Add README (#10)

Author: dpsanders

README.md

@@ -1,3 +1,73 @@
-# MusicTheory
+# MusicTheory.jl
 
 [![Build Status](https://github.com/dpsanders/MusicTheory.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/dpsanders/MusicTheory.jl/actions/workflows/CI.yml?query=branch%3Amain)
+
+A Julia package for the basics of ("Western") music theory.
+(Currently) everything is based on semitones.
+
+## Contents
+- Pitches with scientific notation, e.g. C4 for middle C
+- Intervals
+- Scales
+- Chords
+- Notes and rests with durations
+
+## Pitches
+Pitch names are exported in the `MusicTheory.PitchNames` submodule.
+
+Specifying just the name of a pitch gives a `PitchClass`, representing all notes of that
+pitch, e.g.
+```
+julia> C♯
+C♯
+
+julia> typeof(C♯)
+PitchClass
+```
+
+Indexing gives a pitch with a specific octave, e.g.
+```
+julia> C♯[4]
+C♯₄
+```
+
+## Intervals
+The `Interval` type computes the interval between two pitches:
+```
+julia> Interval(C[4], E[4])
+Major 3rd
+```
+
+## Scales
+General scales are supported; they are specified as a sequence of intervals dividing up an
+octave, e.g.
+```
+julia> show(major_scale)
+Interval[Major 2nd, Major 2nd, Minor 2nd, Major 2nd, Major 2nd, Major 2nd, Minor 2nd]
+```
+
+The `Scale` type is a standard Julia iterator over the scale:
+```
+julia> scale = Scale(C[4], major_scale)
+Scale{Pitch}(C₄, Dict{PitchClass, Interval}(C => Major 2nd, E => Minor 2nd, B => Minor 2nd, F => Major 2nd, D => Major 2nd, G => Major 2nd, A => Major 2nd))
+
+julia> scale_tones = Base.Iterators.take(scale, 8) |> collect;
+
+julia> show(scale_tones)
+Pitch[C₄, D₄, E₄, F₄, G₄, A₄, B₄, C₅]
+```
+
+## Notes
+Notes have a pitch and a duration, which is a rational number, e.g. `1 // 4` for a
+quarter note (crotchet). Rests are specified using `rest`, e.g.
+```
+julia> notes = [C[5] / 4, rest / 8, D[5] / 8]
+3-element Vector{Note}:
+ Note(C₅, 1//4)
+ Note(MusicTheory.Rest(), 1//8)
+ Note(D₅, 1//8)
+```
+
+## Author
+
+Copyright David P. Sanders, 2024