Concertina PBQP Solver

What is the Anglo concertina?

The Anglo concertina is a fun, portable free-reed instrument with wide repertoire. The most common layout is tuned in C/G, and has 30 bisonoric buttons, meaning that each button plays a different note depending on whether you are the bellows are being pushed or pulled. Since each button is its own voice, a concertina can play full harmonies, i.e. it can accompany itself like an accordion, though the individual notes of chords must be played.

Why is playing new pieces hard?

One of the challenges of playing new pieces on the concertina is that the button layout is quote constraining:

• Many notes are only on one direction of one button.
• A few notes are available in multiple places, sometimes in the same direction, and sometimes in the opposite direction.
• Each button has a natural "home" finger for pressing it. Simultaneously pressing multiple buttons on the same home finger is challenging.
• Quick changes of buttons with the same finger may be ergonomically difficult if the buttons are physically far apart.

PBQP for fingering generation

This project maps the problem of generating a fingering for a particular tune (for a particular concertina layout) onto the PBQP NP-hard problem.

• Nodes in the PBQP graph represent notes in the tune
• Edges represent either simultaneous or sequential note constraints
• Weights encode the physical properties of the concertina layout, both what's physically possible as well as the relative ergonomic cost of particular choices.

Mapping concertina fingering into an NP-hard problem might not seem like a huge win off the bat, but heuristic solvers for PBQP exist that work well in practice. This project reuses the PBQP solver from LLVM, which yields good fingerings in practice.

Status

This project is currently a prototype for me to experiment with the concept, and to generate fingerings for my own use. The tune to be generated currently has to be encoded directly in to the C++ source code.

Future Enhancements

• Support tune input from ABC or other formats
• Support tune output to... something
• Represent tunes as intervals rather than notes, enabling the solver to solve for the most playable key on a given concertina layout.
• More convenient representation of typical chord vamps. They're currently a pain to encode by hand.
• Model the choice of when to play partial/inverted chords to improve fingering convenience.