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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"id": "41af0ca5-e67c-405f-9a31-cf49a073b0e3",
"metadata": {},
"outputs": [],
"source": [
"import itertools as it\n",
"import networkx as nx\n",
"from collections import Counter\n",
"import copy\n",
"import matplotlib.pyplot as plt\n",
"import random\n",
"from fractions import Fraction\n",
"import math\n",
"\n",
"def collapse(fraction):\n",
" if fraction < 1:\n",
" while fraction < 1:\n",
" fraction *= Fraction(2, 1)\n",
" elif fraction >= 2:\n",
" while fraction >= 2:\n",
" fraction *= Fraction(1, 2)\n",
" return fraction\n",
"\n",
"def hsPointToFR(point):\n",
" fraction = Fraction(1, 1)\n",
" for dim in point:\n",
" if dim > 0:\n",
" fraction = fraction * dim\n",
" else:\n",
" fraction = fraction * 1/abs(dim)\n",
" return fraction\n",
" \n",
"def pitches(iterable, r):\n",
" for base in it.combinations_with_replacement(iterable, r - 1):\n",
" split = tuple(list(g) for k, g in it.groupby(tuple(b for b in base if b != 1)))\n",
" mults = list(it.product([-1, 1], repeat = len(split)))\n",
" for mult in mults:\n",
" yield tuple(it.chain(*[[val * mult[idx] for val in g] for idx, g in enumerate(split)]))\n",
"\n",
"def expandPitch(pitch):\n",
" num = 1;\n",
" den = 1;\n",
" expandedPitch = list(pitch)\n",
" for dim in pitch:\n",
" if dim > 0:\n",
" num *= dim\n",
" else:\n",
" den *= abs(dim)\n",
" fraction = num/den\n",
" if fraction < 1:\n",
" while fraction < 1:\n",
" fraction *= 2\n",
" expandedPitch = [2] + expandedPitch\n",
" elif fraction >= 2:\n",
" while fraction >= 2:\n",
" fraction *= 1/2\n",
" expandedPitch = [-2] + expandedPitch\n",
" return tuple(expandedPitch)\n",
"\n",
"def expandChord(chord):\n",
" return tuple([expandPitch(p) for p in chord])\n",
"\n",
" \n",
"def transposePitch(pitch, trans):\n",
" transposedPitch = list(pitch)\n",
" for t in trans:\n",
" if (t * -1) in transposedPitch:\n",
" transposedPitch.remove(t * -1)\n",
" else:\n",
" transposedPitch.append(t)\n",
" transposedPitch.sort(key=lambda val: abs(val))\n",
" return transposedPitch\n",
" \n",
"def transposeChord(chord, trans):\n",
" transposedChord = list(chord)\n",
" for pdx, pitch in enumerate(chord):\n",
" transposedPitch = transposePitch(pitch, trans)\n",
" transposedChord[pdx] = tuple(transposedPitch)\n",
" return tuple(transposedChord)\n",
" \n",
"def chords(pitches, r):\n",
" def is_connected(iterable):\n",
" points = comparitors = list(iterable)\n",
" connectedPoints = []\n",
" base = points[0]\n",
" bIdxScroll = 0\n",
" while True:\n",
" for comp in comparitors:\n",
" comps = sorted([base, comp], key=len, reverse=True)\n",
" if ((Counter(comps[0]) - Counter(comps[1])).total() == 1) and (len(comps[0]) - len(comps[1]) == 1):\n",
" comparitors = connectedPoints = connectedPoints + comps\n",
" points.remove(base)\n",
" if comp in points:\n",
" points.remove(comp)\n",
" if(len(points) == 0):\n",
" return True\n",
" else:\n",
" base = points[0]\n",
" bIdxScroll = 0\n",
" break\n",
" else:\n",
" if bIdxScroll < (len(points) - 1):\n",
" bIdxScroll += 1\n",
" base = points[bIdxScroll]\n",
" else:\n",
" return False\n",
" def is_centered(iterable):\n",
" return len(list(iterable)[0]) == 0\n",
" #return filter(is_connected, it.takewhile(is_centered, it.combinations(pitches, r)))\n",
" return {c for c in it.takewhile(is_centered, it.combinations(pitches, r)) if is_connected(c)}\n",
"\n",
"def pitchDifference(frs):\n",
" cents1 = (1200 * math.log(hsPointToFR(frs[0]), 2))\n",
" cents2 = (1200 * math.log(hsPointToFR(frs[1]), 2))\n",
" return abs(cents2 - cents1)\n",
"\n",
"def difference(p1, p2):\n",
" return transposePitch(p1, [p * -1 for p in p2])\n",
" \n",
"def edges(chords): \n",
" def edgeDict(transposition, symDiff):\n",
" dict = {}\n",
" dict['melodic_movement'] = pitchDifference(symDiff)\n",
" dict['transposition'] = transposition\n",
" return dict\n",
" def reverseDict(dict):\n",
" revDict = copy.deepcopy(dict)\n",
" if revDict['transposition'] != ():\n",
" revDict['transposition'] = tuple(t * -1 for t in revDict['transposition'])\n",
" return revDict\n",
" def edgeData(iterable):\n",
" [base, comp] = list(iterable)\n",
" expandedBase = expandChord(base)\n",
" expandedComp = expandChord(comp)\n",
" transpositions = set([tuple(difference(pair[0], pair[1])) for pair in set(it.product(expandedBase, expandedComp))])\n",
" edges = [(expandedBase, expandedComp, edgeDict(t, symDiff)) for t in transpositions if len(symDiff := list(set(expandedBase) ^ set(tChord := transposeChord(expandedComp, t)))) == 2]\n",
" edges = edges + [(e[1], e[0], reverseDict(e[2])) for e in edges]\n",
" if edges != []:\n",
" return edges\n",
" else:\n",
" return None\n",
" return list(it.chain(*[e for c in it.combinations(chords, 2) if (e := edgeData(c)) is not None]))\n",
"\n",
"def graph(edges):\n",
" G = nx.MultiDiGraph()\n",
" G.add_edges_from(edges)\n",
" return G\n",
"\n",
"def hamiltonian(G):\n",
" F = [(G,[list(G.nodes())[0]])]\n",
" n = G.number_of_nodes()\n",
" while F:\n",
" graph,path = F.pop()\n",
" confs = []\n",
" neighbors = (node for node in graph.neighbors(path[-1]) \n",
" if node != path[-1]) #exclude self loops\n",
" for neighbor in neighbors:\n",
" conf_p = path[:]\n",
" conf_p.append(neighbor)\n",
" conf_g = nx.Graph(graph)\n",
" conf_g.remove_node(path[-1])\n",
" confs.append((conf_g,conf_p))\n",
" for g,p in confs:\n",
" if len(p)==n:\n",
" return p\n",
" else:\n",
" F.append((g,p))\n",
" return None\n",
"\n",
"def stochastic_hamiltonian(graph):\n",
" check_graph = graph.copy()\n",
" #next_node = random.choice(list(graph.nodes()))\n",
" next_node = list(graph.nodes())[0]\n",
" check_graph.remove_node(next_node)\n",
" path = [next_node]\n",
" while (nx.number_of_nodes(check_graph) > 0) and (len(path) < 5000):\n",
" neighbors = graph[next_node]\n",
