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: 10

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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 10 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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