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278 lines
11 KiB
Python
278 lines
11 KiB
Python
#!/usr/bin/env python
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# coding: utf-8
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# In[1]:
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from itertools import chain, combinations, permutations, product
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from math import prod, log
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from copy import deepcopy
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import networkx as nx
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from fractions import Fraction
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import json
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from operator import add
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def hs_array_to_fr(hs_array):
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return prod([pow(dims[d], hs_array[d]) for d in range(len(dims))])
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def hs_array_to_cents(hs_array):
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return (1200 * log(hs_array_to_fr(hs_array), 2))
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def expand_pitch(hs_array):
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expanded_pitch = list(hs_array)
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frequency_ratio = hs_array_to_fr(hs_array)
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if frequency_ratio < 1:
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while frequency_ratio < 1:
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frequency_ratio *= 2
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expanded_pitch[0] += 1
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elif frequency_ratio >= 2:
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while frequency_ratio >= 2:
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frequency_ratio *= 1/2
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expanded_pitch[0] += -1
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return tuple(expanded_pitch)
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def expand_chord(chord):
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return tuple(expand_pitch(p) for p in chord)
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def collapse_pitch(hs_array):
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collapsed_pitch = list(hs_array)
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collapsed_pitch[0] = 0
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return tuple(collapsed_pitch)
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def collapse_chord(chord):
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return tuple(collapse_pitch(p) for p in chord)
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def transpose_pitch(pitch, trans):
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return tuple(map(add, pitch, trans))
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def transpose_chord(chord, trans):
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return tuple(transpose_pitch(p, trans) for p in chord)
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def cent_difference(hs_array1, hs_array2):
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return hs_array_to_cents(hs_array2) - hs_array_to_cents(hs_array1)
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def pitch_difference(hs_array1, hs_array2):
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return transpose_pitch(hs_array1, [p * -1 for p in hs_array2])
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# this is modified for different chord sizes like original version
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def grow_chords(chord, root, min_chord_size, max_chord_size):
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#this could use the tranpose_pitch function
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branches = [branch for alt in [-1, 1] for d in range(1, len(root)) if (branch:=(*(r:=root)[:d], r[d] + alt, *r[(d + 1):])) not in chord]
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subsets = chain.from_iterable(combinations(branches, r) for r in range(1, max_chord_size - len(chord) + 1))
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for subset in subsets:
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extended_chord = chord + subset
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if(len(extended_chord) < max_chord_size):
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for branch in subset:
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yield from grow_chords(extended_chord, branch, min_chord_size, max_chord_size)
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if(len(extended_chord) >= min_chord_size):
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yield tuple(sorted(extended_chord, key=hs_array_to_fr))
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def chords(chord, root, min_chord_size, max_chord_size):
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# this will filter out the 4x dups of paths that are loops, there might be a faster way to test this
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return set(grow_chords(chord, root, min_chord_size, max_chord_size))
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# this is very slow, I have an idea in mind that my be faster by simply growing the chords to max_chord_size + max_sim_diff
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# technically at that point you have generated both chords and can get the second chord from the first
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def edges(chords, min_symdiff, max_symdiff, max_chord_size):
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def reverse_movements(movements):
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return {value['destination']:{'destination':key, 'cent_difference':value['cent_difference']} for key, value in movements.items()}
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def is_directly_tunable(intersection, diff):
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# this only works for now when intersection if one element - need to fix that
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return max([sum(abs(p) for p in collapse_pitch(pitch_difference(d, list(intersection)[0]))) for d in diff]) == 1
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for combination in combinations(chords, 2):
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[expanded_base, expanded_comp] = [expand_chord(chord) for chord in combination]
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edges = []
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transpositions = set(pitch_difference(pair[0], pair[1]) for pair in set(product(expanded_base, expanded_comp)))
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for trans in transpositions:
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expanded_comp_transposed = transpose_chord(expanded_comp, trans)
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intersection = set(expanded_base) & set(expanded_comp_transposed)
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symdiff_len = sum([len(chord) - len(intersection) for chord in [expanded_base, expanded_comp_transposed]])
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if (min_symdiff <= symdiff_len <= max_symdiff):
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rev_trans = tuple(t * -1 for t in trans)
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[diff1, diff2] = [list(set(chord) - intersection) for chord in [expanded_base, expanded_comp_transposed]]
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base_map = {val: {'destination':transpose_pitch(val, rev_trans), 'cent_difference': 0} for val in intersection}
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base_map_rev = reverse_movements(base_map)
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maps = []
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diff1 += [None] * (max_chord_size - len(diff1) - len(intersection))
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perms = [list(perm) + [None] * (max_chord_size - len(perm) - len(intersection)) for perm in set(permutations(diff2))]
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for p in perms:
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appended_map = {
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diff1[index]:
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{
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'destination': transpose_pitch(val, rev_trans) if val != None else None,
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'cent_difference': cent_difference(diff1[index], val) if None not in [diff1[index], val] else None
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} for index, val in enumerate(p)}
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yield (tuple(expanded_base), tuple(expanded_comp), {
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'transposition': trans,
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'symmetric_difference': symdiff_len,
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'is_directly_tunable': is_directly_tunable(intersection, diff2),
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'movements': base_map | appended_map
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},)
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yield (tuple(expanded_comp), tuple(expanded_base), {
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'transposition': rev_trans,
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'symmetric_difference': symdiff_len,
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'is_directly_tunable': is_directly_tunable(intersection, diff1),
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'movements': base_map_rev | reverse_movements(appended_map)
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},)
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def graph_from_edges(edges):
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g = nx.MultiDiGraph()
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g.add_edges_from(edges)