" nd_list = list(graph.degree(list(neighbors)))\n",
" neighbors, weights = zip(*[[n, 1/pow(d, 2) if n not in path else 0.0000001] for n, d in nd_list]) \n",
" next_node = random.choices(neighbors, weights=weights)[0]\n",
" path.append(next_node)\n",
" if next_node in check_graph.nodes:\n",
" check_graph.remove_node(next_node)\n",
" return [path, check_graph]\n",
"\n",
"def stochastic_hamiltonian(graph):\n",
" check_graph = graph.copy()\n",
" #next_node = random.choice(list(graph.nodes()))\n",
" next_node = list(graph.nodes())[0]\n",
" check_graph.remove_node(next_node)\n",
" path = []\n",
" while (nx.number_of_nodes(check_graph) > 0) and (len(path) < 5000):\n",
" outEdges = list(graph.out_edges(next_node, data=True))\n",
" weights = [(1 if e[2]['melodic_movement'] < 200 else 0.001) * (1 if e[1] not in [pE[0] for pE in path] else 0.0000001) for e in outEdges]\n",
" edge = random.choices(outEdges, weights=weights)[0]\n",
" next_node = edge[1]\n",
" path.append(edge)\n",
" if next_node in check_graph.nodes:\n",
" check_graph.remove_node(next_node)\n",
" return path"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "38636490-6b16-4346-8ac9-a9ba02a830c1",
"metadata": {},
"outputs": [],
"source": [
"pSet = pitches([1, 3, 5], 4)\n",
"#print(len(list(pSet)))\n",
"cSet = chords(pSet, 4)\n",
"#print(cSet)\n",
"eSet = edges(cSet)\n",
"#for e in eSet:\n",
"# print(e)\n",
"testGraph = graph(eSet)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "cc1fc93b-a737-42f9-9ab1-f123bda58dde",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"76"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(testGraph.nodes)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "f3a85a37-6c81-4d99-9d4e-7435b7e47b4e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1770"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(testGraph.edges)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9f2b39bf-fad3-474f-8bbe-f2decff5d91b",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sGraph = nx.Graph(testGraph)\n",
"pos = nx.draw_spring(sGraph, node_size=5, width=0.1)\n",
"\n",
"# larger figure size\n",
"plt.figure(1, figsize=(12,12)) \n",
"nx.draw(sGraph, pos, node_size=5, width=0.1)\n",
"#plt.show()\n",
"plt.savefig('compact_sets.png', dpi=150)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f8c5c995-c7a7-4f84-bf68-e1551021d26d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"79\n",
"[((), (-2, 3), (-2, -2, 5), (2, 3, -5)), ((), (2, 2, -3), (-2, 3), (-2, -2, 5)), {'melodic_movement': 182.4037121340599, 'transposition': ()}]\n",
"[((), (2, 2, -3), (-2, 3), (-2, -2, 5)), ((), (2, 2, -3), (-2, -2, 5), (-2, -2, -2, -2, 5, 5)), {'melodic_movement': 70.67242686428222, 'transposition': ()}]\n",
"[((), (2, 2, -3), (-2, -2, 5), (-2, -2, -2, -2, 5, 5)), ((), (2, 2, -3), (2, 2, 2, -5), (-2, -2, 5)), {'melodic_movement': 41.0588584054957, 'transposition': ()}]\n",
"[((), (2, 2, -3), (2, 2, 2, -5), (-2, -2, 5)), ((), (2, 2, 2, -5), (-2, -2, 5), (2, 2, 2, 2, 2, -5, -5)), {'melodic_movement': 70.67242686428204, 'transposition': ()}]\n",
"[((), (2, 2, 2, -5), (-2, -2, 5), (2, 2, 2, 2, 2, -5, -5)), ((), (2, 2, -3), (2, 2, 2, -5), (2, 2, 2, 2, 2, -5, -5)), {'melodic_movement': 111.73128526977763, 'transposition': ()}]\n",
"[((), (2, 2, -3), (2, 2, 2, -5), (2, 2, 2, 2, 2, -5, -5)), ((), (2, 2, 2, -5), (2, 3, -5), (2, 2, 2, 2, 2, -5, -5)), {'melodic_movement': 182.4037121340599, 'transposition': ()}]\n",
"[((), (2, 2, 2, -5), (2, 3, -5), (2, 2, 2, 2, 2, -5, -5)), ((), (2, 2, -3), (2, 2, 2, 2, -3, -3), (2, 2, 2, 2, 2, 2, -3, -3, -5)), {'melodic_movement': 182.40371213405996, 'transposition': (-2, 3, 3, -5)}]\n",
"[((), (2, 2, -3), (2, 2, 2, 2, -3, -3), (2, 2, 2, 2, 2, 2, -3, -3, -5)), ((), (-2, 3), (-2, -2, -2, 3, 5), (-2, -2, -2, -2, -2, 3, 3, 5)), {'melodic_movement': 92.17871646099708, 'transposition': (2, 2, 2, 2, 2, 2, 2, -3, -3, -3, -5)}]\n",
"[((), (-2, 3), (-2, -2, -2, 3, 5), (-2, -2, -2, -2, -2, 3, 3, 5)), ((), (2, 2, -3), (-2, 3), (-2, -2, -2, 3, 5)), {'melodic_movement': 92.17871646099718, 'transposition': ()}]\n",
"[((), (2, 2, -3), (-2, 3), (-2, -2, -2, 3, 5)), ((), (-2, 3), (2, 3, -5), (-2, -2, -2, 3, 5)), {'melodic_movement': 182.4037121340599, 'transposition': ()}]\n",
"[((), (-2, 3), (2, 3, -5), (-2, -2, -2, 3, 5)), ((), (-2, 3), (2, 3, -5), (2, 2, 2, 2, 3, -5, -5)), {'melodic_movement': 41.058858405495585, 'transposition': ()}]\n",
"[((), (-2, 3), (2, 3, -5), (2, 2, 2, 2, 3, -5, -5)), ((), (2, 2, 2, -5), (2, 3, -5), (2, 2, 2, 2, 3, -5, -5)), {'melodic_movement': 111.73128526977791, 'transposition': ()}]\n",
"[((), (2, 2, 2, -5), (2, 3, -5), (2, 2, 2, 2, 3, -5, -5)), ((), (-2, 3), (-2, -2, -2, 3, 3), (3, 3, -5)), {'melodic_movement': 111.73128526977777, 'transposition': (2, 2, 2, 2, -3, -5)}]\n",
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" [[], [[], [-2, -2, -2, -2, 5, 5], [-2, -2, -2, -3, 5, 5], [-2, -2, 5]]],\n",
" [[-2, -2, -2, -2, -2, -2, -2, 5, 5, 5],\n",
" [[], [2, 2, 2, -5], [2, 2, 2, 2, -3, -5], [2, 2, 2, 2, 2, -5, -5]]],\n",
" [[], [[], [2, 2, 2, -5], [2, 2, 2, 2, -3, -5], [2, 3, -5]]],\n",
" [[], [[], [2, 2, 2, -5], [2, 2, 2, 2, -3, -5], [-2, -2, 5]]],\n",
" [[], [[], [2, 2, 2, -5], [2, 2, 2, 2, -3, -5], [2, 2, -3]]],\n",
" [[], [[], [2, 2, 2, 2, -3, -3], [2, 2, 2, 2, -3, -5], [2, 2, -3]]],\n",
" [[], [[], [2, 2, 2, 2, -3, -3], [2, 2, 2, 2, 2, -3, -3, -3], [2, 2, -3]]],\n",
" [[], [[], [2, 2, 2, 2, -3, -3], [-2, -2, 5], [2, 2, -3]]],\n",
" [[], [[], [-3, 5], [-2, -2, 5], [2, 2, -3]]],\n",
" [[2, 2, 2, 2, -3, -5],\n",
" [[],\n",
" [-2, -2, -2, -2, 5, 5],\n",
" [-2, -2, -2, -2, -2, -2, 3, 5, 5],\n",
" [-2, -2, 5]]],\n",
" [[-2, -2, -2, -3, 5, 5], [[], [-2, 3], [-2, -2, -2, 3, 3], [2, 3, -5]]],\n",
" [[], [[], [-2, 3], [-2, -2, -2, 3, 3], [2, 2, -3]]],\n",
" [[], [[], [-2, 3], [-2, -2, -2, 3, 3], [-2, -2, 5]]],\n",
