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Research / Internal Frontier Tool

Formula Lab

Frontier workspace for exhaustive 12-TET formula families. Browse cross-octave equivalence classes and extension/truncation trajectories, then label novel families for downstream model training.

This surface is optimized for frontier analysis and corpus labeling. It is intentionally denser than the Learn and Explore sections.
/api/unified/formulas?view=families/api/unified/formulas?parse=(TTP4P4)x3/api/unified/formulas/address?index=42/api/unified/formulas/family-label/api/unified/formulas/ml/api/unified/formulas/math/api/unified/formulas/deep-math
Formulas
10,273
Formula Relations
16,095
Families
10,308
Family Relations
25,366
Frontier Labels
0

Family Explorer

Cross-Octave Family (1-1-1-1-2)4
cross-octave · motif 1-1-1-1-2 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (1-1-1-3)4
cross-octave · motif 1-1-1-3 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (1-1-2)4
cross-octave · motif 1-1-2 · oct 1-4 · rep 3-12
unlabeled
Cross-Octave Family (1-1-2-2)4
cross-octave · motif 1-1-2-2 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (1-1-4)4
cross-octave · motif 1-1-4 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (1-2-3)4
cross-octave · motif 1-2-3 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (1-3)4
cross-octave · motif 1-3 · oct 1-4 · rep 3-12
unlabeled
Cross-Octave Family (1-3-2)4
cross-octave · motif 1-3-2 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (1-5)4
cross-octave · motif 1-5 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (2-4)4
cross-octave · motif 2-4 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (4)4
cross-octave · motif 4 · oct 1-4 · rep 3-12
unlabeled
Cross-Octave Family (6)4
cross-octave · motif 6 · oct 1-4 · rep 2-8
unlabeled
Cross-Octave Family (1-1-1-1-1-7)3
cross-octave · motif 1-1-1-1-1-7 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-1-2-6)3
cross-octave · motif 1-1-1-1-2-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-1-3-5)3
cross-octave · motif 1-1-1-1-3-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-1-4-4)3
cross-octave · motif 1-1-1-1-4-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-1-5-3)3
cross-octave · motif 1-1-1-1-5-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-1-6-2)3
cross-octave · motif 1-1-1-1-6-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-1-8)3
cross-octave · motif 1-1-1-1-8 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-2-1-6)3
cross-octave · motif 1-1-1-2-1-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-2-2-5)3
cross-octave · motif 1-1-1-2-2-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-2-3-4)3
cross-octave · motif 1-1-1-2-3-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-2-4-3)3
cross-octave · motif 1-1-1-2-4-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-2-5-2)3
cross-octave · motif 1-1-1-2-5-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-2-7)3
cross-octave · motif 1-1-1-2-7 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-3-1-5)3
cross-octave · motif 1-1-1-3-1-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-3-2-4)3
cross-octave · motif 1-1-1-3-2-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-3-3-3)3
cross-octave · motif 1-1-1-3-3-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-3-4-2)3
cross-octave · motif 1-1-1-3-4-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-3-6)3
cross-octave · motif 1-1-1-3-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-4-1-4)3
cross-octave · motif 1-1-1-4-1-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-4-2-3)3
cross-octave · motif 1-1-1-4-2-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-4-3-2)3
cross-octave · motif 1-1-1-4-3-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-4-5)3
cross-octave · motif 1-1-1-4-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-5-1-3)3
cross-octave · motif 1-1-1-5-1-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-5-2-2)3
cross-octave · motif 1-1-1-5-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-5-4)3
cross-octave · motif 1-1-1-5-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-6-1-2)3
cross-octave · motif 1-1-1-6-1-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-6-3)3
cross-octave · motif 1-1-1-6-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-7-2)3
cross-octave · motif 1-1-1-7-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-1-9)3
cross-octave · motif 1-1-1-9 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-10)3
cross-octave · motif 1-1-10 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-1-1-6)3
cross-octave · motif 1-1-2-1-1-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-1-2-5)3
cross-octave · motif 1-1-2-1-2-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-1-3-4)3
cross-octave · motif 1-1-2-1-3-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-1-4-3)3
cross-octave · motif 1-1-2-1-4-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-1-5-2)3
cross-octave · motif 1-1-2-1-5-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-1-7)3
cross-octave · motif 1-1-2-1-7 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-2-1-5)3
cross-octave · motif 1-1-2-2-1-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-2-2-4)3
cross-octave · motif 1-1-2-2-2-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-2-3-3)3
cross-octave · motif 1-1-2-2-3-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-2-4-2)3
cross-octave · motif 1-1-2-2-4-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-2-6)3
cross-octave · motif 1-1-2-2-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-3-1-4)3
cross-octave · motif 1-1-2-3-1-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-3-2-3)3
cross-octave · motif 1-1-2-3-2-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-3-3-2)3
cross-octave · motif 1-1-2-3-3-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-3-5)3
cross-octave · motif 1-1-2-3-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-4-1-3)3
cross-octave · motif 1-1-2-4-1-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-4-2-2)3
cross-octave · motif 1-1-2-4-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-4-4)3
cross-octave · motif 1-1-2-4-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-5-1-2)3
cross-octave · motif 1-1-2-5-1-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-5-3)3
cross-octave · motif 1-1-2-5-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-6-2)3
cross-octave · motif 1-1-2-6-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-2-8)3
cross-octave · motif 1-1-2-8 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-1-1-5)3
cross-octave · motif 1-1-3-1-1-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-1-2-4)3