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return g
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def generate_graph(chord_set, min_symdiff, max_symdiff, max_chord_size):
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#chord_set = chords(pitch_set, min_chord_size, max_chord_size)
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edge_set = edges(chord_set, min_symdiff, max_symdiff, max_chord_size)
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res_graph = graph_from_edges(edge_set)
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return res_graph
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def display_graph(graph):
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show_graph = nx.Graph(graph)
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pos = nx.draw_spring(show_graph, node_size=5, width=0.1)
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plt.figure(1, figsize=(12,12))
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nx.draw(show_graph, pos, node_size=5, width=0.1)
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plt.show()
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#plt.savefig('compact_sets.png', dpi=150)
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def path_to_chords(path, start_root):
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current_root = start_root
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start_chord = tuple(sorted(path[0][0], key=hs_array_to_fr))
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chords = ((start_chord, start_chord,),)
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for edge in path:
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trans = edge[2]['transposition']
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movements = edge[2]['movements']
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current_root = transpose_pitch(current_root, trans)
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current_ref_chord = chords[-1][0]
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next_ref_chord = tuple(movements[pitch]['destination'] for pitch in current_ref_chord)
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next_transposed_chord = tuple(transpose_pitch(pitch, current_root) for pitch in next_ref_chord)
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chords += ((next_ref_chord, next_transposed_chord,),)
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return tuple(chord[1] for chord in chords)
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def write_chord_sequence(path):
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file = open("seq.txt", "w+")
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content = json.dumps(path)
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content = content.replace("[[[", "[\n\t[[")
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content = content.replace(", [[", ",\n\t[[")
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content = content.replace("]]]", "]]\n]")
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file.write(content)
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file.close()
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# In[2]:
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dims = (2, 3, 5, 7, 11)
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root = (0, 0, 0, 0, 0)
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chord = (root,)
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chord_set = chords(chord, root, 3, 3)
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graph = generate_graph(chord_set, 4, 4, 3)
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# In[7]:
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from random import choice, choices
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def stochastic_hamiltonian(graph):
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def movement_size_weights(edges):
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def max_cent_diff(edge):
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res = max([abs(v) for val in edge[2]['movements'].values() if (v:=val['cent_difference']) is not None])
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return res
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def min_cent_diff(edge):
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res = [abs(v) for val in edge[2]['movements'].values() if (v:=val['cent_difference']) is not None]
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res.remove(0)
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return min(res)
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for e in edges:
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yield 1000 if ((max_cent_diff(e) < 200) and (min_cent_diff(e)) > 50) else 1
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def hamiltonian_weights(edges):
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for e in edges:
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yield 10 if e[1] not in [path_edge[0] for path_edge in path] else 1 / graph.nodes[e[1]]['count']
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def contrary_motion_weights(edges):
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def is_contrary(edge):
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cent_diffs = [v for val in edge[2]['movements'].values() if (v:=val['cent_difference']) is not None]
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cent_diffs.sort()
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return (cent_diffs[0] < 0) and (cent_diffs[1] == 0) and (cent_diffs[2] > 0)
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for e in edges:
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yield 10 if is_contrary(e) else 1
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def is_directly_tunable_weights(edges):
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for e in edges:
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yield 10 if e[2]['is_directly_tunable'] else 0
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def voice_crossing_weights(edges):
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def has_voice_crossing(edge):
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source = list(edge[0])
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ordered_source = sorted(source, key=hs_array_to_fr)
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source_order = [ordered_source.index(p) for p in source]
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destination = [transpose_pitch(edge[2]['movements'][p]['destination'], edge[2]['transposition']) for p in source]
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ordered_destination = sorted(destination, key=hs_array_to_fr)
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destination_order = [ordered_destination.index(p) for p in destination]
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return source_order != destination_order
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for e in edges:
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yield 10 if not has_voice_crossing(e) else 0
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check_graph = graph.copy()
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#next_node = choice(list(graph.nodes()))
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next_node = list(graph.nodes())[0]
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check_graph.remove_node(next_node)
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for node in graph.nodes(data=True):
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node[1]['count'] = 1
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path = []
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while (nx.number_of_nodes(check_graph) > 0) and (len(path) < 5000):
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out_edges = list(graph.out_edges(next_node, data=True))
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#print([l for l in zip(movement_size_weights(out_edges), hamiltonian_weights(out_edges))])
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factors = [
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movement_size_weights(out_edges),
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hamiltonian_weights(out_edges),
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contrary_motion_weights(out_edges),
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is_directly_tunable_weights(out_edges),
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voice_crossing_weights(out_edges)
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]
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weights = [prod(a) for a in zip(*factors)]
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edge = choices(out_edges, weights=weights)[0]
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#edge = random.choice(out_edges)
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next_node = edge[1]
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node[1]['count'] += 1
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path.append(edge)
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if next_node in check_graph.nodes:
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check_graph.remove_node(next_node)
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return path
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path = stochastic_hamiltonian(graph)
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#for edge in path:
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# print(edge)
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write_chord_sequence(path_to_chords(path, root))
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len(path)
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# In[11]:
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get_ipython().run_line_magic('load_ext', 'line_profiler')
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# In[134]:
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chord_set = chords(chord, root, 3, 3)
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# In[136]:
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lprun -f edge_data edges(chord_set, 3, 3, 4)
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