" [[-2, -2, -2, -2, 3, 5], [[], [2, 2, 2, -5], [2, 3, -5], [2, 2, -3]]],\n",
" [[], [[], [-2, 3], [2, 3, -5], [2, 2, -3]]],\n",
" [[], [[], [-2, 3], [2, 2, 2, -5], [2, 2, -3]]],\n",
" [[], [[], [-3, 5], [2, 2, 2, -5], [2, 2, -3]]],\n",
" [[2, 2, 2, 2, -3, -5], [[], [-2, -2, -2, -2, 5, 5], [-2, 3], [-2, -2, 5]]],\n",
" [[], [[], [-3, 5], [-2, 3], [-2, -2, 5]]],\n",
" [[], [[], [-3, 5], [2, 2, 2, -5], [-2, -2, 5]]],\n",
" [[], [[], [-2, -2, -2, -2, 5, 5], [2, 2, 2, -5], [-2, -2, 5]]],\n",
" [[], [[], [-2, 3], [2, 2, 2, -5], [-2, -2, 5]]],\n",
" [[], [[], [-2, 3], [2, 2, 2, -5], [2, 2, 2, 2, 2, -5, -5]]],\n",
" [[2, 3, -5], [[], [-2, -2, 5], [2, 2, -3], [2, 2, 2, 2, -3, -5]]],\n",
" [[-2, -2, 3], [[2, 2, -3], [-3, 5], [2, 2, 2, 2, -3, -3], []]],\n",
" [[-2, -2, -2, -3, 5, 5],\n",
" [[2, 2, 2, 2, 2, -5, -5],\n",
" [2, 2, 2, -5],\n",
" [2, 2, 2, 2, 2, 2, 2, -3, -5, -5],\n",
" []]],\n",
" [[2, 2, 2, 2, 2, 2, 2, -5, -5, -5],\n",
" [[-2, -2, 5], [-2, -2, -2, -2, 5, 5], [-3, 5], []]],\n",
" [[], [[-2, -2, 5], [-2, -2, -2, -2, 5, 5], [-2, -2, -2, 3, 5], []]],\n",
" [[], [[-2, -2, 5], [-2, -2, -2, -2, -2, 3, 3, 5], [-2, -2, -2, 3, 5], []]],\n",
" [[], [[-2, -2, 5], [2, 2, -3], [-2, -2, -2, 3, 5], []]],\n",
" [[],\n",
" [[-2, -2, 5], [-2, -2, -2, -2, -2, -2, 3, 5, 5], [-2, -2, -2, 3, 5], []]],\n",
" [[], [[-2, -2, 5], [-3, 5], [-2, -2, -2, 3, 5], []]],\n",
" [[], [[-2, -2, 5], [2, 2, 2, -5], [-2, -2, -2, 3, 5], []]],\n",
" [[], [[-2, -2, 5], [-2, 3], [-2, -2, -2, 3, 5], []]],\n",
" [[], [[-2, -2, -2, -2, -2, -2, 3, 5, 5], [-2, 3], [-2, -2, -2, 3, 5], []]],\n",
" [[], [[-2, -2, -2, 3, 3], [-2, 3], [-2, -2, -2, 3, 5], []]],\n",
" [[], [[2, 2, 2, -5], [-2, 3], [-2, -2, -2, 3, 5], []]],\n",
" [[-2, -2, -2, -2, 3, 5],\n",
" [[2, 2, 2, 2, 2, 2, 2, -3, -5, -5],\n",
" [2, 2, 2, -5],\n",
" [],\n",
" [2, 2, 2, 2, -3, -5]]],\n",
" [[],\n",
" [[2, 2, 2, 2, 2, 2, 2, -3, -5, -5], [2, 2, -3], [], [2, 2, 2, 2, -3, -5]]],\n",
" [[2, 2, 2, 2, -3, -5], [[2, 2, 2, -5], [-2, -2, 5], [2, 3, -5], []]],\n",
" [[-2, 3, 3, -5], [[2, 2, 2, 2, -3, -3], [], [2, 2, -3], [2, -3, -3, 5]]],\n",
" [[2, -3, -3, 5], [[2, 2, 2, -5], [3, 3, -5], [2, 3, -5], []]],\n",
" [[], [[-2, 3], [3, 3, -5], [2, 3, -5], []]],\n",
" [[-2, -2, -2, -2, 3, 5],\n",
" [[2, 2, 2, -5], [2, 2, 2, 2, 3, -5, -5], [2, 2, 2, 2, 2, -5, -5], []]],\n",
" [[],\n",
" [[2, 2, 2, -5],\n",
" [2, 2, 2, 2, 2, 2, 2, -5, -5, -5],\n",
" [2, 2, 2, 2, 2, -5, -5],\n",
" []]],\n",
" [[2, 2, 2, 2, 2, 2, 2, -5, -5, -5],\n",
" [[-2, -2, -2, -2, 5, 5],\n",
" [],\n",
" [-2, -2, 5],\n",
" [-2, -2, -2, -2, -2, -2, 5, 5, 5]]],\n",
" [[], [[-2, -2, -2, -2, 5, 5], [], [-2, -2, 5], [-2, -2, -2, 3, 5]]],\n",
" [[], [[2, 2, 2, -5], [], [-2, -2, 5], [-2, -2, -2, 3, 5]]],\n",
" [[], [[-3, 5], [], [-2, -2, 5], [-2, -2, -2, 3, 5]]],\n",
" [[-2, -2, 5], [[2, 2, -3], [2, 2, 2, 2, -3, -3], [], [-2, 3]]],\n",
" [[], [[2, 2, -3], [-3, 5], [], [-2, 3]]],\n",
" [[], [[2, 2, -3], [-3, 5], [], [2, 2, 2, -5]]]]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def reconcilePath(ham):\n",
" def sortByOther(c1, c2, trans):\n",
" indices = list(range(len(c1)))\n",
" sortedChord = copy.deepcopy(c2)\n",
" for pitch in c2:\n",
" transposedPitch = tuple(transposePitch(pitch, trans))\n",
" if transposedPitch in c1:\n",
" index = c1.index(transposedPitch)\n",
" sortedChord[index] = pitch\n",
" indices.remove(index)\n",
" else:\n",
" diff = pitch\n",
" sortedChord[indices[0]] = diff\n",
" return sortedChord\n",
" rPath = [[[], [list(p) for p in ham[0][0]]]]\n",
" for cdx in range(len(ham)-1):\n",
" c1 = list(ham[cdx][0])\n",
" c2 = list(ham[cdx][1])\n",
" trans = list(ham[cdx][2]['transposition'])\n",
" c2 = sortByOther(c1, c2, trans)\n",
" ham[cdx+1][0] = c2\n",
" rPath.append([trans, [list(p) for p in c2]])\n",
" return rPath\n",
"\n",
"ham = stochastic_hamiltonian(testGraph)\n",
"ham = [list(e) for e in ham]\n",
"print(len(ham))\n",
"for e in ham:\n",
" print(e)\n",
"rPath = reconcilePath(ham)\n",
"rPath"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "7a4b85ab-79cf-4cbf-9dde-505f465a5b46",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[[1.0, 1.5, 1.25, 1.2],\n",
" [1.0, 1.5, 1.25, 1.3333333333333333],\n",
" [1.0, 1.5625, 1.25, 1.3333333333333333],\n",
" [1.0, 1.6, 1.25, 1.3333333333333333],\n",
" [1.0, 1.6, 1.25, 1.28],\n",
" [1.0, 1.6, 1.3333333333333333, 1.28],\n",
" [1.0, 1.6, 1.2, 1.28],\n",
" [0.9, 1.6, 1.2, 1.28],\n",
" [0.8533333333333334, 1.6, 1.2, 1.28],\n",
" [0.8533333333333334, 1.6, 1.1377777777777778, 1.28],\n",
" [0.8533333333333334, 1.6, 1.024, 1.28],\n",
" [0.8533333333333334, 1.6384, 1.024, 1.28],\n",
" [0.8533333333333334, 1.6384, 1.024, 1.3653333333333333],\n",
" [0.9102222222222223, 1.6384, 1.024, 1.3653333333333333],\n",
" [0.9102222222222223, 1.536, 1.024, 1.3653333333333333],\n",
" [0.96, 1.536, 1.024, 1.3653333333333333],\n",
" [0.96, 1.536, 1.024, 1.44],\n",
" [0.96, 1.536, 1.08, 1.44],\n",
" [0.96, 1.536, 1.152, 1.44],\n",
" [1.024, 1.536, 1.152, 1.44],\n",
" [1.08, 1.536, 1.152, 1.44],\n",
" [1.08, 1.62, 1.152, 1.44],\n",
" [1.08, 1.8, 1.152, 1.44],\n",
" [1.08, 1.8, 1.125, 1.44],\n",
" [1.08, 1.8, 1.2, 1.44],\n",
" [1.08, 1.8, 1.2, 1.35],\n",
" [1.08, 1.8, 1.125, 1.35],\n",
" [1.08, 1.6875, 1.125, 1.35],\n",
" [1.0546875, 1.6875, 1.125, 1.35],\n",
" [1.0546875, 1.6875, 1.125, 1.265625],\n",
" [1.0546875, 1.6875, 1.125, 1.318359375],\n",
" [1.0546875, 1.6875, 1.125, 1.40625],\n",
" [1.0546875, 1.875, 1.125, 1.40625],\n",
" [1.0546875, 1.875, 1.25, 1.40625],\n",
" [1.0546875, 1.875, 1.318359375, 1.40625],\n",
" [1.0546875, 1.7578125, 1.318359375, 1.40625],\n",
" [1.125, 1.7578125, 1.318359375, 1.40625],\n",
" [1.171875, 1.7578125, 1.318359375, 1.40625],\n",
" [1.171875, 1.7578125, 1.318359375, 1.5625],\n",
" [1.171875, 1.7578125, 1.318359375, 1.46484375],\n",
" [1.0986328125, 1.7578125, 1.318359375, 1.46484375],\n",
