Triangular Maps

The array returned by load_file() contains the triangular map of pitch-class distributions. To use NumPy’s efficient linear storage, it is flattened by starting at the top and then going row by row, thus, it contains a total number of n(n+1)/2 pitch-class distributions.

from musicflower.loader import load_file
resolution = 10
scape = load_file(data='Prelude_No._1_BWV_846_in_C_Major.mxl', n=resolution)
print(scape.shape)
print(resolution * (resolution + 1) / 2)

Out:

(55, 12)
55.0

To handle this kind of flattened triangular maps, the TMap class from the TriangularMap package can be used. It takes a linear storage and allows for efficiently accessing its content as if it was a triangular map (see the TriangularMap documentation for more details). For multidimensional arrays, the first dimension is assumed to represent the triangular map.

from triangularmap import TMap
import numpy as np
tmap = TMap(np.arange(6))
print(tmap.pretty())

Out:

     ╱╲
    ╱ 0╲
   ╱╲  ╱╲
  ╱ 1╲╱ 2╲
 ╱╲  ╱╲  ╱╲
╱ 3╲╱ 4╲╱ 5╲

The functionalities include slicing at a specific level/depth (this returns views of the underlying storage)

print(tmap.dslice(0))  # depth starts a 0 from the top
print(tmap.lslice(1))  # levels start at 1 from the bottom

Out:

[0]
[3 4 5]

and slicing “skewed columns” for a specific start/end index (this returns copies of the underlying storage, note the different syntax using square brackets), which always run left-to-right (i.e. bottom-up for start-slices, top-down for end-slices)

print(tmap.sslice[0])  # start indices run from 0 to n - 1
print(tmap.eslice[3])  # end indices run from 1 to n

Out:

[3 1 0]
[0 2 5]