cross-octave · motif 1-1-3-1-2-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-1-3-3)3
cross-octave · motif 1-1-3-1-3-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-1-4-2)3
cross-octave · motif 1-1-3-1-4-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-1-6)3
cross-octave · motif 1-1-3-1-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-2-1-4)3
cross-octave · motif 1-1-3-2-1-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-2-2-3)3
cross-octave · motif 1-1-3-2-2-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-2-3-2)3
cross-octave · motif 1-1-3-2-3-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-2-5)3
cross-octave · motif 1-1-3-2-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-3-1-3)3
cross-octave · motif 1-1-3-3-1-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-3-2-2)3
cross-octave · motif 1-1-3-3-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-3-4)3
cross-octave · motif 1-1-3-3-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-4-1-2)3
cross-octave · motif 1-1-3-4-1-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-4-3)3
cross-octave · motif 1-1-3-4-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-5-2)3
cross-octave · motif 1-1-3-5-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-3-7)3
cross-octave · motif 1-1-3-7 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-1-2-3)3
cross-octave · motif 1-1-4-1-2-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-1-3-2)3
cross-octave · motif 1-1-4-1-3-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-1-5)3
cross-octave · motif 1-1-4-1-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-2-1-3)3
cross-octave · motif 1-1-4-2-1-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-2-2-2)3
cross-octave · motif 1-1-4-2-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-2-4)3
cross-octave · motif 1-1-4-2-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-3-1-2)3
cross-octave · motif 1-1-4-3-1-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-3-3)3
cross-octave · motif 1-1-4-3-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-4-2)3
cross-octave · motif 1-1-4-4-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-4-6)3
cross-octave · motif 1-1-4-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-5-1-2-2)3
cross-octave · motif 1-1-5-1-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-5-1-4)3
cross-octave · motif 1-1-5-1-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-5-2-1-2)3
cross-octave · motif 1-1-5-2-1-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-5-2-3)3
cross-octave · motif 1-1-5-2-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-5-3-2)3
cross-octave · motif 1-1-5-3-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-5-5)3
cross-octave · motif 1-1-5-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-6-1-3)3
cross-octave · motif 1-1-6-1-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-6-2-2)3
cross-octave · motif 1-1-6-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-6-4)3
cross-octave · motif 1-1-6-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-7-1-2)3
cross-octave · motif 1-1-7-1-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-7-3)3
cross-octave · motif 1-1-7-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-1-8-2)3
cross-octave · motif 1-1-8-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-11)3
cross-octave · motif 1-11 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2)3
cross-octave · motif 1-2 · oct 1-3 · rep 4-12
unlabeled
Cross-Octave Family (1-2-1-2-1-5)3
cross-octave · motif 1-2-1-2-1-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-2-2-4)3
cross-octave · motif 1-2-1-2-2-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-2-3-3)3
cross-octave · motif 1-2-1-2-3-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-2-4-2)3
cross-octave · motif 1-2-1-2-4-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-2-6)3
cross-octave · motif 1-2-1-2-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-3-1-4)3
cross-octave · motif 1-2-1-3-1-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-3-2-3)3
cross-octave · motif 1-2-1-3-2-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-3-3-2)3
cross-octave · motif 1-2-1-3-3-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-3-5)3
cross-octave · motif 1-2-1-3-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-4-1-3)3
cross-octave · motif 1-2-1-4-1-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-4-2-2)3
cross-octave · motif 1-2-1-4-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-4-4)3
cross-octave · motif 1-2-1-4-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-5-3)3
cross-octave · motif 1-2-1-5-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-6-2)3
cross-octave · motif 1-2-1-6-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-1-8)3
cross-octave · motif 1-2-1-8 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-1-2-4)3
cross-octave · motif 1-2-2-1-2-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-1-3-3)3
cross-octave · motif 1-2-2-1-3-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-1-4-2)3
cross-octave · motif 1-2-2-1-4-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-1-6)3
cross-octave · motif 1-2-2-1-6 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-2-1-4)3
cross-octave · motif 1-2-2-2-1-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-2-2-3)3
cross-octave · motif 1-2-2-2-2-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-2-3-2)3
cross-octave · motif 1-2-2-2-3-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-2-5)3
cross-octave · motif 1-2-2-2-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-3-1-3)3
cross-octave · motif 1-2-2-3-1-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-3-2-2)3
cross-octave · motif 1-2-2-3-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-3-4)3
cross-octave · motif 1-2-2-3-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-4-3)3
cross-octave · motif 1-2-2-4-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-5-2)3
cross-octave · motif 1-2-2-5-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-2-7)3
cross-octave · motif 1-2-2-7 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-3-1-3-2)3
cross-octave · motif 1-2-3-1-3-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-3-1-5)3
cross-octave · motif 1-2-3-1-5 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-3-2-1-3)3
cross-octave · motif 1-2-3-2-1-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-3-2-2-2)3
cross-octave · motif 1-2-3-2-2-2 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-3-2-4)3
cross-octave · motif 1-2-3-2-4 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-3-3-3)3
cross-octave · motif 1-2-3-3-3 · oct 2-4 · rep 2-4
unlabeled
Cross-Octave Family (1-2-3-4-2)3
cross-octave · motif 1-2-3-4-2 · oct 2-4 · rep 2-4
unlabeled