" [1.0986328125, 1.64794921875, 1.318359375, 1.46484375],\n",
" [1.0986328125, 1.64794921875, 1.7578125, 1.46484375],\n",
" [1.0986328125, 1.8310546875, 1.7578125, 1.46484375],\n",
" [1.171875, 1.8310546875, 1.7578125, 1.46484375],\n",
" [1.171875, 1.953125, 1.7578125, 1.46484375],\n",
" [1.171875, 1.953125, 1.875, 1.46484375],\n",
" [1.171875, 1.8310546875, 1.875, 1.46484375],\n",
" [1.171875, 1.7578125, 1.875, 1.46484375],\n",
" [1.171875, 1.7578125, 1.875, 1.5],\n",
" [1.40625, 1.7578125, 1.875, 1.5],\n",
" [1.40625, 1.7578125, 1.875, 1.0546875],\n",
" [1.40625, 1.7578125, 1.875, 1.0986328125],\n",
" [1.40625, 1.7578125, 1.875, 1.125],\n",
" [1.40625, 1.7578125, 2.109375, 1.125],\n",
" [1.40625, 1.58203125, 2.109375, 1.125],\n",
" [1.40625, 1.5, 2.109375, 1.125],\n",
" [1.40625, 1.318359375, 2.109375, 1.125],\n",
" [1.40625, 1.875, 2.109375, 1.125],\n",
" [1.40625, 1.8, 2.109375, 1.125],\n",
" [1.40625, 1.6875, 2.109375, 1.125],\n",
" [1.318359375, 1.6875, 2.109375, 1.125],\n",
" [1.265625, 1.6875, 2.109375, 1.125],\n",
" [1.8, 1.6875, 2.109375, 1.125],\n",
" [1.8, 1.6875, 1.0546875, 1.125],\n",
" [1.8, 1.40625, 1.0546875, 1.125],\n",
" [1.8, 1.40625, 1.35, 1.125],\n",
" [1.8, 1.0125, 1.35, 1.125],\n",
" [1.8, 2.025, 1.35, 1.125],\n",
" [1.6875, 2.025, 1.35, 1.125],\n",
" [1.6875, 2.025, 1.35, 1.0546875],\n",
" [1.6875, 1.08, 1.35, 1.0546875],\n",
" [1.6875, 1.08, 1.35, 2.109375],\n",
" [1.6875, 1.08, 1.35, 2.025],\n",
" [1.728, 1.08, 1.35, 2.025],\n",
" [1.8, 1.08, 1.35, 2.025],\n",
" [1.8, 2.4, 1.35, 2.025],\n",
" [1.8, 2.25, 1.35, 2.025],\n",
" [1.8, 2.25, 1.35, 2.16]]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def pathToChords(path):\n",
" curRoot = Fraction(1, 1)\n",
" chords = []\n",
" for trans, points in path:\n",
" curRoot = curRoot * hsPointToFR(trans)\n",
" chord = [float(curRoot * hsPointToFR(p)) for p in points]\n",
" chords.append(chord)\n",
" return chords\n",
"\n",
"fPath = pathToChords(rPath)\n",
"len(set([tuple(p) for p in fPath]))\n",
"fPath"
]
},
{
"cell_type": "code",
"execution_count": 284,
"id": "806a4471-61c7-4d83-81a1-6f6d54be66b2",
"metadata": {},
"outputs": [],
"source": [
"# Opening a file in write mode{\n",
"file = open(\"seq.txt\", \"w+\")\n",
"\n",
"# Converting the array to a string and writing to the file\n",
"content = str(fPath)\n",
"file.write(content)\n",
"\n",
"# Closing the file\n",
"file.close()"
]
},
{
"cell_type": "code",
"execution_count": 279,
"id": "6a58ae52-b813-4936-86db-9712e5e20d42",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, 2, -13), (2, 2, 2, 2, 2, 2, 2, -5, -13), (2, 2, 2, 2, 2, 3, -5, -13)), {'melodic_movement': 128.2982446998143, 'transposition': (-2, -7, 13)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (2, 3, -5), (3, 3, -5)), {'melodic_movement': 1248.7703813968149, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (2, 3, -5), (-2, -5, 11)), {'melodic_movement': 396.17832203079695, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (-2, -2, 7), (2, 3, -5)), {'melodic_movement': 1200.0, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (-2, -2, -2, 13), (2, 3, -5)), {'melodic_movement': 1071.7017553001858, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, -3), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 48.770381396815196, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -7), (2, 2, 2, 2, -11), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 101.86667710381573, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (2, 3, -5), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 1276.0344731969155, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -7), (2, 2, 3, -7), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 386.31371386483465, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -7), (2, 2, 2, 2, -13), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 187.34304230073815, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 2, 2, 2, 2, -5, -5, -7)), {'melodic_movement': 111.7312852697778, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), {'melodic_movement': 342.905378800653, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), {'melodic_movement': 235.67665536420407, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, -5, -7, 11)), {'melodic_movement': 150.6370585006307, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (2, 3, -5), (-2, -2, 3, -5, 13)), {'melodic_movement': 1387.3430423007383, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (2, 3, -5), (-5, 7)), {'melodic_movement': 813.6862861351653, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 2, 2, -7, -7)), {'melodic_movement': 84.46719346967768, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (2, 3, -5), (2, 2, 2, 2, 2, 3, -5, -13)), {'melodic_movement': 906.287718762117, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, -3), (2, 2, 2, -5), (-2, -3, 7)), {'melodic_movement': 1311.7312852697778, 'transposition': (2, 3, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -7), (-2, -2, -2, 11), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 4.502561833329082, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), ((), (2, 2, 2, -5), (2, 3, -5), (2, 2, 2, 2, 3, -5, -7)), {'melodic_movement': 777.9894740623026, 'transposition': (2, 2, 2, -7)})\n",
