# -*- coding: utf-8 -*- # ------------------------------------------------------------------------------ # Name: scale.intervalNetwork.py # Purpose: A graph of intervals, for scales and harmonies. # # Authors: Christopher Ariza # Michael Scott Asato Cuthbert # # Copyright: Copyright © 2010-2023 Michael Scott Asato Cuthbert # License: BSD, see license.txt # ------------------------------------------------------------------------------ ''' An IntervalNetwork defines a scale or harmonic unit as a (weighted) digraph, or directed graph, where pitches are nodes and intervals are edges. Nodes, however, are not stored; instead, an ordered list of edges (Intervals) is provided as an archetype of adjacent nodes. IntervalNetworks are unlike conventional graphs in that each graph must define a low and high terminus. These points are used to create a cyclic graph and are treated as point of cyclical overlap. IntervalNetwork permits the definition of conventional octave repeating scales or harmonies (abstract chords), non-octave repeating scales and chords, and ordered interval sequences that might move in multiple directions. A scale or harmony may be composed of one or more IntervalNetwork objects. Both nodes and edges can be weighted to suggest tonics, dominants, finals, or other attributes of the network. Changed in v8: nodeId and nodeName standardized. TERMINUS and DIRECTION are now Enums. ''' from __future__ import annotations from collections import OrderedDict from collections.abc import Sequence import copy import enum import typing as t from music21 import common from music21 import environment from music21 import exceptions21 from music21 import interval from music21 import note from music21 import pitch from music21 import prebase environLocal = environment.Environment('scale.intervalNetwork') class Terminus(enum.Enum): ''' One of the two Termini of a scale, either Terminus.LOW or Terminus.HIGH ''' LOW = 'terminusLow' HIGH = 'terminusHigh' def __repr__(self): return 'Terminus.' + self.name def __str__(self): return 'Terminus.' + self.name class Direction(enum.Enum): ''' An enumerated Direction for a scale, either Direction.ASCENDING, Direction.DESCENDING, or Direction.BI (bidirectional) ''' BI = 'bi' ASCENDING = 'ascending' DESCENDING = 'descending' def __repr__(self): return 'Direction.' + self.name def __str__(self): return 'Direction.' + self.name CacheKey = tuple[ int|Terminus, str, str|None, str|None, bool, bool|None] def _gte(a, b): ''' check if a > b or abs(a - b) < epsilon ''' if a > b: return True elif abs(a - b) < 0.00001: return True return False def _lte(a, b): ''' check if a < b or abs(a - b) < epsilon ''' if a < b: return True elif abs(a - b) < 0.00001: return True return False class EdgeException(exceptions21.Music21Exception): pass class Edge(prebase.ProtoM21Object): ''' Abstraction of an Interval as an Edge. Edges store an Interval object as well as a pathway direction specification. The pathway is the route through the network from terminus to terminus, and can either by ascending or descending. For directed Edges, the direction of the Interval may be used to suggest non-pitch ascending movements (even if the pathway direction is ascending). Weight values, as well as other attributes, can be stored. >>> i = interval.Interval('M3') >>> e = scale.intervalNetwork.Edge(i) >>> e.interval is i True >>> e.direction Direction.BI Return the stored Interval object >>> i = interval.Interval('M3') >>> e1 = scale.intervalNetwork.Edge(i, id=0) >>> n1 = scale.intervalNetwork.Node(id=0, degree=0) >>> n2 = scale.intervalNetwork.Node(id=1, degree=1) >>> e1.addDirectedConnection(n1, n2, scale.Direction.ASCENDING) >>> e1.interval Return the direction of the Edge. >>> i = interval.Interval('M3') >>> e1 = scale.intervalNetwork.Edge(i, id=0) >>> n1 = scale.intervalNetwork.Node(id=0, degree=0) >>> n2 = scale.intervalNetwork.Node(id=1, degree=1) >>> e1.addDirectedConnection(n1, n2, scale.Direction.ASCENDING) >>> e1.direction Direction.ASCENDING ''' # noinspection PyShadowingBuiltins # pylint: disable=redefined-builtin def __init__(self, intervalData: interval.Interval|str, id=None, # id is okay: @ReservedAssignment direction=Direction.BI): if isinstance(intervalData, str): i = interval.Interval(intervalData) else: i = intervalData self.interval: interval.Interval = i # direction will generally be set when connections added self.direction: Direction = direction self.weight = 1.0 # store id self.id = id # one or two pairs of Node ids that this Edge connects # if there are two, it is a bidirectional, w/ first ascending self._connections: list[tuple[int|Terminus, int|Terminus]] = [] def __eq__(self, other): ''' >>> i1 = interval.Interval('M3') >>> i2 = interval.Interval('M3') >>> i3 = interval.Interval('m3') >>> e1 = scale.intervalNetwork.Edge(i1) >>> e2 = scale.intervalNetwork.Edge(i2) >>> e3 = scale.intervalNetwork.Edge(i3) >>> e1 == e2 True >>> e1 == e3 False ''' return (isinstance(other, self.__class__) and self.__dict__ == other.__dict__) def _reprInternal(self): return f'{self.direction} {self.interval.name} {self._connections!r}' def addDirectedConnection( self, node1: Node|int|Terminus, node2: Node|int|Terminus, direction=None ) -> None: ''' Provide two Node objects that are connected by this Edge, in the direction from the first to the second. When calling directly, a direction, either ascending or descending, should be set here; this will override whatever the interval is. If None, this will not be set. >>> i = interval.Interval('M3') >>> e1 = scale.intervalNetwork.Edge(i, id=0) >>> n1 = scale.intervalNetwork.Node(id=0, degree=0) >>> n2 = scale.intervalNetwork.Node(id=1, degree=1) >>> e1.addDirectedConnection(n1, n2, scale.Direction.ASCENDING) >>> e1.connections [(0, 1)] >>> e1 ''' # may be Node objects, or number, or Terminus if isinstance(node1, (Terminus, int)): n1Id = node1 else: # assume an Node n1Id = node1.id if isinstance(node2, (Terminus, int)): n2Id = node2 else: # assume an Node n2Id = node2.id self._connections.append((n1Id, n2Id)) # must specify a direction if direction not in (Direction.ASCENDING, Direction.DESCENDING): raise EdgeException('must request a direction') self.direction = direction def addBiDirectedConnections(self, node1, node2): ''' Provide two Edge objects that pass through this Node, in the direction from the first to the second. >>> i = interval.Interval('M3') >>> e1 = scale.intervalNetwork.Edge(i, id=0) >>> n1 = scale.intervalNetwork.Node(id=scale.Terminus.LOW, degree=0) >>> n2 = scale.intervalNetwork.Node(id=1, degree=1) >>> e1.addBiDirectedConnections(n1, n2) >>> e1.connections [(Terminus.LOW, 1), (1, Terminus.LOW)] >>> e1 ''' # must assume here that n1 to n2 is ascending; need to know self.addDirectedConnection(node1, node2, Direction.ASCENDING) self.addDirectedConnection(node2, node1, Direction.DESCENDING) self.direction = Direction.BI # can be ascending, descending def getConnections( self, direction: None|Direction = None ) -> list[tuple[int|Terminus, int|Terminus]]: ''' Callable as a property (.connections) or as a method (.getConnections(direction)): Return a list of connections between Nodes, represented as pairs of Node ids. If a direction is specified, and if the Edge is directional, only the desired directed values will be returned. >>> i = interval.Interval('M3') >>> e1 = scale.intervalNetwork.Edge(i, id=0) >>> n1 = scale.intervalNetwork.Node(id=scale.Terminus.LOW, degree=1) >>> n2 = scale.intervalNetwork.Node(id=1, degree=2) >>> e1.addBiDirectedConnections(n1, n2) >>> e1.connections [(Terminus.LOW, 1), (1, Terminus.LOW)] >>> e1.getConnections(scale.Direction.ASCENDING) [(Terminus.LOW, 1)] >>> e1.getConnections(scale.Direction.DESCENDING) [(1, Terminus.LOW)] ''' if direction is None: direction = self.direction # assign native direction # do not need to supply direction, because direction is defined # in this Edge. if self.direction == direction: return self._connections # if requesting bi from a mono directional edge is an error if (direction == Direction.BI and self.direction in (Direction.ASCENDING, Direction.DESCENDING)): raise EdgeException('cannot request a bi direction from a mono direction') # if bi and we get an ascending/descending request if (direction in (Direction.ASCENDING, Direction.DESCENDING) and self.direction == Direction.BI): # assume that in a bi-representation, the first is ascending # the second is descending # NOTE: this may not mean that we are actually ascending, we may # use the direction of the interval to determine if direction == Direction.ASCENDING: return [self._connections[0]] elif direction == Direction.DESCENDING: return [self._connections[1]] # if no connections are possible, return empty list return [] # keep separate property, since getConnections takes a direction argument. @property def connections(self) -> list[tuple[int|Terminus, int|Terminus]]: return self.getConnections() class Node(prebase.ProtoM21Object, common.SlottedObjectMixin): ''' Abstraction of an unrealized Pitch Node. The Node `id` is used to store connections in Edges and has no real meaning. Terminal Nodes have special ids: Terminus.LOW, Terminus.HIGH The Node `degree` is translated to scale degrees in various applications, and is used to request a pitch from the network. The `weight` attribute is used to probabilistically select between multiple nodes when multiple nodes satisfy either a branching option in a pathway or a request for a degree. TODO: replace w/ NamedTuple; eliminate id, and have a terminus: low, high, None ''' __slots__ = ('id', 'degree', 'weight') # noinspection PyShadowingBuiltins # pylint: disable=redefined-builtin def __init__(self, id: Terminus|int, degree: int, weight: float = 1.0): # store id, either as string, such as terminusLow, or a number. # ids are unique to any node in the network self.id: Terminus|int = id # the degree is used to define ordered node counts from the bottom # the degree is analogous to scale degree or degree # more than one node may have the same degree self.degree: int = degree # node weight might be used to indicate importance of scale positions self.weight: float = weight def __hash__(self): hashTuple = (self.id, self.degree, self.weight) return hash(hashTuple) def __eq__(self, other): ''' Nodes are equal if everything in the object.__slots__ is equal. >>> n1 = scale.intervalNetwork.Node(id=3, degree=1) >>> n2 = scale.intervalNetwork.Node(id=3, degree=1) >>> n3 = scale.intervalNetwork.Node(id=2, degree=1) >>> n1 == n2 True >>> n1 == n3 False >>> n2.weight = 2.0 >>> n1 == n2 False >>> n4 = scale.intervalNetwork.Node(id=scale.Terminus.LOW, degree=1) >>> n5 = scale.intervalNetwork.Node(id=scale.Terminus.LOW, degree=1) >>> n4 == n5 True ''' return hash(self) == hash(other) def _reprInternal(self): return f'id={self.id!r}' # ------------------------------------------------------------------------------ class IntervalNetworkException(exceptions21.Music21Exception): pass # presently edges are interval objects, can be marked as # ascending, descending, or bidirectional # edges are stored in dictionary by index values # Nodes are undefined pitches; pitches are realized on demand. # Nodes are stored as an unordered list of coordinate pairs. # Pairs are edge indices: showing which edges connect to this node # could model multiple connections within an object # up: a M2 b m2 C M2 D # down: a M2 b m3 D # edges M2(1+-), m2(2+), M2(3+) # edges m3(4-) # ------------------------------------------------------------------------------ class IntervalNetwork: ''' A graph of undefined Pitch nodes connected by a defined, ordered list of :class:`~music21.interval.Interval` objects as edges. An `octaveDuplicating` boolean, if defined, can be used to optimize pitch realization routines. The `deterministic` boolean, if defined, can be used to declare that there is no probabilistic or multi-pathway segments of this network. The `pitchSimplification` method specifies how to simplify the pitches if they spiral out into double and triple sharps, etc. The default is 'maxAccidental' which specifies that each note can have at most one accidental; double-flats and sharps are not allowed. The other choices are 'simplifyEnharmonic' (which also converts C-, F-, B#, and E# to B, E, C, and F respectively, see :meth:`~music21.pitch.Pitch.simplifyEnharmonic`), 'mostCommon' (which adds to simplifyEnharmonic the requirement that the most common accidental forms be used, so A# becomes B-, G- becomes F#, etc. the only ambiguity allowed is that both G# and A- are acceptable), and None (or 'none') which does not do any simplification. ''' def __init__(self, edgeList: Sequence[interval.Interval|str] = (), octaveDuplicating=False, deterministic=True, pitchSimplification='maxAccidental'): # store each edge with an index that is incremented when added # these values have no fixed meaning but are only for reference self.edgeIdCount = 0 self.nodeIdCount = 0 # a dictionary of Edge object, where keys are edgeId values # Edges store directed connections between Node ids self.edges: OrderedDict[Terminus|int, Edge] = OrderedDict() # nodes suggest Pitches, but Pitches are not stored self.nodes: OrderedDict[Terminus|int, Node] = OrderedDict() if edgeList: # auto initialize self.fillBiDirectedEdges(edgeList) # define if pitches duplicate each octave self.octaveDuplicating = octaveDuplicating self.deterministic = deterministic # could be 'simplifyEnharmonic', 'mostCommon' or None self.pitchSimplification = pitchSimplification # store segments self._ascendingCache: OrderedDict[ CacheKey, tuple[list[pitch.Pitch], list[Terminus|int]] ] = OrderedDict() self._descendingCache: OrderedDict[ CacheKey, tuple[list[pitch.Pitch], list[Terminus|int]] ] = OrderedDict() def clear(self): ''' Remove and reset all Nodes and Edges. ''' self.edgeIdCount = 0 self.nodeIdCount = 0 self.edges = OrderedDict() self.nodes = OrderedDict() self._ascendingCache = OrderedDict() self._descendingCache = OrderedDict() def __eq__(self, other): ''' >>> edgeList1 = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> edgeList2 = ['M2', 'M2', 'm2', 'M2', 'A3', 'm2'] >>> net1 = scale.intervalNetwork.IntervalNetwork() >>> net1.fillBiDirectedEdges(edgeList1) >>> net2 = scale.intervalNetwork.IntervalNetwork() >>> net2.fillBiDirectedEdges(edgeList1) >>> net3 = scale.intervalNetwork.IntervalNetwork() >>> net3.fillBiDirectedEdges(edgeList2) >>> net1 == net2 True >>> net1 == net3 False ''' # compare all nodes and edges; if the same, and all keys are the same, # then matched if not isinstance(other, self.__class__): return False for attr in ('edgeIdCount', 'nodeIdCount', 'edges', 'nodes', 'octaveDuplicating', 'deterministic', 'pitchSimplification'): if getattr(self, attr) != getattr(other, attr): return False return True def fillBiDirectedEdges(self, edgeList: Sequence[interval.Interval|str]): # noinspection PyShadowingNames ''' Given an ordered list of bi-directed edges given as :class:`~music21.interval.Interval` specifications, create and define appropriate Nodes. This assumes that all edges are bi-directed and all edges are in order. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.nodes OrderedDict() >>> net.edges OrderedDict() >>> net.fillBiDirectedEdges(edgeList) >>> net.nodes OrderedDict([(Terminus.LOW, ), (0, ), (1, ), ... (5, ), (Terminus.HIGH, )]) >>> net.edges OrderedDict([(0, ), (1, ), (2, ), ... (5, ), (6, )]) >>> [str(p) for p in net.realizePitch('g4')] ['G4', 'A4', 'B4', 'C5', 'D5', 'E5', 'F#5', 'G5'] >>> net.degreeMin, net.degreeMax (1, 8) Using another fill method creates a new network >>> net.fillBiDirectedEdges(['M3', 'M3', 'M3']) >>> [str(p) for p in net.realizePitch('g4')] ['G4', 'B4', 'D#5', 'G5'] >>> net.degreeMin, net.degreeMax (1, 4) >>> net.fillBiDirectedEdges([interval.Interval('M3'), ... interval.Interval('M3'), ... interval.Interval('M3')]) >>> [str(p) for p in net.realizePitch('c2')] ['C2', 'E2', 'G#2', 'B#2'] ''' self.clear() degreeCount = 1 # steps start from one nLow = Node(id=Terminus.LOW, degree=degreeCount) degreeCount += 1 self.nodes[nLow.id] = nLow nPrevious = nLow for i, eName in enumerate(edgeList): # first, create the next node if i < len(edgeList) - 1: # if not last n = Node(id=self.nodeIdCount, degree=degreeCount) self.nodeIdCount += 1 degreeCount += 1 nFollowing = n else: # if last # degree is same as start nHigh = Node(id=Terminus.HIGH, degree=degreeCount) nFollowing = nHigh # add to node dictionary self.nodes[nFollowing.id] = nFollowing # then, create edge and connection e = Edge(eName, id=self.edgeIdCount) self.edges[e.id] = e # store self.edgeIdCount += 1 e.addBiDirectedConnections(nPrevious, nFollowing) # update previous with the node created after this edge nPrevious = nFollowing def fillDirectedEdges(self, ascendingEdgeList, descendingEdgeList): ''' Given two lists of edges, one for ascending :class:`~music21.interval.Interval` objects and another for descending, construct appropriate Nodes and Edges. Note that the descending :class:`~music21.interval.Interval` objects should be given in ascending form. ''' self.clear() # if both are equal, then assigning steps is easy if len(ascendingEdgeList) != len(descendingEdgeList): # problem here is that we cannot automatically assign degree values raise IntervalNetworkException('cannot manage unequal sized directed edges') degreeCount = 1 # steps start from one nLow = Node(id=Terminus.LOW, degree=degreeCount) degreeCount += 1 self.nodes[nLow.id] = nLow nPrevious = nLow for i, eName in enumerate(ascendingEdgeList): # first, create the next node if i < len(ascendingEdgeList) - 1: # if not last n = Node(id=self.nodeIdCount, degree=degreeCount) self.nodeIdCount += 1 degreeCount += 1 nFollowing = n else: # if last nHigh = Node(id=Terminus.HIGH, degree=degreeCount) # degree is same as start nFollowing = nHigh # add to node dictionary self.nodes[nFollowing.id] = nFollowing # then, create edge and connection; eName is interval e = Edge(eName, id=self.edgeIdCount) self.edges[e.id] = e self.edgeIdCount += 1 e.addDirectedConnection(nPrevious, nFollowing, direction=Direction.ASCENDING) # update previous with the node created after this edge nPrevious = nFollowing # repeat for descending, but reverse direction, and use # same low and high nodes degreeCount = 1 # steps start from one nLow = self.nodes[Terminus.LOW] # get node; do not need to add degreeCount += 1 nPrevious = nLow for i, eName in enumerate(descendingEdgeList): # first, create the next node if i < len(descendingEdgeList) - 1: # if not last n = Node(id=self.nodeIdCount, degree=degreeCount) self.nodeIdCount += 1 degreeCount += 1 nFollowing = n # add to node dictionary self.nodes[nFollowing.id] = nFollowing else: # if last nHigh = self.nodes[Terminus.HIGH] nFollowing = nHigh # then, create edge and connection e = Edge(eName, id=self.edgeIdCount) self.edges[e.id] = e self.edgeIdCount += 1 # order here is reversed from above e.addDirectedConnection(nFollowing, nPrevious, direction=Direction.DESCENDING) # update previous with the node created after this edge nPrevious = nFollowing def fillArbitrary(self, nodes, edges): # noinspection PyShadowingNames ''' Fill any arbitrary network given node and edge definitions. Nodes must be defined by a dictionary of id and degree values. There must be a terminusLow and terminusHigh id as string:: nodes = ({'id': Terminus.LOW, 'degree': 1}, {'id': 0, 'degree': 2}, {'id': Terminus.HIGH, 'degree': 3}, ) Edges must be defined by a dictionary of :class:`~music21.interval.Interval` strings and connections. Values for `id` will be automatically assigned. Each connection must define direction and pairs of valid node ids:: edges = ({'interval': 'm2', 'connections': ([Terminus.LOW, 0, Direction.BI],) }, {'interval': 'M3', 'connections': ([0, Terminus.HIGH, Direction.BI],) }, ) >>> nodes = ({'id': scale.Terminus.LOW, 'degree': 1}, ... {'id': 0, 'degree': 2}, ... {'id': scale.Terminus.HIGH, 'degree': 3}) >>> edges = ({'interval': 'm2', ... 'connections': ([scale.Terminus.LOW, 0, scale.Direction.BI],)}, ... {'interval': 'M3', ... 'connections': ([0, scale.Terminus.HIGH, scale.Direction.BI],)},) >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillArbitrary(nodes, edges) >>> net.realizePitch('c4', 1) [, , ] ''' self.clear() for nDict in nodes: n = Node(id=nDict['id'], degree=nDict['degree']) if 'weight' in nDict: n.weight = nDict['weight'] self.nodes[n.id] = n eId = 0 for eDict in edges: e = Edge(eDict['interval'], id=eId) for nId1, nId2, direction in eDict['connections']: # do not need to access from nodes dictionary here # but useful as a check that the node has been defined. if direction == Direction.BI: e.addBiDirectedConnections(self.nodes[nId1], self.nodes[nId2]) else: e.addDirectedConnection(self.nodes[nId1], self.nodes[nId2], direction=direction) self.edges[e.id] = e eId += 1 def fillMelodicMinor(self): ''' A convenience routine for testing a complex, bi-directional scale. >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillMelodicMinor() >>> [str(p) for p in net.realizePitch('c4')] ['C4', 'D4', 'E-4', 'F4', 'G4', 'A4', 'B4', 'C5'] ''' nodes = ({'id': Terminus.LOW, 'degree': 1}, # a {'id': 0, 'degree': 2}, # b {'id': 1, 'degree': 3}, # c {'id': 2, 'degree': 4}, # d {'id': 3, 'degree': 5}, # e {'id': 4, 'degree': 6}, # f# ascending {'id': 5, 'degree': 6}, # f {'id': 6, 'degree': 7}, # g# ascending {'id': 7, 'degree': 7}, # g {'id': Terminus.HIGH, 'degree': 8}, # a ) edges = ({'interval': 'M2', 'connections': ([Terminus.LOW, 0, Direction.BI],) # a to b }, {'interval': 'm2', 'connections': ([0, 1, Direction.BI],) # b to c }, {'interval': 'M2', 'connections': ([1, 2, Direction.BI],) # c to d }, {'interval': 'M2', 'connections': ([2, 3, Direction.BI],) # d to e }, {'interval': 'M2', 'connections': ([3, 4, Direction.ASCENDING],) # e to f# }, {'interval': 'M2', 'connections': ([4, 6, Direction.ASCENDING],) # f# to g# }, {'interval': 'm2', 'connections': ([6, Terminus.HIGH, Direction.ASCENDING],) # g# to a }, {'interval': 'M2', 'connections': ([Terminus.HIGH, 7, Direction.DESCENDING],) # a to g }, {'interval': 'M2', 'connections': ([7, 5, Direction.DESCENDING],) # g to f }, {'interval': 'm2', 'connections': ([5, 3, Direction.DESCENDING],) # f to e }, ) self.fillArbitrary(nodes, edges) self.octaveDuplicating = True self.deterministic = True # -------------------------------------------------------------------------- # for weighted selection of nodes def weightedSelection(self, edges, nodes): ''' Perform weighted random selection on a parallel list of edges and corresponding nodes. >>> n1 = scale.intervalNetwork.Node(id=1, degree=1, weight=1000000) >>> n2 = scale.intervalNetwork.Node(id=2, degree=1, weight=1) >>> e1 = scale.intervalNetwork.Edge(interval.Interval('m3'), id=1) >>> e2 = scale.intervalNetwork.Edge(interval.Interval('m3'), id=2) >>> net = scale.intervalNetwork.IntervalNetwork() >>> e, n = net.weightedSelection([e1, e2], [n1, n2]) Note: this may fail as there is a slight chance to get 2 >>> e.id 1 >>> n.id 1 ''' # use index values as values iValues = list(range(len(edges))) weights = [n.weight for n in nodes] # environLocal.printDebug(['weights', weights]) i = common.weightedSelection(iValues, weights) # return corresponding edge and node return edges[i], nodes[i] # -------------------------------------------------------------------------- @property def degreeMin(self): ''' Return the lowest degree value. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.degreeMin 1 ''' x = None for n in self.nodes.values(): if x is None: x = n.degree else: x = min(x, n.degree) return x @property def degreeMax(self): ''' Return the largest degree value. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.degreeMax # returns eight, as this is the last node 8 ''' x = None for n in self.nodes.values(): if x is None: x = n.degree else: x = max(x, n.degree) return x @property def degreeMaxUnique(self): ''' Return the largest degree value that represents a pitch level that is not a terminus of the scale. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.degreeMaxUnique 7 ''' x = None for nId, n in self.nodes.items(): # reject terminus high, as this duplicates terminus low if nId == Terminus.HIGH: continue if x is None: x = n.degree else: x = max(x, n.degree) return x @property def terminusLowNodes(self) -> list[Node]: ''' Return a list of first Nodes, or Nodes that contain Terminus.LOW. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.terminusLowNodes [] Note that this list currently always has one element. ''' post = [] # for now, there is only one post.append(self.nodes[Terminus.LOW]) return post @property def terminusHighNodes(self): ''' Return a list of last Nodes, or Nodes that contain Terminus.HIGH. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.terminusHighNodes [] ''' post = [] # for now, there is only one post.append(self.nodes[Terminus.HIGH]) return post # -------------------------------------------------------------------------- def getNodeDegreeDictionary(self, equateTermini: bool = True): ''' Return a dictionary of node-id, node-degree pairs. The same degree may be given for each node There may not be an unambiguous way to determine the degree. Or, a degree may have different meanings when ascending or descending. If `equateTermini` is True, the terminals will be given the same degree. ''' post: OrderedDict[Terminus|int, int] = OrderedDict() for nId, n in self.nodes.items(): if equateTermini: if nId == Terminus.HIGH: # get the same degree as the low post[nId] = self.nodes[Terminus.LOW].degree else: post[nId] = n.degree else: # directly assign from attribute post[nId] = n.degree return post def nodeIdToDegree(self, nId): ''' Given a strict node id (the .id attribute of the Node), return the degree. There may not be an unambiguous way to determine the degree. Or, a degree may have different meanings when ascending or descending. ''' nodeStep = self.getNodeDegreeDictionary() return nodeStep[nId] # gets degree integer def nodeIdToEdgeDirections(self, nId): ''' Given a Node id, find all edges associated with this node and report on their directions >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillMelodicMinor() >>> net.nodeIdToEdgeDirections(scale.Terminus.LOW) [Direction.BI] >>> net.nodeIdToEdgeDirections(0) [Direction.BI, Direction.BI] >>> net.nodeIdToEdgeDirections(6) [Direction.ASCENDING, Direction.ASCENDING] >>> net.nodeIdToEdgeDirections(5) [Direction.DESCENDING, Direction.DESCENDING] This node has bi-directional (from below), ascending (to above), and descending (from above) edge connections connections >>> net.nodeIdToEdgeDirections(3) [Direction.BI, Direction.ASCENDING, Direction.DESCENDING] ''' collection = [] if isinstance(nId, Node): nObj = nId nId = nObj.id else: nObj = self.nodes[nId] for eId in self.edges: eObj = self.edges[eId] # environLocal.printDebug(['nodeIdToEdgeDirections()', eObj]) for x, y in eObj.connections: # pairs of node ids if x == nId: # this node is a source collection.append(eObj.direction) break # only get one direction for each edge elif y == nId: # this node is a destination collection.append(eObj.direction) break if not collection: raise IntervalNetworkException('failed to match any edges', nObj) return collection def degreeModulus(self, degree: int) -> int: ''' Return the degree modulus degreeMax - degreeMin. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.degreeModulus(3) 3 >>> net.degreeModulus(8) 1 >>> net.degreeModulus(9) 2 >>> net.degreeModulus(0) 7 ''' if degree is None: raise IntervalNetworkException('Degree of None given to degreeModulus') # TODO: these need to be cached sMin = self.degreeMin sMax = self.degreeMax # the number of unique values; assumes redundancy in # top and bottom value, so 8 steps, from 1 to 8, have # seven unique values spanCount = sMax - sMin # assume continuous span, assume start at min # example for diatonic scale degree 3: # ((3 - 1) % 7) + 1 # if (((id - 1) % spanCount) + sMin) == nStep: return ((degree - 1) % spanCount) + sMin def nodeNameToNodes(self, nodeId: Node|int|Terminus|None, *, equateTermini=True, permitDegreeModuli=True): ''' The `nodeId` parameter may be a :class:`~music21.scale.intervalNetwork.Node` object, a node degree (as a number), a terminus string, or a None (indicating Terminus.LOW). Return a list of Node objects that match this identification. If `equateTermini` is True, and the name given is a degree number, then the first terminal will return both the first and last. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.nodeNameToNodes(1)[0] >>> net.nodeNameToNodes(scale.Terminus.HIGH) [] >>> net.nodeNameToNodes(scale.Terminus.LOW) [] Test using a nodeStep, or an integer nodeName >>> net.nodeNameToNodes(1) [, ] >>> net.nodeNameToNodes(1, equateTermini=False) [] >>> net.nodeNameToNodes(2) [] With degree moduli, degree zero is the top-most non-terminal (since terminals are redundant) >>> net.nodeNameToNodes(0) [] >>> net.nodeNameToNodes(-1) [] >>> net.nodeNameToNodes(8) [, ] ''' # if a number, this is interpreted as a node degree if isinstance(nodeId, int): post = [] nodeStep = self.getNodeDegreeDictionary( equateTermini=equateTermini) for nId, nStep in nodeStep.items(): if nodeId == nStep: post.append(self.nodes[nId]) # if no matches, and moduli comparisons are permitted if not post and permitDegreeModuli: for nId, nStep in nodeStep.items(): if self.degreeModulus(nodeId) == nStep: post.append(self.nodes[nId]) return post elif isinstance(nodeId, Terminus): if nodeId == Terminus.LOW: return self.terminusLowNodes # returns a list elif nodeId == Terminus.HIGH: return self.terminusHighNodes # returns a list elif isinstance(nodeId, Node): # look for direct match for nId in self.nodes: n = self.nodes[nId] if n is nodeId: # could be a == comparison? return [n] # return only one elif isinstance(nodeId, str): raise IntervalNetworkException(f'Strings like {nodeId!r} are no longer valid nodeIds.') else: # match coords raise IntervalNetworkException(f'cannot filter by: {nodeId}') def