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mbarbin committed Sep 29, 2024
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This project is meant to help me reason about and build a "microtonal geography
of the cello fingerboard".
This project is meant to help me reason about and build a "microtonal geography of the cello fingerboard".

## What's in the repo?

The repo implements the tools necessary to model microtonal geography systems
based on various scales. As we go over some specific pythagorean, just and
tempered scales and double stops, some specific notations are introduced for
each of the fingerboard locations required to play each note. Then, we can
reason about and exhibit various facts involving these positions, while being
able to verify these facts programmatically, and display them with various
format.
The repo implements the tools necessary to model microtonal geography systems based on various scales. As we go over some specific pythagorean, just and tempered scales and double stops, some specific notations are introduced for each of the fingerboard locations required to play each note. Then, we can reason about and exhibit various facts involving these positions, while being able to verify these facts programmatically, and display them with various format.

An example extracted from file [systems/cello/just/scales.ml](systems/cello/just/scales.ml)
displaying the names of the positions involved in playing the E Major
Just Scale on a cello tuned in perfect fifth:
An example extracted from file [systems/cello/just/scales.ml](systems/cello/just/scales.ml) displaying the names of the positions involved in playing the E Major Just Scale on a cello tuned in perfect fifth:

```scheme
((IV ((E2 M3p) (F#2 A4p)))
Expand All @@ -30,11 +21,7 @@ Just Scale on a cello tuned in perfect fifth:
(A5 0-2) (B5 M2p-2) (C#6 M3z-2) (D#6 A4z-2) (E6 5p-2))))
```

Another example from file [systems/cello/e53/scales.ml](systems/cello/e53/scales.ml) explores the
difference between the scales of D Flat Major Pythagorean and its Just
counterpart, approximated in a [53
edo](https://en.wikipedia.org/wiki/53_equal_temperament) system mapped
onto the cello fingerboard.
Another example from file [systems/cello/e53/scales.ml](systems/cello/e53/scales.ml) explores the difference between the scales of D Flat Major Pythagorean and its Just counterpart, approximated in a [53 edo](https://en.wikipedia.org/wiki/53_equal_temperament) system mapped onto the cello fingerboard.

D Flat Major Pythagorean in a 53 edo system:
```scheme
Expand Down Expand Up @@ -62,9 +49,7 @@ D Flat Major Just in the same 53 edo system:
(F6 m6p-e53-2))))
```

Example of positions and intervals in the E flat Major double stops
scale in thirds from
[systems/cello/just/thirds.ml](systems/cello/just/thirds.ml):
Example of positions and intervals in the E flat Major double stops scale in thirds from [systems/cello/just/thirds.ml](systems/cello/just/thirds.ml):
```
┌─────┬────────┬───────┬───────┬──────┬────────┬───────┬───────┬──────────────────┬───────┐
│ Low │ String │ Pos │ Cents │ High │ String │ Pos │ Cents │ Interval │ Cents │
Expand Down Expand Up @@ -100,5 +85,4 @@ scale in thirds from

## Code Documentation

The code documentation of the latest release is built with `odoc` and published
to `GitHub` pages [here](https://mbarbin.github.io/fingerboard).
The code documentation of the latest release is built with `odoc` and published to `GitHub` pages [here](https://mbarbin.github.io/fingerboard).

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