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"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (-2, -2, -2, 3, 3), (2, 2, 2, 3, -13)), {'melodic_movement': 1173.1586243658548, 'transposition': (2, 2, 2, 2, -3, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, -2, -2, 11), (-2, -3, 11), (-2, -2, -2, -2, -3, 5, 11)), {'melodic_movement': 347.407940633982, 'transposition': (2, 2, 2, 2, 3, -5, -11)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, -5), (-2, -2, 7), (2, 2, 2, 2, -3, -5)), {'melodic_movement': 653.1846194685724, 'transposition': ()})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, -2, -2, 13), (-2, -2, -2, -2, -2, 3, 13), (-2, -2, -2, -2, -2, -2, 5, 13)), {'melodic_movement': 138.57266090392307, 'transposition': (2, 2, 2, 2, 2, 2, -5, -13)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (2, 2, 2, -5), (2, 3, -5)), {'melodic_movement': 590.2237155956096, 'transposition': ()})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (-2, -2, -2, 3, 3), (2, 2, 3, -7)), {'melodic_movement': 1044.8603796660402, 'transposition': (2, 2, 2, 2, -3, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (-2, -2, -2, 3, 3), (-2, -2, -2, -2, -2, 3, 3, 7)), {'melodic_movement': 1284.4671934696776, 'transposition': (2, 2, 2, 2, -3, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, -7), (2, 2, 3, -7), (3, 3, -7)), {'melodic_movement': 119.44280826109728, 'transposition': (2, -3, -5, 7)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 2, 2, 2, -3, -5, -7)), {'melodic_movement': 546.8153805314276, 'transposition': (-2, -2, -2, 7)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, -3), (-2, 3), (-2, -2, 5)), {'melodic_movement': 1200.0, 'transposition': (2, 2, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, -3, -7), (2, 2, 2, 2, 2, 2, -3, -3, -7)), {'melodic_movement': 84.46719346967761, 'transposition': (-2, -2, 3, -5, 7)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, 2, -13), (2, 2, 2, 3, -13), (3, 5, -13)), {'melodic_movement': 563.3823399614641, 'transposition': (-3, -5, 13)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (-2, -2, -2, 3, 3), (2, 3, 3, -11)), {'melodic_movement': 964.3233446357958, 'transposition': (2, 2, 2, 2, -3, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (-2, -2, -2, 3, 3), (-2, -2, -2, -2, -2, -2, 3, 3, 13)), {'melodic_movement': 1156.1689487698634, 'transposition': (2, 2, 2, 2, -3, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, -5), (2, 3, -5), (-2, -2, 3, -5, 11)), {'melodic_movement': 755.2279440955314, 'transposition': ()})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, 2, -13), (2, 2, 2, 2, 2, 2, -3, -13), (2, 2, 2, 2, 2, 2, 2, -3, -3, -13)), {'melodic_movement': 43.83105123013685, 'transposition': (-2, -2, -2, 3, -5, 13)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, -2, 5), (-3, 5), (-2, -2, -2, -3, 5, 5)), {'melodic_movement': 182.40371213406002, 'transposition': (2, 2, 2, 3, -5, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (2, 2, 2, -7), (-2, -2, -2, 3, 3)), {'melodic_movement': 342.905378800653, 'transposition': (2, 2, 2, 2, -3, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (-2, -2, -2, 3, 3), (2, 3, 3, -13)), {'melodic_movement': 675.1136252312422, 'transposition': (2, 2, 2, 2, -3, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (-2, 3), (-2, -2, -2, 3, 3), (3, 3, -5)), {'melodic_movement': 1129.3275731357178, 'transposition': (2, 2, 2, 2, -3, -5)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, 2, -11), (2, 2, 2, 2, 2, 2, -3, -11), (2, 2, 2, 2, 2, 2, 2, -3, -3, -11)), {'melodic_movement': 333.04077063469083, 'transposition': (-2, -2, -2, 3, -5, 11)})\n",
"(((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 3, -5)), ((), (2, 2, 2, -5), (-2, -2, 5), (2, 3, -5)), {'melodic_movement': 274.5824285950571, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 3, -5, -7)), {'melodic_movement': 235.67665536420407, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, -3), (2, 2, 2, -5), (-2, -2, -2, 11)), {'melodic_movement': 729.2190926654876, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (-7, 11), (-7, 13)), {'melodic_movement': 26.841375634145606, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (-7, 11), (2, 2, 2, -7, -7, 11)), {'melodic_movement': 31.19425023953329, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -5), (-2, -2, -2, 11), (-7, 11)), {'melodic_movement': 1013.6661294265068, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -5), (-2, -2, -2, 11), (-5, 7)), {'melodic_movement': 813.6862861351651, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, 2, -7, -11), (-7, 11)), {'melodic_movement': 165.00422849992162, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (-2, 3), (2, 2, 2, -5), (-2, -2, -2, 11)), {'melodic_movement': 933.1290943962625, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -5), (-2, -2, -2, 11), (-2, -2, -2, -2, -2, 3, 11)), {'melodic_movement': 284.4470367610192, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, -3), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 284.44703676101926, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 2, 2, -11), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 133.80997826038833, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (-7, 11), (2, 2, -5, -7, 11)), {'melodic_movement': 648.6820576352433, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -5), (2, 2, 2, 2, -11), (-2, -2, -2, 11)), {'melodic_movement': 879.8561511661185, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, -3), (-2, -3, 7), (-2, -3, 11)), {'melodic_movement': 1311.7312852697778, 'transposition': (2, 3, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -5), (-2, -2, -2, 11), (2, 2, 2, 2, 2, 2, 2, -5, -13)), {'melodic_movement': 1404.33271789673, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 3, -7), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 150.6370585006306, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (-2, -2, -2, 13), (-11, 13), (-2, -2, -2, 7, -11, 13)), {'melodic_movement': 1102.896005539719, 'transposition': (2, 2, 2, -7, 11, -13)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, -3), (2, 2, 2, -7), (-7, 11)), {'melodic_movement': 546.8153805314278, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 2, 2, -11), (-7, 11)), {'melodic_movement': 396.17832203079683, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 2, 2, -13), (2, 2, 2, 2, 2, 2, -5, -7)), {'melodic_movement': 423.0196976649422, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -5), (-2, -2, -2, 11), (2, 2, 2, 2, 2, -5, -5)), {'melodic_movement': 658.5466658012056, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, 2, 2, 2, 2, 2, 2, -5, -5, -7)), {'melodic_movement': 123.94537009442627, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (-7, 11), (-2, -2, -2, -2, -7, 11, 11)), {'melodic_movement': 911.0504014056519, 'transposition': ()})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -7, -7), (2, 2, 2, -7, -7, 11)), {'melodic_movement': 1276.0344731969155, 'transposition': (-2, -2, -2, 7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -5), (-2, -2, -2, 11), (-2, -2, -2, -2, -2, -2, 11, 11)), {'melodic_movement': 1333.8099782603886, 'transposition': (2, 2, 2, -7)})\n",