Cross-Octave Family (1-2)

formula-family:motif:1-2
Kind
cross-octave
Canonical motif
1-2
Formula count
3
operation profile: none

Novelty Labeling

Mark this family as novel/promising/known and store notes for downstream model training.

novel
0
promising
0
known
0
duplicate
0
unresolved
0

Member Formulas (3/3)

(H W)x4
formula:1-2x4@12 · span 12 semitones · LT 3
motif 2 · repeat 4 · card 8
(H W)x8
formula:1-2x8@24 · span 24 semitones · LT 3
motif 2 · repeat 8 · card 8
(H W)x12
formula:1-2x12@36 · span 36 semitones · LT 3
motif 2 · repeat 12 · card 8

Family Relation Context

formula-family:motif:1 → formula-family:motif:1-2
extends · weight 0.25
formula-family:motif:1-1-2 → formula-family:motif:1-2
contracts · weight 0.25
formula-family:motif:1-2 → formula:1-2x12@36
contains · weight 1.00 · formula formula:1-2x12@36
formula-family:motif:1-2 → formula:1-2x4@12
contains · weight 1.00 · formula formula:1-2x4@12
formula-family:motif:1-2 → formula:1-2x8@24
contains · weight 1.00 · formula formula:1-2x8@24
formula-family:motif:1-2 → formula-family:motif:1
contracts · weight 0.25
formula-family:motif:1-2 → formula-family:motif:2
contracts · weight 0.25
formula-family:motif:1-2 → formula-family:motif:1-1-2
extends · weight 0.25
formula-family:motif:1-2 → formula-family:motif:1-2-3
extends · weight 0.50
formula-family:motif:1-2-3 → formula-family:motif:1-2
contracts · weight 0.50
formula-family:motif:1-2-6 → formula-family:motif:1-2
contracts · weight 0.25
formula-family:motif:1-2-9 → formula-family:motif:1-2
contracts · weight 0.25
formula-family:motif:1-3-2 → formula-family:motif:1-2
contracts · weight 0.50
formula-family:motif:1-6-2 → formula-family:motif:1-2
contracts · weight 0.25
formula-family:motif:1-9-2 → formula-family:motif:1-2
contracts · weight 0.25
formula-family:motif:2 → formula-family:motif:1-2
extends · weight 0.25
formula-family:trajectory:0001 → formula-family:motif:1-2
overlaps · weight 0.17
formula-family:trajectory:0005 → formula-family:motif:1-2
overlaps · weight 0.00
formula-family:trajectory:0015 → formula-family:motif:1-2
overlaps · weight 0.33