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A microtonal geography of the cello fingerboard

Home Page: https://mbarbin.github.io/fingerboard/

License: GNU Affero General Public License v3.0

Makefile 0.03% OCaml 99.94% Shell 0.04%
cello intonation scales temperaments double-stops

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fingerboard's Issues

Invalid sixths double-stops more than 1 string apart

As shown by systems/cello/e12/sixths.ml, there's a bug in the generation of double-stops that results in double stops played on strings IV-II:

┌─────┬────────┬───────┬───────┬──────┬────────┬───────┬───────┬──────────────┬───────┐
│ Low │ String │ Pos   │ Cents │ High │ String │ Pos   │ Cents │ Interval     │ Cents │
├─────┼────────┼───────┼───────┼──────┼────────┼───────┼───────┼──────────────┼───────┤
│ F2  │ IV     │ 4e    │ 500   │ D3   │ II     │ 0     │ 0     │ M6 - 9-12edo │ 900   │
└─────┴────────┴───────┴───────┴──────┴────────┴───────┴───────┴──────────────┴───────┘

In this specific example, the higher D is meant to be played on string III. This bug is visible in a few other lines in files sixths.ml, also in other systems.

Adjust degree IV in C major just edo 53 scale in third

As seen in systems/cello/e53/thirds.ml, the interval of the minor third shown below is 13-53edo. I intend for it to be adjusted to 14-53edo like the rest of the minor thirds in this table. This would be by making use of one of the Zarlinean combination with the changing degree on the F (degree IV) : specifically by adjusting the F3 to m3z-e53.

┌─────┬────────┬───────────┬───────┬──────┬────────┬───────────┬───────┬───────────────┬───────┐
│ Low │ String │ Pos       │ Cents │ High │ String │ Pos       │ Cents │ Interval      │ Cents │    
├─────┼────────┼───────────┼───────┼──────┼────────┼───────────┼───────┼───────────────┼───────┤
│ D3  │ III    │ 5p-e53    │ 702   │ F3   │ II     │ m3p-e53   │ 294   │ m3 - 13-53edo │ 294   │
└─────┴────────┴───────────┴───────┴──────┴────────┴───────────┴───────┴───────────────┴───────┘

I haven't determined yet whether to do this systematically as part of the scale constructor, or whether this should be overridden manually. I need to spend some time thinking about whether there exists a principal criteria that would lead to that particular choice for the changing degree. I intuitively suspect that such criteria exists.

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