Basic objects¶

Note

Apart from the scales module discussed in Quickstart, mscales also contains the basic module. At the moment, they are alternatives with partially overlapping functionalities but they will be merged in the futured.

As a rule of thumb, use the scales module whenever possible and only revert to basic when you need very specific things.

The basic module implements classic definitions of and transformations on pitch-class sets known from Set Theory.

Pitch classes¶

The fundamental objects of set theory are pitch classes. Pitch classes incorporate two fundamental assumptions about how pitches relate to one another:

Octave equivalence: pitches that are related by (multiples of) octaves are considered equivalent.
Enharmonic equivalence: pitches that are mapped to the same key on a piano (irrespective of the octave) are considered equivalent.

In mscales, pitch classes are instantiated by passing an integer to the PitchClass class:

>>> from mscales import PitchClass
>>> p = PitchClass(3) # E-flat

For now, this is the only instantiation method. One can see that PitchClass instances incorporate enharmonic equivalence:

>>> PitchClass(3) == PitchClass(15)
True

Pitch-class intervals¶

Pitch classes can be transposed by adding a PitchClassInterval:

>>> from mscales import PitchClassInterval
>>> i = PitchClassInterval(7) # perfect fifth
>>> p + i
PitchClass(10)

Intervals are here understood as ascending. For descending intervals, we can either initialize it with PitchClassInterval(-j) for some integer j, or simply subtract an ascending interval from a pitch class:

>>> p - i
PitchClass(5)

Pitch-class sets¶

Pitch-class sets (from now on pcsets) can be instantiated as follows:

>>> from mscales import PitchClassSet
>>> s = PitchClassSet({0,4,1,6})
[0  4  1  6]

We can also look at the vector representation of a pitch-class set:

>>> v = s.to_vector()
>>> v
array([1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0])

The PitchClassSet class has lots of transformations implemented, and their results are stored in the .info() method.

>>> s.info()
"""
 ========================
 PitchClassSet([0 1 4 6])
 ========================

 Set Theory
 ==========
 cardin. (d, c)  : 4 12
 pc vector       : [1 1 0 0 1 0 1 0 0 0 0 0]
 complement      : [ 2  3  5  7  8  9 10 11]
 transposed      : [2 3 6 8]
 inverted        : [ 0 11  8  6]
 T2I             : [ 2  1 10  8]
 normal form     : [0 1 4 6]
 prime form      : [0 1 7 9]
 interval vector : [1 1 1 1 1 1]

 Serialism
 =========
 original        : [0 1 4 6]
 retrograde      : [6 4 1 0]
 inversion       : [ 0 11  8  6]
 retro.-inv.     : [ 6  8 11  0]
 matrix          : [[ 0  1  4  6]
                 [11  0  3  5]
                 [ 8  9  0  2]
                 [ 6  7 10  0]]
 """

API

All methods currently implemented are: