Pitch array notation

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. null for 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:

• music-scale
• music-chord
• music-gamut
• pitch-transpose
• pitch-op

Other libraries using this format:

• tonal

License

MIT License