getNext(self, nodeStart, direction): ''' Given a Node, get two lists, one of next Edges, and one of next Nodes, searching all Edges to find all matches. There may be more than one possibility. If so, the caller must look at the Edges and determine which to use >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.nodeNameToNodes(1)[0] ''' postEdge = [] postNodeId = [] # search all edges to find Edges that start with this node id srcId = nodeStart.id # if we are at terminus low and descending, must wrap around if srcId == Terminus.LOW and direction == Direction.DESCENDING: srcId = Terminus.HIGH # if we are at terminus high and ascending, must wrap around elif srcId == Terminus.HIGH and direction == Direction.ASCENDING: srcId = Terminus.LOW for k in self.edges: e = self.edges[k] # only getting ascending connections pairs = e.getConnections(direction) if not pairs: continue for src, dst in pairs: # environLocal.printDebug(['getNext()', 'src, dst', src, dst, # 'trying to match source', srcId]) if src == srcId: postEdge.append(e) postNodeId.append(dst) # this should actually never happen if not postEdge: environLocal.printDebug(['nodeStart', nodeStart, 'direction', direction, 'postEdge', postEdge]) # return None raise IntervalNetworkException('could not find any edges') # if we have multiple edges, we may need to select based on weight postNode = [self.nodes[nId] for nId in postNodeId] return postEdge, postNode def processAlteredNodes(self, alteredDegrees, n, p, *, direction): ''' Return an altered pitch for given node, if an alteration is specified in the alteredDegrees dictionary ''' if not alteredDegrees: return p if n.degree not in alteredDegrees: return p directionSpec = alteredDegrees[n.degree]['direction'] # environLocal.printDebug(['processing altered node', n, p, # 'direction', direction, 'directionSpec', directionSpec]) match = False # if ascending or descending, and this is a bidirectional alteration # then apply if direction == directionSpec: match = True # if request is bidrectional and the spec is for ascending and # descending elif (direction == Direction.BI and directionSpec in (Direction.ASCENDING, Direction.DESCENDING)): match = True elif (direction in (Direction.ASCENDING, Direction.DESCENDING) and directionSpec == Direction.BI): match = True if match: # environLocal.printDebug(['matched direction', direction]) pPost = self.transposePitchAndApplySimplification( alteredDegrees[n.degree]['interval'], p) return pPost return p def getUnalteredPitch( self, pitchObj, nodeObj, *, direction=Direction.BI, alteredDegrees=None ) -> pitch.Pitch: ''' Given a node and alteredDegrees get the unaltered pitch, or return the current object ''' if not alteredDegrees: return pitchObj # TODO: need to take direction into account # do reverse transposition if nodeObj.degree in alteredDegrees: p = self.transposePitchAndApplySimplification( alteredDegrees[nodeObj.degree]['interval'].reverse(), pitchObj) return p return pitchObj def nextPitch( self, pitchReference: pitch.Pitch|str, nodeName: Node|int|Terminus|None, pitchOrigin: pitch.Pitch|str, *, direction: Direction = Direction.ASCENDING, stepSize=1, alteredDegrees=None, getNeighbor: bool|Direction = True ): # noinspection PyShadowingNames ''' Given a pitchReference, nodeName, and a pitch origin, return the next pitch. The `nodeName` parameter may be a :class:`~music21.scale.intervalNetwork.Node` object, a node degree, a Terminus Enum, or a None (indicating Terminus.LOW). >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.nextPitch('g', 1, 'f#5', direction=scale.Direction.ASCENDING) >>> net.nextPitch('g', 1, 'f#5', direction=scale.Direction.DESCENDING) The `stepSize` parameter can be configured to permit different sized steps in the specified direction. >>> net.nextPitch('g', 1, 'f#5', ... direction=scale.Direction.ASCENDING, ... stepSize=2) Altered degrees can be given to temporarily change the pitches returned without affecting the network as a whole. >>> alteredDegrees = {2: {'direction': scale.Direction.BI, ... 'interval': interval.Interval('-a1')}} >>> net.nextPitch('g', 1, 'g2', ... direction=scale.Direction.ASCENDING, ... alteredDegrees=alteredDegrees) >>> net.nextPitch('g', 1, 'a-2', ... direction=scale.Direction.ASCENDING, ... alteredDegrees=alteredDegrees) ''' if pitchOrigin is None: raise TypeError('No pitch origin for calling next on this pitch!') if isinstance(pitchOrigin, str): pitchOriginObj = pitch.Pitch(pitchOrigin) else: pitchOriginObj = copy.deepcopy(pitchOrigin) pCollect = None # get the node id that we are starting with nodeId = self.getRelativeNodeId(pitchReference, nodeId=nodeName, pitchTarget=pitchOriginObj, direction=direction, alteredDegrees=alteredDegrees) # environLocal.printDebug(['nextPitch()', 'got node Id', nodeId, # 'direction', direction, 'self.nodes[nodeId].degree', self.nodes[nodeId].degree, # 'pitchOriginObj', pitchOriginObj]) usedNeighbor = False # if no match, get the neighbor if (nodeId is None and getNeighbor in (True, Direction.ASCENDING, Direction.DESCENDING, Direction.BI)): usedNeighbor = True lowId, highId = self.getNeighborNodeIds(pitchReference=pitchReference, nodeName=nodeName, pitchTarget=pitchOriginObj, direction=direction) # must add direction # environLocal.printDebug(['nextPitch()', 'looking for neighbor', # 'getNeighbor', getNeighbor, 'source nodeId', nodeId, # 'lowId/highId', lowId, highId]) # replace the node with the nearest neighbor if getNeighbor == Direction.DESCENDING: nodeId = lowId else: nodeId = highId # realize the pitch from the found node degree # we may be getting an altered # tone, and we need to transpose an unaltered tone, thus # leave out altered nodes argument p = self.getPitchFromNodeDegree( pitchReference=pitchReference, nodeName=nodeName, nodeDegreeTarget=self.nodes[nodeId].degree, direction=direction, minPitch=None, # not using a range here to maxPitch=None, # get natural expansion alteredDegrees=None # need unaltered tone here, thus omitted ) # environLocal.printDebug(['nextPitch()', 'pitch obtained based on nodeName', # nodeName, 'p', p, 'nodeId', nodeId, 'self.nodes[nodeId].degree', # self.nodes[nodeId].degree]) # transfer octave from origin to new pitch derived from node # note: this assumes octave equivalence and may be a problem p.octave = pitchOriginObj.octave # correct for derived pitch crossing octave boundary # https://github.com/cuthbertLab/music21/issues/319 alterSemitones = 0 degree = self.nodeIdToDegree(nodeId) if alteredDegrees and degree in alteredDegrees: alterSemitones = alteredDegrees[degree]['interval'].semitones if ((usedNeighbor and getNeighbor == Direction.DESCENDING) or (not usedNeighbor and direction == Direction.ASCENDING)): while p.octave is not None and p.transpose(alterSemitones) > pitchOriginObj: p.octave -= 1 else: while p.octave is not None and p.transpose(alterSemitones) < pitchOriginObj: p.octave += 1 # pitchObj = p n = self.nodes[nodeId] # pCollect = p # usually p, unless altered for i in range(stepSize): postEdge, postNode = self.getNext(n, direction) if len(postEdge) > 1: # do a weighted selection based on node weights, e, n = self.weightedSelection(postEdge, postNode) intervalObj = e.interval else: intervalObj = postEdge[0].interval # get first n = postNode[0] # n is passed on # environLocal.printDebug(['nextPitch()', 'intervalObj', intervalObj, # 'p', p, 'postNode', postNode]) # n = postNode[0] # for now, only taking first edge if direction == Direction.ASCENDING: p = self.transposePitchAndApplySimplification(intervalObj, p) else: