# Harmonex
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This is a collection of tools for music theory called _Harmonex_ (pronounced
“harmonics”).
**See what’s changed lately by reading [the project history][project-history].**
## Usage
What can you do with Harmonex? Its functions can answer textbook music theory
questions such as:
* [x] **Are C♯ and D♭ enharmonically equivalent pitches?**
_Answer:_ `Harmonex.Pitch.enharmonic?(:c_sharp, :d_flat) == true`
* [x] **What are the enharmonic equivalents of F𝄪?**
_Answer:_
`Harmonex.Pitch.enharmonics(:f_double_sharp) == [:g_natural, :a_double_flat]`
* [x] **How far apart, in semitones, are the pitches A♭ and D♯?**
_Answer:_ `Harmonex.Pitch.semitones(:a_flat, :d_sharp) == 7`
* [x] **What is the interval between the pitches F♮ and B𝄫?**
_Answer:_
`Harmonex.Pitch.interval(:f, :b_double_flat) == %Harmonex.Interval{quality:
:diminished, size: 4}`
_Answer:_
`Harmonex.Interval.between_pitches(:f, :b_double_flat) ==
%Harmonex.Interval{quality: :diminished, size: 4}`
* [ ] **What is the key signature of G harmonic minor?**
_Answer: two flats, one sharp — B♭, E♭, and F♯._
* [ ] **What keys and modes have the signature of three sharps?**
_Answer: A major/Ionian, B Dorian, C♯ Phrygian, D Lydian, E Mixolydian, F♯
minor/Aeolian, and G♯ Locrian._
* [ ] **Does A♮ occur diatonically in the key of E♭ minor?**
_Answer: no._
* [ ] **What are the pitches of the simplest voicing of a D♭ minor triad in
second inversion?**
_Answer: A♭, D♭, and F♭._
* [ ] **What is the name and inversion of the chord described by the pitches C♮,
F♯, and A♮?**
_Answer: F♯ diminished triad in second inversion._
**of the chord described by A♭, C, and F♯?**
_Answer: A♭ Italian sixth._
**of the chord described by B, D♯, E, and G♯?**
_Answer: E major seventh in second inversion._
* [ ] **What are the jazz chart symbols of the chords just mentioned?**
_Answer: F<sup>O</sup>/A♭, A♭<sup>7(no 5)</sup>, and E<sup>△7</sup>/B._
* [ ] **What is the functional-harmonic symbol of the chord described by the
pitches C♮, F♯, and A♮ in C major?**
_Answer: vii<sup>O</sup>/V._
**of the chord described by A♭, C, and F♯ in C minor?**
_Answer: It<sup>6</sup>._
**of the chord described by B, D♯, E, and G♯ in E major?**
_Answer: I<sup>7</sup>._
Harmonex also will have functions for exploring compositional questions such as:
* [ ] **What is the set of triads and seventh chords, including enharmonic
equivalents of same, that the keys of B Mixolydian and D Lydian have in
common?**
* [ ] **What is the set of seventh chords, including enharmonic equivalents, that
are within one degree of difference (by shifting one note by a half or whole
step) from an F major seventh chord?** **within two degrees?** **three?**
**four?**
* [ ] **What are sets of three-chord changes for modulating from the key of D
minor to F♯ major?** **sets of four-chord changes?** **sets of five-chord
changes?**
## Installation
Install [the Hex package][Hex-release] by adding `:harmonex` to the list of
dependencies in your project’s _mix.exs_ file:
```elixir
# mix.exs
# ...
def deps do
[{:harmonex, "~> 0.4.0"}]
end
# ...
```
## Contributing
To submit a patch to the project:
1. [Fork][fork-project] the official repository.
2. Create your feature branch: `git checkout -b my-new-feature`.
3. Commit your changes: `git commit -am 'Add some feature'`.
4. Push to the branch: `git push origin my-new-feature`.
5. [Create][compare-project-branches] a new pull request.
After cloning the repository, `mix deps.get` to install dependencies. Then
`mix test` to run the tests. You can also `iex` to get an interactive prompt that
will allow you to experiment. To build this package, `mix hex.build`.
To release a new version:
1. Update [the project history in _History.md_][project-history], and then
commit.
2. Update the version number in [_mix.exs_][mix-dot-exs-file] respecting
[Semantic Versioning][Semantic-Versioning], update
[the “Installation” section](#installation) of
[this readme][readme-dot-md-file] to reference the new version, and then
commit.
3. Build and publish [the Hex package][Hex-release] with `mix hex.publish`.
4. Tag with a name like `vMAJOR.MINOR.PATCH` corresponding to the new version,
and then push commits and tags.
## License
Released under the [MIT License][MIT-License].
[Travis-CI-build-status]: http://travis-ci.org/njonsson/harmonex "Travis CI build status for ‘Harmonex’"
[HexFaktor-deps-status]: https://beta.hexfaktor.org/github/njonsson/harmonex "HexFaktor dependencies status for ‘Harmonex’"
[Coveralls-test-coverage-status]: https://coveralls.io/r/njonsson/harmonex?branch=master "Coveralls test coverage status"
[Hex-release]: https://hex.pm/packages/harmonex "Hex release of ‘Harmonex’"
[project-history]: https://github.com/njonsson/harmonex/blob/master/History.md "‘Harmonex’ project history"
[fork-project]: https://github.com/njonsson/harmonex/fork "Fork the official repository of ‘Harmonex’"
[compare-project-branches]: https://github.com/njonsson/harmonex/compare "Compare branches of ‘Harmonex’ repositories"
[mix-dot-exs-file]: https://github.com/njonsson/harmonex/blob/master/mix.exs "‘Harmonex’ project ‘mix.exs’ file"
[Semantic-Versioning]: http://semver.org/
[readme-dot-md-file]: https://github.com/njonsson/harmonex/blob/master/README.md#installation "‘Harmonex’ project ‘README.md’ file"
[MIT-License]: http://github.com/njonsson/harmonex/blob/master/License.md "MIT License claim for ‘Harmonex’"
