Pitch array notation
October 19, 2015 · View on GitHub
pitch-array is a format to represent music pitches and intervals in a simple and unified way. The aim of this project is to create an exchangeable pitch and interval format and allow music libraries to work regardless of the string representations and with no need to parse.
Features
- Works equally for pitches and intervals
- It allows to represent tonal pitch classes (pitch without octaves)
- All numeric values, no need to parse
- Easy to understand for computers and humans
Format description
The pitch-array is an array of 3 integers with the form [num, alteration, octave] with the following characteristics:
- num: must be a integer between 0 and 6. If the number is negative will be converted to positive (-1 is 6, -2 is 5, ...). Values greater than 6 will be mod to 6 (7 and 0 is the same value). Required.
- alteration: any integer. 0 means no alteration, negative numbers are for flats and positive for sharps. In theory there's no value limit, but most of the parsers set the aceptable values from -4 to +4. Required.
- octave: a integer to represent the octave. In pitches it's just the octave, but with intervals a negative octave means descendent interval. Optional, can be
null.nullfor pitches is used to represent pitch classes (pitch without octaves). For intervals, 0 and null are same value.
Encoding pitches
The way to represent pitches is quite straight forward. Some self-explanatory examples:
| Note in scientific notation | pitch-array notation |
|---|---|
| C2 | [0, 0, 2] |
| C#4 | [0, 1, 4] |
| Db4 | [1, -1, 4] |
| D4 | [1, 0, 4] |
| E5 | [2, 0, 5] |
| F#5 | [3, 1, 4] |
| G###5 | [4, 3, 4] |
| Bbbbb3 | [6, -4, 3] |
| ... | ... |
Pitch array description
The a-pitch array [num, alteration, octave] when representing pitches:
| Index | Name | Meaning | Possible values |
|---|---|---|---|
| 0 | num | The letter of the pitch with 0-based index | 0=C, 1=D, 2=E, ... 6=B |
| 1 | alteration | The accidentals of the pitch | In theory any integer, in practice a value between -4 and +4 ..., -2='bb', -1='b', 0='', 1='#', 2='##', ... |
| 2 | octave | the octave number | In theory any integer, in practice a value between 0 and 8. Can be null |
Pitch class
Pitch classes (pitches without octaves) can be expressed by setting the octave to null
| Pitch class | pitch-array notation |
|---|---|
| C | [0, 0, null] |
| Db | [1, -1, null] |
| ... | ... |
Encoding intervals
Any interval can be represented with an pitch-array array almost the same way that pitches (in fact they have a direct equivalence) but there are some semantic differences. Here are some examples:
| Interval | pitch-array notation |
|---|---|
| Perfect unison (1P) | [0, 0, 0] |
| Augmented unison (1A) | [0, 1, 0] |
| Major second (2M) | [1, 0, 0] |
| Augmented second (2A) | [1, 1, 0] |
| Minor second (2m) | [1, -1, 0] |
| Major ninth (9M) | [1, 0, 1] |
| Descending major second | [6, -1, -1] |
Interval array description
The a-pitch array [num, alteration, octave] when representing intervals:
| Index | Name | Meaning | Possible values |
|---|---|---|---|
| 0 | num | The simplified interval number using a 0-based index | 0=unison, 1=second, ... 6=seventh |
| 1 | alteration | The alteration of the interval compared to the natural form | 0=perfect or major. |
| 2 | octave | the number of octaves the interval spawns | 0 means simple intervals. > 0 means compound intervals. < 0 means descending intervals |
Descending intervals
The first number of the pitch-array array must be always positive so descending intervals are encoded by inverting the interval and lowering an octave. For example, a descending major second is encoded as ascending minor seventh with an octave down: descending major second [-2, 1, 0], inverted [6, -1, 0] with an octave lower [6, -1, -1]
In fact, all descending intervals has an octave < 0
Pitch-interval equivalence
Any pitch-array value can represent indistinctly pitches or intervals. Here is the equivalence:
pitch-array | Pitch | Interval |
|---|---|---|
| [0, 0, 0] | C0 | 1P (perfect unison) |
| [1, 0, 0] | D0 | 2M (major second) |
| [4, -1, 0] | Gb0 | 4d (diminished fourth) |
| ... | ... | .... |
Libraries
Convert to string to a-pitch:
- pitch-parser: convert from pitch scientific notation to a-pitch (and the opposite)
- interval-parser: convert from interval strings to a-pitch (and the opposite)
Working with music elements:
Other libraries using this format:
License
MIT License