"(((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (-7, 11)), ((), (2, 2, 2, -7), (2, 2, 2, 2, 2, 2, -5, -7), (2, 2, -5, -7, 11)), {'melodic_movement': 386.31371386483477, 'transposition': ()})\n"
]
}
],
"source": [
"for edge in list(testGraph.edges(data=True))[:1000]:\n",
" print(edge)"
]
},
{
"cell_type": "code",
"execution_count": 161,
"id": "3a4d43a7-fa7d-40e5-bd36-4fa15c3c1cc5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 1584.96x1000 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import networkx as nx\n",
"from matplotlib import pyplot as plt\n",
"import math\n",
"\n",
"G = nx.grid_graph(dim=(range(-3, 4), range(-3, 4)))\n",
"\n",
"def getLabel(x, y):\n",
" num = 1\n",
" den = 1\n",
" if x >= 0:\n",
" num *= math.pow(3, x)\n",
" else:\n",
" den *= math.pow(3, abs(x))\n",
" if y >= 0:\n",
" num *= math.pow(2, y)\n",
" else:\n",
" den *= math.pow(2, abs(y))\n",
" return str(int(num)) + \"/\" + str(int(den))\n",
" \n",
" \n",
"\n",
"plt.figure(figsize=(10 * math.log2(3), 10 * math.log2(2)))\n",
"#plt.figure(figsize=(10, 10))\n",
"pos = {(x, y):(x * math.log2(3), y * math.log2(2)) for x,y in G.nodes()}\n",
"labels = {(x, y):getLabel(x, y) for x,y in G.nodes()}\n",
"nx.draw_networkx_labels(G, pos, labels=labels)\n",
"nx.draw(G, pos=pos, \n",
" node_color='white', \n",
" with_labels=False,\n",
" node_size=1000)"
]
},
{
"cell_type": "code",
"execution_count": 160,
"id": "49d0416c-dd26-4454-b4bf-743922683c27",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA5cAAAJ2CAYAAADL+nZ2AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAABlHUlEQVR4nO3de3zP9f//8ft7RzuYYQ4xh89QMnOOKbM5yyGGEpEalRD65CtFWaEPifTVQc4+pZKtSBrlkFBySuXTR8kpKTnMcYfY9vz94bv3z9t7m/HcKLtdL5f35dKer+fr9X6+1mNvz/v7/Xo93w5jjBEAAAAAABY8rvcAAAAAAAB/f4RLAAAAAIA1wiUAAAAAwBrhEgAAAABgjXAJAAAAALBGuAQAAAAAWCNcAgAAAACsES4BAAAAANYIlwAAAAAAa4RLAAAAAIA1wiUAAAAAwBrhEgAAAABgjXAJAAAAALBGuAQAAAAAWCNcAgAAAACsES4BAAAAANYIlwAAAAAAa4RLAAAAAIA1wiUAAAAAwBrhEgAAAABgjXAJAAAAALBGuAQAAAAAWCNcAgAAAACsES4BAAAAANYIlwAAAAAAa4RLAAAAAIA1wiUAAAAAwBrhEgAAAABgjXAJAAAAALBGuAQAAAAAWCNcAgAAAACsES4BAAAAANYIlwAAAAAAa4RLAAAAAIA1wiUAAAAAwBrhEgAAAABgjXAJAAAAALBGuAQAAAAAWCNcAgAAAACsES4BAAAAANYIlwAAAAAAa4RLAAAAAIA1wiUAAAAAwBrhEgAAAABgjXAJAAAAALBGuAQAAAAAWCNcAgAAAACsES4BAAAAANYIlwAAAAAAa4RLAAAAAIA1wiUAAAAAwBrhEgAAAABgjXAJAAAAALBGuAQAAAAAWCNcStqxY4c6duyoypUry8/PT6VKlVLTpk319ttvu/U9f/68pk6dqoiICPn5+Sk4OFi33367vvzyyxyP3a1bN3Xp0kWS9MEHH6hXr16qXr26/Pz8VLVqVd13333avXu3234xMTFyOBxuj/bt2xfsyQO52Lx5s9q1a6fixYsrMDBQLVq00MaNG3Pt/9FHH8nLy0tHjx6VpBzr1+FwaOLEidfqFIA82db44cOHNWTIEIWFhcnPz09VqlRR//799csvv1yrUwCcZs+eLYfDocDAQJf2Bx54IMfX4po1a+Z6rIvnLqtWrVKbNm1UoUIF+fr6qmzZsmrZsqU++eQTl31Onz6tCRMmKCYmRuXLl1dgYKAiIiI0adIkpaenF/wJ429pzZo1iouLU82aNRUQEKCKFSuqS5cu2rZtm7NPZmampk6dqvbt2ys0NFT+/v669dZbNWrUKJ08edLtmFc630hOTpa3t7c+/PBDSdLHH3+s+++/XxEREfL29pbD4chxv23btmnw4MGKiIhQ8eLFVa5cObVu3Vpr1qzJsX9iYqLuuOMOlSpVSsHBwWrcuLHeeuutK/yN/f14Xe8B/BWcPHlSlSpVUq9evVSxYkWlpKRo4cKF6tu3r/bv368xY8ZIulDssbGx2rBhg0aOHKnbb79dKSkp2rZtm1JSUtyOm5KSohUrVmjGjBmSpEmTJql8+fIaPXq0wsLCdPDgQb3wwgtq0KCBNm3apPDwcJf9w8LCtHDhQpe24ODgwvklABfZsmWLmjdv7nwhNMboxRdfVKtWrbR27Vo1bdrUbZ/ExEQ1b95cZcqUcbb16NFDTzzxhEu/ypUrF/r4gcuxrfE///xTzZs314kTJ/Tcc8+pVq1a+vHHHzV27FitXLlS//3vf1W8ePHrcGYoig4dOqQRI0aoQoUKOnXqlNt2Pz8/twmwn59fjse6dO5y/PhxhYeHa8CAASpfvrySk5M1Y8YMdezYUW+99Zb69OkjSfrll180bdo09e3bV//85z8VGBio9evXKz4+Xp999pk+++yzXCftKDreeOMNHT9+XMOGDVOtWrV09OhRTZkyRZGRkVq5cqVatmyptLQ0xcfHq1evXhowYIBCQkK0fft2jR8/XsuWLdPWrVvd6vdK5htLly6Vj4+P8wObDz/8UJs2bVL9+vXl6+vrEnQv9u6772rz5s2Ki4tT3bp1lZKSohkzZqhVq1ZasGCB7r//fmffuXPnqn///urevbvGjBkjh8Ph7HPs2DE9/vjjNr/GvzaDXDVp0sRUqlTJ+fPLL79sPDw8zFdffZWv/d9//33j7e1tkpOTjTHG/PHHH259Dh06ZLy9vU3//v1d2qOjo014eLjF6IGr165dO1OuXDmTkpLibDt9+rQJCQkxt99+u1v/c+fOmeDgYPPqq6862ySZwYMHX5PxAlfKtsY/++wzI8nMnj3bpd8777xjJJkPPvigcE8AuEinTp1M586dTb9+/UxAQIDLtpza8nLp3CUn586dMxUrVjRRUVHOtrNnz5qzZ8+69Z08ebKRZNavX5/vMeDGldNc+MyZM6ZcuXKmVatWxhhjMjIyzLFjx9z6LV682Egyb731lkv7lc43OnToYHr06OH8OTMz0/nfgwcPNrnFo5zGnpGRYerUqWOqVavm0n7HHXeYKlWquBw7KyvL1KxZ09SpUyffY/074rLYPISEhMjL6/9/uPvKK6+oefPmioyMzNf+iYmJatmypUqWLClJKlu2rFufChUqKDQ0VAcPHiyYQQMFYOPGjYqJiZG/v7+zrXjx4mrevLm+/PJL/f777y79V69erVOnTik2NvZaDxW4KrY17u3tLUkqUaKES7/sq0uKFStWiKMH/r+3335b69at0+uvv14gx7t07pITb29vBQcHu8yRAgICFBAQ4Na3cePGksQ8B5JyngsHBgaqVq1azhrx9PRU6dKl3foVRC2dPn1aq1atUvfu3Z1tHh75i0M5jd3T01MNGzZ0G5O3t7cCAwNdju1wOBQUFHTD//tAuLxIVlaWMjIydPToUb3++utauXKlnnzySUkXCnn//v2KiIjQ008/rXLlysnLy0vh4eFasGCB27HS09O1fPlyl+LNyd69e3XgwAG3S2Ilac+ePSpVqpS8vLxUrVo1jR49WmlpaQVzskAezp07J19fX7f27Lbvv//epT0xMVFNmzZVhQoVXNrfeecd+fn5ydfXVw0bNtS8efMKb9DAFbCt8TvuuEMNGzZUfHy8tmzZorNnz2r79u16+umn1aBBA7Vu3brwTwJF3pEjRzR8+HBNnDhRoaGhufZLS0tT+fLl5enpqdDQUA0ZMkTJyclu/fKau2TPkX777TeNHTtWP/30k9tliDnJvhw3p3kOIEmnTp3S9u3bL1sjedVSfucby5Ytk8PhUMeOHe0HLikjI0Pr1693G9Njjz2m//73v5owYYKOHj2qY8eO6aWXXtK2bds0YsSIAnnuv6zr/dHpX8kjjzxiJBlJxsfHx7z++uvObV999ZWRZIKCgkytWrXM+++/b1auXGl69OhhJJmZM2e6HGvJkiXG09PTHDlyJNfnO3/+vImJiTFBQUHml19+cdk2evRo8/rrr5s1a9aY5cuXmyFDhhgvLy/TvHlzl4/YgcJQr149c/PNN7vU2vnz501YWJiRZN555x1ne0ZGhgkJCTFTpkxxOUbv3r3NwoULzRdffGESEhLMnXfeaSSZMWPGXLPzAHJTEDV++vRp07lzZ+e/G5JMTEyMOX78+DU7DxRt3bt3N7fffrvJysoyxuR8CezUqVPN1KlTzaeffmo+/fRTM3r0aOPv729q1qxpzpw549I3r7lLu3btnHUeFBSUr0u/v/32W+Pn52diY2MtzhI3uvvuu894eXmZrVu35trn119/NeXKlTONGjVymwdfyXyja9eupnPnzrk+T16XxeZk9OjRRpJZsmSJ27YlS5aYEiVKOP9u/Pz8zNtvv53vY/9dES4vcuDAAbNlyxazfPlyM3DgQOPh4WEmT55sjDFm48aNztC5f/9+5z5ZWVmmQYMGJjQ01OVYffv2NTExMbk+V1ZWlrn//vuNp6dnjgWZk5deeol7eXBNzJkzx0gyjz76qPn111/NL7/8Yvr37288PT2NJPPee+85+65evdpIMvv27bvscTt16mS8vLz
"text/plain": [
"<Figure size 1160.96x792.481 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import networkx as nx\n",
"from matplotlib import pyplot as plt\n",
"import math\n",
"\n",
"G = nx.grid_graph(dim=(range(-2, 3), range(-2, 3)))\n",
"\n",
"def collapseLabel(fraction):\n",
" if fraction < 1:\n",
" while fraction < 1:\n",
" fraction *= Fraction(2, 1)\n",
" elif fraction >= 2:\n",
" while fraction >= 2:\n",
" fraction *= Fraction(1, 2)\n",
" return fraction\n",
" \n",
"def getLabel(x, y):\n",
" num = 1\n",
" den = 1\n",
" if x >= 0:\n",
" num *= math.pow(5, x)\n",
" else:\n",
" den *= math.pow(5, abs(x))\n",
" if y >= 0:\n",
" num *= math.pow(3, y)\n",
" else:\n",
" den *= math.pow(3, abs(y))\n",
" fraction = collapse(Fraction(int(num), int(den)))\n",
" num = fraction.numerator\n",
" den = fraction.denominator\n",
" return str(int(num)) + \"/\" + str(int(den))\n",
"\n",
"plt.figure(figsize=(5 * math.log2(5), 5 * math.log2(3)))\n",
"#plt.figure(figsize=(10, 10))\n",
"pos = {(x, y):(x, y) for x,y in G.nodes()}\n",
"labels = {(x, y):getLabel(x, y) for x,y in G.nodes()}\n",
"nx.draw_networkx_labels(G, pos, labels=labels)\n",
"nx.draw(G, pos=pos, \n",
" node_color='white', \n",
" with_labels=False,\n",
" node_size=2000)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "281f2daf-6613-46ca-ad59-2561cc0c13b4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, 3), (-2, -2, 5), (2, 3, -5)), {'melodic_movement': 631.2825740011051, 'transposition': (2, 3, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, 3), (-2, -2, 5), (-3, 5)), {'melodic_movement': 1200.0, 'transposition': (2, 3, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, -2, 5), (-2, -2, -2, 3, 5), (-2, -2, -2, -2, 5, 5)), {'melodic_movement': 70.67242686428227, 'transposition': (2, 2, 2, 3, -5, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, 3), (-2, -2, 5), (-2, -2, -2, -2, 5, 5)), {'melodic_movement': 1088.2687147302222, 'transposition': (2, 3, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, -2, 5), (-2, -2, -2, -2, 5, 5), (-2, -2, -2, -3, 5, 5)), {'melodic_movement': 1088.2687147302224, 'transposition': (2, 2, 2, 3, -5, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (2, 2, -3), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5)), {'melodic_movement': 203.91000173077484, 'transposition': (-2, -2, -2, 3, 3)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, 3), (2, 2, 2, -5), (-2, -2, 5)), {'melodic_movement': 1129.3275731357178, 'transposition': (2, 3, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (2, 2, -3), (-2, 3), (-2, -2, 5)), {'melodic_movement': 813.6862861351653, 'transposition': (2, 3, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (2, 2, -3), (-3, 5), (2, -3, -3, 5)), {'melodic_movement': 1200.0, 'transposition': (-2, 3, 3, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, 3), (-2, -2, 5), (-2, -2, -2, 3, 3)), {'melodic_movement': 519.5512887313275, 'transposition': (2, 3, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (2, 2, 2, -5), (2, 2, 2, 2, 2, -5, -5), (2, 2, 2, 2, 3, -5, -5)), {'melodic_movement': 111.73128526977777, 'transposition': (-2, -2, -2, -2, 3, 5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, 3), (-2, -2, 5), (-2, -2, -2, 3, 5)), {'melodic_movement': 1403.9100017307749, 'transposition': (2, 2, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (-2, 3), (-2, -2, 5), (-2, -2, -2, 3, 5)), {'melodic_movement': 1403.9100017307749, 'transposition': (2, 3, -5)})\n",
"(((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (2, 2, 2, -5), (2, 2, 2, 2, -3, -5), (2, 2, 2, 2, 2, -5, -5)), {'melodic_movement': 1129.3275731357178, 'transposition': (-2, -2, -2, -2, 3, 5)})\n"
]
}
],
"source": [
"for node in list(testGraph.nodes)[2:3]:\n",
" edges = list(testGraph.out_edges(node, data=True))\n",
" for edge in edges:\n",
" if list(edge)[2]['transposition'] != ():\n",
" print(edge)"
]
},
{
"cell_type": "code",
"execution_count": 251,
"id": "cf072042-3513-4a96-b08c-3b5734299210",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 1000x1000 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import networkx as nx\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"# The graph to visualize\n",
"G = nx.grid_graph(dim=(range(-1, 2), range(-1, 2), range(-1, 2)))\n",
"\n",
"# 3d spring layout\n",
"#pos = nx.spring_layout(G, dim=3, seed=779)\n",
"pos = {(x, y, z):(math.log2(2) * x, math.log2(3) * y, math.log2(5) * z) for x,y,z in G.nodes()}\n",
"# Extract node and edge positions from the layout\n",
"node_xyz = np.array([pos[v] for v in sorted(G)])\n",
"edge_xyz = np.array([(pos[u], pos[v]) for u, v in G.edges()])\n",
"\n",
"# Create the 3D figure\n",
"fig = plt.figure(figsize=(10, 10))\n",
"ax = fig.add_subplot(111, projection=\"3d\")\n",
"\n",
"# Plot the nodes - alpha is scaled by \"depth\" automatically\n",
"ax.scatter(*node_xyz.T, s=100, ec=\"w\")\n",
"\n",
"ax.view_init(elev=30, azim=45, roll=15)\n",
"\n",
"ax.axis('equal')\n",
"\n",
"# Plot the edges\n",
"for vizedge in edge_xyz:\n",
" ax.plot(*vizedge.T, color=\"tab:gray\")\n",
"\n",
"\n",
"def _format_axes(ax):\n",
" \"\"\"Visualization options for the 3D axes.\"\"\"\n",
" # Turn gridlines off\n",
" ax.grid(False)\n",
" # Suppress tick labels\n",
" for dim in (ax.xaxis, ax.yaxis, ax.zaxis):\n",
" dim.set_ticks([])\n",
" # Set axes labels\n",
" ax.set_xlabel(\"x\")\n",
" ax.set_ylabel(\"y\")\n",
" ax.set_zlabel(\"z\")\n",