p = self.transposePitchAndApplySimplification(intervalObj.reverse(), p) pCollect = self.processAlteredNodes(alteredDegrees=alteredDegrees, n=n, p=p, direction=direction) return pCollect # TODO: need to collect intervals as well def _getCacheKey( self, nodeObj: Node, pitchReference: pitch.Pitch, minPitch: pitch.Pitch|None, maxPitch: pitch.Pitch|None, *, includeFirst: bool, reverse: bool|None = None, # only meaningful for descending ) -> CacheKey: ''' Return key for caching based on critical components. ''' if minPitch is not None: minKey = minPitch.nameWithOctave else: minKey = None if maxPitch is not None: maxKey = maxPitch.nameWithOctave else: maxKey = None return (nodeObj.id, pitchReference.nameWithOctave, minKey, maxKey, includeFirst, reverse, ) def realizeAscending( self, pitchReference: pitch.Pitch|str, nodeId: Node|int|Terminus|None = None, minPitch: pitch.Pitch|str|None = None, maxPitch: pitch.Pitch|str|None = None, *, alteredDegrees=None, fillMinMaxIfNone=False ) -> tuple[list[pitch.Pitch], list[Terminus|int]]: # noinspection PyShadowingNames ''' Given a reference pitch, realize upwards to a maximum pitch. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> (pitches, nodeKeys) = net.realizeAscending('c2', 1, 'c5', 'c6') >>> [str(p) for p in pitches] ['C5', 'D5', 'E5', 'F5', 'G5', 'A5', 'B5', 'C6'] >>> nodeKeys [Terminus.HIGH, 0, 1, 2, 3, 4, 5, Terminus.HIGH] >>> net = scale.intervalNetwork.IntervalNetwork(octaveDuplicating=True) >>> net.fillBiDirectedEdges(edgeList) >>> (pitches, nodeKeys) = net.realizeAscending('c2', 1, 'c5', 'c6') >>> [str(p) for p in pitches] ['C5', 'D5', 'E5', 'F5', 'G5', 'A5', 'B5', 'C6'] >>> nodeKeys [Terminus.LOW, 0, 1, 2, 3, 4, 5, Terminus.HIGH] ''' if isinstance(pitchReference, str): pitchReference = pitch.Pitch(pitchReference) else: pitchReference = copy.deepcopy(pitchReference) # get first node if no node is provided if isinstance(nodeId, Node): nodeObj = nodeId elif nodeId is None: # assume first nodeObj = self.terminusLowNodes[0] else: nodeObj = self.nodeNameToNodes(nodeId)[0] # must set an octave for pitch reference, even if not given if pitchReference.octave is None: pitchReference.octave = pitchReference.implicitOctave if isinstance(minPitch, str): minPitch = pitch.Pitch(minPitch) if isinstance(maxPitch, str): maxPitch = pitch.Pitch(maxPitch) if fillMinMaxIfNone and minPitch is None and maxPitch is None: minPitch, maxPitch = self.realizeMinMax(pitchReference, nodeObj, alteredDegrees=alteredDegrees) # when the pitch reference is altered, we need to get the # unaltered version of this pitch. pitchReference = self.getUnalteredPitch(pitchReference, nodeObj, direction=Direction.ASCENDING, alteredDegrees=alteredDegrees) # see if we can get from cache if self.deterministic: # environLocal.printDebug('using cached scale segment') ck = self._getCacheKey(nodeObj, pitchReference, minPitch, maxPitch, includeFirst=False) if ck in self._ascendingCache: return self._ascendingCache[ck] else: ck = None # if this network is octaveDuplicating, then we can shift # reference up octaves to just below minPitch if self.octaveDuplicating and minPitch is not None: pitchReference.transposeBelowTarget(minPitch, minimize=True, inPlace=True) # first, go upward from this pitch to the high terminus n = nodeObj p = pitchReference # we start with the pitch that is the reference pCollect = p # usually p, unless the tone has been altered post = [] postNodeId = [] # store node ids as well # environLocal.printDebug(['realizeAscending()', 'n', n]) attempts = 0 maxAttempts = 100 while attempts < maxAttempts: attempts += 1 # environLocal.printDebug(['realizeAscending()', 'p', p]) appendPitch = False if (minPitch is not None and _gte(pCollect.ps, minPitch.ps) and maxPitch is not None and _lte(pCollect.ps, maxPitch.ps)): appendPitch = True elif (minPitch is not None and _gte(pCollect.ps, minPitch.ps) and maxPitch is None): appendPitch = True elif (maxPitch is not None and _lte(pCollect.ps, maxPitch.ps) and minPitch is None): appendPitch = True elif minPitch is None and maxPitch is None: appendPitch = True if appendPitch: post.append(pCollect) postNodeId.append(n.id) if maxPitch is not None and _gte(p.ps, maxPitch.ps): break # environLocal.printDebug(['realizeAscending()', 'n', n, 'n.id', n.id]) # must check first, and at end if n.id == Terminus.HIGH: if maxPitch is None: # if not defined, stop at terminus high break n = self.terminusLowNodes[0] # this returns a list of possible edges and nodes nextBundle = self.getNext(n, Direction.ASCENDING) # environLocal.printDebug(['realizeAscending()', 'n', n, 'nextBundle', nextBundle]) # if we cannot continue to ascend, then we must break if nextBundle is None: break postEdge, postNode = nextBundle # make probabilistic selection here if more than one if len(postEdge) > 1: # do a weighted selection based on node weights, # return on edge, one node # environLocal.printDebug(['realizeAscending()', 'doing weighted selection']) e, n = self.weightedSelection(postEdge, postNode) intervalObj = e.interval else: intervalObj = postEdge[0].interval # get first n = postNode[0] # n is passed on p = self.transposePitchAndApplySimplification(intervalObj, p) pCollect = p pCollect = self.processAlteredNodes(alteredDegrees=alteredDegrees, n=n, p=p, direction=Direction.ASCENDING) if attempts >= maxAttempts: raise IntervalNetworkException( 'Cannot realize these pitches; is your scale ' + "well-formed? (especially check if you're giving notes without octaves)") # store in cache if self.deterministic and ck is not None: self._ascendingCache[ck] = post, postNodeId # environLocal.printDebug(['realizeAscending()', 'post', post, 'postNodeId', postNodeId]) return post, postNodeId def realizeDescending( self, pitchReference: pitch.Pitch|str, nodeId: Node|int|Terminus|None = None, minPitch: pitch.Pitch|str|None = None, maxPitch: pitch.Pitch|str|None = None, *, alteredDegrees=None, includeFirst=False, fillMinMaxIfNone=False, reverse=True ): # noinspection PyShadowingNames ''' Given a reference pitch, realize downward to a minimum. If no minimum is given, the terminus is used. If `includeFirst` is False, the starting (highest) pitch will not be included. If `fillMinMaxIfNone` is True, a min and max will be artificially derived from an ascending scale and used as min and max values. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.realizeDescending('c2', 1, 'c3') # minimum is above ref ([], []) >>> (pitches, nodeKeys) = net.realizeDescending('c3', 1, 'c2') >>> [str(p) for p in pitches] ['C2', 'D2', 'E2', 'F2', 'G2', 'A2', 'B2'] >>> nodeKeys [Terminus.LOW, 0, 1, 2, 3, 4, 5] >>> (pitches, nodeKeys) = net.realizeDescending('c3', 1, 'c2', includeFirst=True) >>> [str(p) for p in pitches] ['C2', 'D2', 'E2', 'F2', 'G2', 'A2', 'B2', 'C3'] >>> nodeKeys [Terminus.LOW, 0, 1, 2, 3, 4, 5, Terminus.LOW] >>> (pitches, nodeKeys) = net.realizeDescending('a6', scale.Terminus.HIGH) >>> [str(p) for p in pitches] ['A5', 'B5', 'C#6', 'D6', 'E6', 'F#6', 'G#6'] >>> nodeKeys [Terminus.LOW, 0, 1, 2, 3, 4, 5] >>> (pitches, nodeKeys) = net.realizeDescending('a6', scale.Terminus.HIGH, ... includeFirst=True) >>> [str(p) for p in pitches] ['A5', 'B5', 'C#6', 'D6', 'E6', 'F#6', 'G#6', 'A6'] >>> nodeKeys [Terminus.LOW, 0, 1, 2, 3, 4, 5, Terminus.HIGH] >>> net = scale.intervalNetwork.IntervalNetwork(octaveDuplicating=True) >>> net.fillBiDirectedEdges(edgeList) >>> (pitches, nodeKeys) = net.realizeDescending('c2', 1, 'c0', 'c1') >>> [str(p) for p in pitches] ['C0', 'D0', 'E0', 