, -4.5, +0.0, +1.4, +0.0, +0.0, +0.0, -3.4, +0.0, +0.0, +0.0]
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18. Prinz Equal-Beating
PianoScope · bucket 2 · Fred 1 · score 1.2553 · id 6151
[-8.9, -6.0, -4.0, -2.7, +0.0, -2.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0]
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19. Werckmeister III
PianoScope · bucket 2 · Fred 1 · score 1.2505 · id 6441
[-5.9, -5.9, -5.9, +0.0, +0.0, -5.9, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0]
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20. Tuner's Guide #3
PianoScope · bucket 2 · Fred 1 · score 1.2484 · id 6492
[-2.9, -1.9, -2.6, -1.7, +0.0, -1.5, -2.0, -2.7, -1.8, -2.4, -1.6, -2.2]
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21. Tans'ur
PianoScope · bucket 2 · Fred 1 · score 1.2356 · id 6168
[-5.1, -3.4, -4.6, -3.1, +0.0, +0.0, -0.6, +0.0, +0.0, +0.0, -2.9, -3.8]
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22. Tuner's Guide #1
PianoScope · bucket 2 · Fred 1 · score 1.2314 · id 6490
[-3.9, -2.6, -3.5, -1.2, -1.6, -2.1, +0.0, +0.0, +0.0, -3.3, -2.2, -3.0]
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23. Prelleur
PianoScope · bucket 2 · Fred 1 · score 1.2311 · id 6169
[-4.0, -2.7, -3.5, -2.4, -3.2, -1.2, -1.6, -0.3, +0.0, -0.7, -1.0, -3.0]
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24. Jousse Well
PianoScope · bucket 2 · Fred 1 · score 1.2206 · id 6150
[-4.0, -2.6, -3.5, -2.4, +0.0, +0.0, +0.0, +0.0, -2.5, -3.3, -2.2, -3.0]
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25. Pythagorean
PianoScope · bucket 2 · Fred 1 · score 1.2176 · id 6197
[-23.5, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0]
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26. 1/4 Syntonic
PianoScope · bucket 2 · Fred 1 · score 1.2002 · id 6189
[-5.4, -5.4, -5.4, -5.4, -5.4, -5.4, -5.4, -5.4, -5.4, -5.4, -5.4, +35.7]
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27. Huygens
PianoScope · bucket 2 · Fred 1 · score 1.1967 · id 6188
[-5.2, -5.2, -5.2, -5.2, -5.2, -5.2, -5.2, -5.2, -5.2, -5.2, -5.2, +33.5]
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28. Johann C. G. Graupner
CyberTuner · bucket 3 · Fred 0 · score 1.0214 · id 6510
[-2.7, -1.8, -2.4, -1.6, -2.1, -1.5, -1.9, -2.5, -1.7, -2.3, -1.5, -2.0]
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29. Britannica
PianoScope · bucket 1 · Fred 1 · score 0.6086 · id 6177
[-4.3, -4.3, -4.3, -4.3, -4.3, -4.3, -4.3, -4.3, -4.3, -4.3, +8.4, +11.1]
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30. 1/7 Syntonic
PianoScope · bucket 1 · Fred 1 · score 0.6078 · id 6181
[-3.2, -3.1, -3.1, -3.1, -3.1, -3.2, -3.1, -3.1, -3.1, -3.1, -3.1, +10.3]
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31. Rameau
PianoScope · bucket 1 · Fred 1 · score 0.6000 · id 6180
[-5.9, -5.9, -5.9, -5.9, -5.9, -5.9, +0.0, +0.0, +0.0, +0.0, +5.9, +5.9]
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32. Coleman 10
PianoScope · bucket 1 · Fred 1 · score 0.5875 · id 6138
[-3.0, -2.5, -3.0, -2.5, -1.0, -1.0, -2.0, -2.0, -1.0, -1.0, -2.5, -2.5]
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33. Bemetzrieder Reverse
PianoScope · bucket 1 · Fred 1 · score 0.5855 · id 6152
[-5.9, +0.0, +0.0, +0.0, +0.0, -3.9, -3.9, -3.9, -3.9, -3.9, -3.9, +5.9]
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34. Coleman 16
