Bowing, Computed

A slur group is a partition: the notes inside one group are taken in a single stroke, and the bow reverses at every boundary. That is the whole model, and everything a bowing page needs falls out of it.

Bowing looks like an art and behaves like arithmetic. A slur group is a partition of a note sequence: the notes inside a group are taken in one stroke and the bow reverses at every boundary. Declare the group lengths and everything else — the directions, where the strokes start, where the accents land — is derived.

The three patterns

Bowing patterns over eight notes — partitions and directions, derived
PatternGroup cycleStrokes per 8 notesDirections
The shuffle2–1–16D U D U D U
Slur groups24D U D U
String crossing18D U D U D U D U
The ShuffleLong-short-short — the groove that turns a tempo into a dance.Pattern 1 of 3 Slur GroupsTwo notes to a stroke — the fastest way to hear what a bow change costs.Pattern 2 of 3 String CrossingOne note per stroke, the arm changing plane — clean or lumpy is decided here.Pattern 3 of 3

Why a partition

Because it is checkable. A bowing that overlapped would ask the bow to be in two places at once, and one with a gap would leave a note unbowed. CI recomputes every partition from the declared cycle and asserts it covers the sequence exactly — no overlap, no gap — and that the directions alternate across every boundary.

Crossings are a physical fact

A bow leans between two NEIGHBOURING strings. On this instrument that means G–D, D–A, A–E and nothing else, derived from the registry's true open pitches. Any crossing published here is checked against that list.

The left hand's half of all this is the positions; the two together are what a tune map actually is.