"\n",
"\n",
"_format_axes(ax)\n",
"fig.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "7d8ed658-ff00-42fd-98fc-cbe78e8fad32",
"metadata": {},
"outputs": [],
"source": [
"from tikzpy import TikzPicture\n",
"\n",
"def collapseLabel(fraction):\n",
" if fraction < 1:\n",
" while fraction < 1:\n",
" fraction *= Fraction(2, 1)\n",
" elif fraction >= 2:\n",
" while fraction >= 2:\n",
" fraction *= Fraction(1, 2)\n",
" return fraction\n",
"\n",
"def getLabel(x, y, z, collapse = False):\n",
" num = 1\n",
" den = 1\n",
" if x >= 0:\n",
" num *= math.pow(3, x)\n",
" else:\n",
" den *= math.pow(3, abs(x))\n",
" \n",
" if y >= 0:\n",
" num *= math.pow(5, y)\n",
" else:\n",
" den *= math.pow(5, abs(y))\n",
" \n",
" if z >= 0:\n",
" num *= math.pow(2, z)\n",
" else:\n",
" den *= math.pow(2, abs(z))\n",
" if collapse:\n",
" fraction = collapseLabel(Fraction(int(num), int(den)))\n",
" else:\n",
" fraction = Fraction(int(num), int(den))\n",
" num = fraction.numerator\n",
" den = fraction.denominator\n",
" return str(int(num)) + \"/\" + str(int(den))\n",
" \n",
"def chord2Points(chord):\n",
" points = []\n",
" for n in chord:\n",
" counter = Counter(n)\n",
" points.append(tuple([counter[d] - counter[-d] for d in [2, 3, 5]]))\n",
" return tuple(points)\n",
"\n",
"def genLattice(chord = None, ranges = None, filename = \"tikz\", collapse = False, scale = 1):\n",
"\n",
" dx = math.log2(3) * scale\n",
" dy = math.log2(5) * scale\n",
" dz = math.log2(2) * scale\n",
"\n",
" if chord:\n",
" set = chord2Points(chord)\n",
"\n",
" if ranges:\n",
" rz,rx,ry = ranges\n",
" else:\n",
" rz,rx,ry = [[min(t), max(t) + 1] for t in list(zip(*set))]\n",
"\n",
" if collapse:\n",
" rz = [0, 1]\n",
" \n",
" tikz = TikzPicture(center=True)\n",
" tikz.set_tdplotsetmaincoords(30, -30)\n",
" tikz.options = \"tdplot_main_coords\"\n",
" \n",
" for x in range(*rx):\n",
" for y in range(*ry):\n",
" for z in range(*rz):\n",
" line = tikz.line((x * dx - dx / 2, y * dy, z * dz), (x * dx + dx / 2, y * dy, z * dz), options=\"thick, black, -\")\n",
" line = tikz.line((x * dx, y * dy - dy / 2, z * dz), (x * dx, y * dy + dy / 2, z * dz), options=\"thick, black, -\")\n",
" if not collapse:\n",
" line = tikz.line((x * dx, y * dy, z * dz - dz / 2), (x * dx, y * dy, z * dz + dz / 2), options=\"thick, black, -\")\n",
" node = tikz.node((x * dx, y * dy, z * dz), options=\"draw, fill=white, scale=0.5\", text=getLabel(x,y,z, collapse))\n",
"\n",
" if chord:\n",
" for e in set:\n",
" z,x,y = e\n",
" if collapse:\n",
" z = 0\n",
" line = tikz.line((x * dx - dx / 2, y * dy, z * dz), (x * dx + dx / 2, y * dy, z * dz), options=\"thick, black, -\")\n",
" line = tikz.line((x * dx, y * dy - dy / 2, z * dz), (x * dx, y * dy + dy / 2, z * dz), options=\"thick, black, -\")\n",
" if not collapse:\n",
" line = tikz.line((x * dx, y * dy, z * dz - dz / 2), (x * dx, y * dy, z * dz + dz / 2), options=\"thick, black, -\")\n",
" node = tikz.node((x * dx, y * dy, z * dz), options=\"draw, fill=yellow, scale=0.5\", text=getLabel(x,y,z, collapse))\n",
"\n",
" tikz.compile(filename + \".pdf\", True)\n",
" \n",
" texFile = open(filename + \".tex\", \"w+\")\n",
" texFile.write(tikz.code())\n",
" texFile.close()"
]
},
{
"cell_type": "code",
"execution_count": 72,
"id": "1dee07b7-0c28-4ca7-8481-43e3bd80dcb2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rc files read:\n",
" NONE\n",
"Latexmk: Run number 1 of rule 'pdflatex'\n",
"This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Arch Linux) (preloaded format=pdflatex)\n",
" restricted \\write18 enabled.\n",
"entering extended mode\n",
"Latexmk: Getting log file 'tmp/tex_file.log'\n",
"\n"
]
}
],
"source": [
"edge = (((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (2, 2, -3), (-2, 3), (-2, -2, 5)), {'melodic_movement': 813.6862861351653, 'transposition': (2, 3, -5)})\n",
"chord = transposeChord(edge[0], (-2, -3, 5))\n",
"#genLattice(chord, path=\"figure.pdf\", collapse=False)\n",
"genLattice(chord, ranges=[[-2, 2], [-2, 2], [-2, 2]], filename=\"compact_set_1_transposed_expanded_padded\", collapse=False, scale=2)"
]
},
{
"cell_type": "code",
"execution_count": 79,
"id": "0d808e30-c8d8-4e43-868f-5245f892f0d3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rc files read:\n",
" NONE\n",
"Latexmk: Run number 1 of rule 'pdflatex'\n",
"This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Arch Linux) (preloaded format=pdflatex)\n",
" restricted \\write18 enabled.\n",
"entering extended mode\n",
"Latexmk: Getting log file 'tmp/tex_file.log'\n",
"\n"
]
}
],
"source": [
"edge = (((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (2, 2, -3), (-2, 3), (-2, -2, 5)), {'melodic_movement': 813.6862861351653, 'transposition': (2, 3, -5)})\n",
"chord = transposeChord(edge[0], (-2, -3, 5))\n",
"#genLattice(chord, path=\"figure.pdf\", collapse=False)\n",
"genLattice(chord, ranges=[[-2, 2], [-1, 3], [-1, 2]], filename=\"compact_set_1_transposed_expanded_padded\", collapse=False, scale=2)"
]
},
{
"cell_type": "code",
"execution_count": 80,
"id": "b8ceb8b7-69b0-40b2-9388-e1806c70dfeb",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rc files read:\n",
" NONE\n",
"Latexmk: Run number 1 of rule 'pdflatex'\n",
"This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Arch Linux) (preloaded format=pdflatex)\n",
" restricted \\write18 enabled.\n",
"entering extended mode\n",
"Latexmk: Getting log file 'tmp/tex_file.log'\n",
"\n"
]
}
],
"source": [
"edge = (((), (-2, 3), (2, 3, -5), (3, 3, -5)), ((), (2, 2, -3), (-2, 3), (-2, -2, 5)), {'melodic_movement': 813.6862861351653, 'transposition': (2, 3, -5)})\n",
"chord = edge[0]\n",
"#genLattice(chord, path=\"figure.pdf\", collapse=False)\n",
"genLattice(chord, ranges=[[-2, 2], [-1, 3], [-1, 2]], filename=\"compact_set_1_expanded_padded\", collapse=False, scale=2)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}