PianoScope · bucket 1 · Fred 1 · score 0.5809 · id 6135
[-4.0, -4.0, -4.0, -4.0, -2.0, -2.0, +0.0, -1.0, -1.0, +0.0, +0.0, -2.0]
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35. Neidhard Große Stadt
PianoScope · bucket 1 · Fred 1 · score 0.5799 · id 6173
[-5.9, -2.0, -3.9, -2.0, +0.0, -2.0, -2.0, -2.0, +0.0, -2.0, -2.0, +0.0]
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36. Coleman 11
PianoScope · bucket 1 · Fred 1 · score 0.5786 · id 6139
[-4.0, -3.0, -4.0, -3.0, +0.0, +0.0, -2.0, -2.0, +0.0, +0.0, -3.0, -3.0]
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37. Boulliau
PianoScope · bucket 1 · Fred 1 · score 0.5738 · id 6196
[-14.7, +0.0, +0.0, +0.0, +0.0, -8.7, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0]
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38. Hawkes
PianoScope · bucket 1 · Fred 1 · score 0.5708 · id 6176
[-4.3, -4.3, -4.3, -4.3, -4.3, -4.3, -4.3, -4.3, -4.3, +0.0, +7.6, +7.6]
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39. D'Alembert
PianoScope · bucket 1 · Fred 1 · score 0.5605 · id 6179
[-5.4, -5.4, -5.4, -5.4, -4.7, -4.7, -4.7, -4.7, +4.2, +4.2, +4.2, +4.2]
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40. 1/6 Syntonic
PianoScope · bucket 1 · Fred 1 · score 0.5598 · id 6178
[-4.0, -4.0, -4.0, -3.0, -3.0, -4.0, +16.0, -4.0, -3.0, -4.0, -4.0, -3.0]
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41. Lambert
PianoScope · bucket 1 · Fred 1 · score 0.5595 · id 6164
[-3.4, -3.4, -3.3, -3.4, -3.4, -3.3, -3.4, +0.0, +0.0, +0.0, +0.0, +0.0]
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42. Wendell Bold Synchronous
PianoScope · bucket 1 · Fred 1 · score 0.5593 · id 6125
[-4.3, -4.3, -4.3, -4.3, +0.0, +0.0, -4.3, +0.0, +0.0, -2.0, +0.0, +0.0]
Graph Editor Scale Explorer
43. Ellis Equal-Beating
PianoScope · bucket 1 · Fred 1 · score 0.5578 · id 6116
[-2.5, -1.9, -2.2, -1.8, -2.0, -1.6, -1.8, -2.3, -1.9, -2.1, -1.7, -1.9]
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44. Secor #2
PianoScope · bucket 1 · Fred 1 · score 0.5570 · id 6144
[-5.4, -5.4, -5.4, -3.7, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0, -3.7]
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45. Marpurg III
PianoScope · bucket 1 · Fred 1 · score 0.5553 · id 6171
[-17.6, +0.0, +0.0, +0.0, +0.0, -5.9, +0.0, +0.0, +0.0, +0.0, +0.0, +0.0]
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46. Equal Temperament
PianoScope · bucket 1 · Fred 1 · score 0.5548 · id 6198
[-2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0]
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47. Stanhope Theoretical
PianoScope · bucket 1 · Fred 1 · score 0.5544 · id 6153
[-7.2, -7.2, -7.2, +0.0, -1.0, +0.0, +0.0, +0.0, -1.0, +0.0, +0.0, +0.0]
Graph Editor Scale Explorer
48. Pyle Equal-Beating
PianoScope · bucket 1 · Fred 1 · score 0.5541 · id 6118
[-2.4, -1.9, -2.1, -1.7, -1.9, -2.1, -2.0, -2.2, -1.8, -2.0, -1.6, -1.8]
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49. Wendell Synchronous ET Equivalent
PianoScope · bucket 1 · Fred 1 · score 0.5489 · id 6131
[-4.3, +0.0, -4.3, +0.0, -4.3, +0.0, -4.3, +0.0, -4.3, +0.0, -2.0, +0.0]
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50. Neidhardt / Marpurg / De Morgan
PianoScope · bucket 1 · Fred 1 · score 0.5455 · id 6193
[-3.9, +0.0, -2.9, -3.0, +0.0, -2.0, -3.9, +0.0, -2.0, -3.9, +0.0, -2.0]
Graph Editor Scale Explorer