'F0', 'G0', 'A0', 'B0'] >>> nodeKeys [Terminus.LOW, 0, 1, 2, 3, 4, 5] ''' ck = None if isinstance(pitchReference, str): pitchRef = pitch.Pitch(pitchReference) else: pitchRef = copy.deepcopy(pitchReference) # must set an octave for pitch reference, even if not given if pitchRef.octave is None: pitchRef.octave = 4 # get first node if no node is provided if isinstance(nodeId, Node): nodeObj = nodeId elif nodeId is None: # assume low terminus by default # this is useful for appending a descending segment with an # ascending segment nodeObj = self.terminusLowNodes[0] else: nodeObj = self.nodeNameToNodes(nodeId)[0] minPitchObj: pitch.Pitch|None if isinstance(minPitch, str): minPitchObj = pitch.Pitch(minPitch) else: minPitchObj = minPitch maxPitchObj: pitch.Pitch|None if isinstance(maxPitch, str): maxPitchObj = pitch.Pitch(maxPitch) else: maxPitchObj = maxPitch if fillMinMaxIfNone and minPitchObj is None and maxPitchObj is None: # environLocal.printDebug(['realizeDescending()', 'fillMinMaxIfNone']) minPitchObj, maxPitchObj = self.realizeMinMax(pitchRef, nodeObj, alteredDegrees=alteredDegrees) # when the pitch reference is altered, we need to get the # unaltered version of this pitch. pitchRef = self.getUnalteredPitch(pitchRef, nodeObj, direction=Direction.DESCENDING, alteredDegrees=alteredDegrees) # see if we can get from cache if self.deterministic: ck = self._getCacheKey(nodeObj, pitchRef, minPitch=minPitchObj, maxPitch=maxPitchObj, includeFirst=includeFirst, reverse=reverse, ) if ck in self._descendingCache: return self._descendingCache[ck] # if this network is octaveDuplicating, then we can shift # reference down octaves to just above minPitch if self.octaveDuplicating and maxPitchObj is not None: pitchRef.transposeAboveTarget(maxPitchObj, minimize=True, inPlace=True) n = nodeObj p = pitchRef pCollect = p # usually p, unless the tone has been altered pre = [] preNodeId = [] # store node ids as well isFirst = True while True: appendPitch = False if (minPitchObj is not None and _gte(p.ps, minPitchObj.ps) and maxPitchObj is not None and _lte(p.ps, maxPitchObj.ps)): appendPitch = True elif (minPitchObj is not None and _gte(p.ps, minPitchObj.ps) and maxPitchObj is None): appendPitch = True elif (maxPitchObj is not None and _lte(p.ps, maxPitchObj.ps) and minPitchObj is None): appendPitch = True elif minPitchObj is None and maxPitchObj is None: appendPitch = True # environLocal.printDebug(['realizeDescending', 'appending pitch', pCollect, # 'includeFirst', includeFirst]) if (appendPitch and not isFirst) or (appendPitch and isFirst and includeFirst): pre.append(pCollect) preNodeId.append(n.id) isFirst = False if minPitchObj is not None and p.ps <= minPitchObj.ps: break if n.id == Terminus.LOW: if minPitchObj is None: # if not defined, stop at terminus high break # get high and continue n = self.terminusHighNodes[0] if n.id == Terminus.LOW: if minPitchObj is None: # if not defined, stop at terminus high break nextBundle = self.getNext(n, Direction.DESCENDING) # environLocal.printDebug(['realizeDescending()', 'n', n, 'nextBundle', nextBundle]) if nextBundle is None: break postEdge, postNode = nextBundle if len(postEdge) > 1: # do a weighted selection based on node weights, # return on edge, one node # environLocal.printDebug(['realizeDescending()', 'doing weighted selection']) e, n = self.weightedSelection(postEdge, postNode) intervalObj = e.interval else: intervalObj = postEdge[0].interval # get first n = postNode[0] # n is passed on p = self.transposePitchAndApplySimplification(intervalObj.reverse(), p) pCollect = self.processAlteredNodes(alteredDegrees=alteredDegrees, n=n, p=p, direction=Direction.DESCENDING) if reverse: pre.reverse() preNodeId.reverse() # store in cache if self.deterministic and ck is not None: self._descendingCache[ck] = pre, preNodeId return pre, preNodeId def realize(self, pitchReference: str|pitch.Pitch, nodeId: Node|int|Terminus|None = None, minPitch: pitch.Pitch|str|None = None, maxPitch: pitch.Pitch|str|None = None, direction: Direction = Direction.ASCENDING, alteredDegrees=None, reverse=False): # noinspection PyShadowingNames ''' Realize the nodes of this network based on a pitch assigned to a valid `nodeId`, where `nodeId` can be specified by integer (starting from 1) or key (a tuple of origin, destination keys). Without a min or max pitch, the given pitch reference is assigned to the designated node, and then both ascends to the terminus and descends to the terminus. The `alteredDegrees` dictionary permits creating mappings between node degree and direction and :class:`~music21.interval.Interval` based transpositions. Returns two lists, a list of pitches, and a list of Node keys. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> (pitches, nodeKeys) = net.realize('c2', 1, 'c2', 'c3') >>> [str(p) for p in pitches] ['C2', 'D2', 'E2', 'F2', 'G2', 'A2', 'B2', 'C3'] >>> nodeKeys [Terminus.LOW, 0, 1, 2, 3, 4, 5, Terminus.HIGH] >>> alteredDegrees = {7: {'direction': scale.Direction.BI, ... 'interval': interval.Interval('-a1')}} >>> (pitches, nodeKeys) = net.realize('c2', 1, 'c2', 'c4', alteredDegrees=alteredDegrees) >>> [str(p) for p in pitches] ['C2', 'D2', 'E2', 'F2', 'G2', 'A2', 'B-2', 'C3', 'D3', 'E3', 'F3', 'G3', 'A3', 'B-3', 'C4'] >>> nodeKeys [Terminus.LOW, 0, 1, 2, 3, 4, 5, Terminus.HIGH, 0, 1, 2, 3, 4, 5, Terminus.HIGH] ''' # get first node if no node is provided # environLocal.printDebug(['got pre pitch:', pre]) # environLocal.printDebug(['got pre node:', preNodeId]) if pitchReference is None: raise IntervalNetworkException('pitchReference cannot be None') if isinstance(pitchReference, str): pitchRef = pitch.Pitch(pitchReference) else: # make a copy b/c may manipulate pitchRef = copy.deepcopy(pitchReference) # must set an octave for pitch reference, even if not given if pitchRef.octave is None: pitchRef.octave = pitchRef.implicitOctave minPitchObj: pitch.Pitch|None if isinstance(minPitch, str): minPitchObj = pitch.Pitch(minPitch) else: minPitchObj = minPitch maxPitchObj: pitch.Pitch|None if isinstance(maxPitch, str): maxPitchObj = pitch.Pitch(maxPitch) else: maxPitchObj = maxPitch directedRealization = False if self.octaveDuplicating: directedRealization = True # environLocal.printDebug(['directedRealization', directedRealization, # 'direction', direction, 'octaveDuplicating', self.octaveDuplicating]) # realize by calling ascending/descending if directedRealization: # assumes we have min and max pitch as not none if direction == Direction.ASCENDING: # move pitch reference to below minimum if self.octaveDuplicating and minPitchObj is not None: pitchRef.transposeBelowTarget(minPitchObj, inPlace=True) mergedPitches, mergedNodes = self.realizeAscending( pitchReference=pitchRef, nodeId=nodeId, minPitch=minPitchObj, maxPitch=maxPitchObj, alteredDegrees=alteredDegrees, fillMinMaxIfNone=True) elif direction == Direction.DESCENDING: # move pitch reference to above minimum if self.octaveDuplicating and maxPitchObj is not None: pitchRef.transposeAboveTarget(maxPitchObj, inPlace=True) # fillMinMaxIfNone will result in a complete scale # being returned if no min and max are given (otherwise # we would just get the reference pitch). mergedPitches, mergedNodes = self.realizeDescending( pitchReference=pitchRef, nodeId=nodeId, minPitch=minPitchObj, maxPitch=maxPitchObj, alteredDegrees=alteredDegrees, includeFirst=True, fillMinMaxIfNone=True) elif direction == Direction.BI: # this is a union of both ascending and descending pitchReferenceA = copy.deepcopy(pitchRef) pitchReferenceB = copy.deepcopy(pitchRef) if self.octaveDuplicating and minPitchObj is not None: pitchReferenceA.transposeBelowTarget(minPitchObj, inPlace=True) # pitchReferenceA.transposeBelowTarget(minPitchObj, inPlace=True) post, postNodeId = self.realizeAscending(pitchReference=pitchReferenceA, nodeId=nodeId, minPitch=minPitchObj, maxPitch=maxPitchObj, alteredDegrees=alteredDegrees) if self.octaveDuplicating and maxPitchObj is not None: pitchReferenceB.transposeAboveTarget(maxPitchObj, inPlace=True) # pitchReferenceB.transposeAboveTarget(maxPitchObj, inPlace=True) pre, preNodeId = self.realizeDescending(pitchReference=pitchReferenceB, nodeId=nodeId, minPitch=minPitchObj, maxPitch=maxPitchObj, alteredDegrees=alteredDegrees, includeFirst=True) # We need to create union of both lists, but keep order, # and also keep the nodeId list in order merged = [] foundPitches = [] # just for membership comparison i = 0 j = 0 preventPermanentRecursion = 9999 while preventPermanentRecursion > 0: preventPermanentRecursion -= 1 if i < len(post) and post[i] not in foundPitches: foundPitches.append(post[i]) merged.append((post[i], postNodeId[i])) i += 1 if j < len(pre) and pre[j] not in foundPitches: foundPitches.append(pre[j]) merged.append((pre[j], preNodeId[j])) j += 1 # after increment, will be eq to len of list # when both complete, break if i >= len(post) and j >= len(pre): break # transfer to two lists mergedPitches = [] mergedNodes = [] for x, y in merged: mergedPitches.append(x) mergedNodes.append(y) else: raise IntervalNetworkException( f'cannot match direction specification: {direction!r}') else: # non directed realization # TODO: if not octave repeating, and ascending or descending, # have to travel to a pitch # at the proper extreme, and then go the opposite way # presently, this will realize ascending from reference, # then descending from reference post, postNodeId = self.realizeAscending(pitchReference=pitchRef, nodeId=nodeId, minPitch=minPitchObj, maxPitch=maxPitchObj, alteredDegrees=alteredDegrees) pre, preNodeId = self.realizeDescending(pitchReference=pitchRef, nodeId=nodeId, minPitch=minPitchObj, maxPitch=maxPitchObj, alteredDegrees=alteredDegrees, includeFirst=False) # environLocal.printDebug(['realize()', 'pre', pre, preNodeId]) mergedPitches, mergedNodes = pre + post, preNodeId + postNodeId if reverse: # Make new objects, because this value might be cached in intervalNetwork's # _descendingCache, and mutating it would be dangerous. mergedPitches = list(reversed(mergedPitches)) mergedNodes = list(reversed(mergedNodes)) return mergedPitches, mergedNodes def realizePitch( self, pitchReference: str|pitch.Pitch, nodeId: Node|int|Terminus|None = None, minPitch: pitch.Pitch|str|None = None, maxPitch: pitch.Pitch|str|None = None, direction: Direction = Direction.ASCENDING, alteredDegrees=None, reverse=False, ) -> list[pitch.Pitch]: ''' Realize the native nodes of this network based on a pitch assigned to a valid `nodeId`, where `nodeId` can be specified by integer (starting from 1) or key (a tuple of origin, destination keys). The nodeId, when a simple, linear network, can be used as a scale degree value starting from one. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> [str(p) for p in net.realizePitch(pitch.Pitch('G3'))] ['G3', 'A3', 'B3', 'C4', 'D4', 'E4', 'F#4', 'G4'] G3 is the fifth (scale) degree >>> [str(p) for p in net.realizePitch(pitch.Pitch('G3'), 5)] ['C3', 'D3', 'E3', 'F3', 'G3', 'A3', 'B3', 'C4'] G3 is the seventh (scale) degree >>> [str(p) for p in net.realizePitch(pitch.Pitch('G3'), 7) ] ['A-2', 'B-2', 'C3', 'D-3', 'E-3', 'F3', 'G3', 'A-3'] >>> [str(p) for p in net.realizePitch(pitch.Pitch('f#3'), 1, 'f2', 'f3') ] ['E#2', 'F#2', 'G#2', 'A#2', 'B2', 'C#3', 'D#3', 'E#3'] >>> [str(p) for p in net.realizePitch(pitch.Pitch('a#2'), 7, 'c6', 'c7')] ['C#6', 'D#6', 'E6', 'F#6', 'G#6', 'A#6', 'B6'] Circle of fifths >>> edgeList = ['P5'] * 6 + ['d6'] + ['P5'] * 5 >>> net5ths = scale.intervalNetwork.IntervalNetwork() >>> net5ths.fillBiDirectedEdges(edgeList) >>> [str(p) for p in net5ths.realizePitch(pitch.Pitch('C1'))] ['C1', 'G1', 'D2', 'A2', 'E3', 'B3', 'F#4', 'D-5', 'A-5', 'E-6', 'B-6', 'F7', 'C8'] >>> [str(p) for p in net5ths.realizePitch(pitch.Pitch('C2'))] ['C2', 'G2', 'D3', 'A3', 'E4', 'B4', 'F#5', 'D-6', 'A-6', 'E-7', 'B-7', 'F8', 'C9'] ''' components = self.realize( pitchReference=pitchReference, nodeId=nodeId, minPitch=minPitch, maxPitch=maxPitch, direction=direction, alteredDegrees=alteredDegrees, reverse=reverse) return components[0] # just return first component def realizeIntervals( self, nodeId: Node|int|Terminus|None = None, minPitch: pitch.Pitch|str|None = None, maxPitch: pitch.Pitch|str|None = None, direction: Direction = Direction.ASCENDING, alteredDegrees=None, reverse=False, ) -> list[interval.Interval]: ''' Realize the sequence of intervals between the specified pitches, or the termini. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.realizeIntervals() [, , , , , , ] ''' # note: there may be a more efficient way to do this, but we still # need to realize the intervals due to probabilistic selection # provide an arbitrary pitch reference pitchReference = 'c4' pList = self.realize(pitchReference=pitchReference, nodeId=nodeId, minPitch=minPitch, maxPitch=maxPitch, direction=direction, alteredDegrees=alteredDegrees, reverse=reverse)[0] # just return first component iList = [] for i, p1 in enumerate(pList): if i < len(pList) - 1: p2 = pList[i + 1] iList.append(interval.Interval(p1, p2)) return iList def realizeTermini( self, pitchReference: str|pitch.Pitch, nodeId: Node|int|Terminus|None = None, alteredDegrees=None, ) -> tuple[pitch.Pitch, pitch.Pitch]: ''' Realize the pitches of the 'natural' terminus of a network. This (presently) must be done by ascending, and assumes only one valid terminus for both extremes. This suggests that in practice termini should not be affected by directionality. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.realizeTermini(pitch.Pitch('G3')) (, ) >>> net.realizeTermini(pitch.Pitch('a6')) (, ) ''' # must do a non-directed realization with no min/max # will go up from reference, then down from reference, stopping # at the termini post = self.realizeAscending( pitchReference=pitchReference, nodeId=nodeId, alteredDegrees=alteredDegrees, fillMinMaxIfNone=False)[0] # avoid recursion by setting false pre = self.realizeDescending( pitchReference=pitchReference, nodeId=nodeId, alteredDegrees=alteredDegrees, includeFirst=False, fillMinMaxIfNone=False)[0] # avoid recursion by setting false # environLocal.printDebug(['realize()', 'pre', pre, preNodeId]) mergedPitches = pre + post # environLocal.printDebug(['realizeTermini()', 'pList', mergedPitches, # 'pitchReference', pitchReference, 'nodeId', nodeId]) return mergedPitches[0], mergedPitches[-1] def realizeMinMax( self, pitchReference: str|pitch.Pitch, nodeId: Node|int|Terminus|None = None, alteredDegrees=None, ) -> tuple[pitch.Pitch, pitch.Pitch]: ''' Realize the min and max pitches of the scale, or the min and max values found between two termini. This suggests that min and max might be beyond the terminus. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) >>> net.realizeMinMax(pitch.Pitch('C4')) (, ) >>> net.realizeMinMax(pitch.Pitch('B-5')) (, ) Note that it might not always be two octaves apart # s = scale.AbstractDiatonicScale('major') # s._net.realizeMinMax(pitch.Pitch('D2')) # (, ) ''' # first, get termini, then extend by an octave. low, high = self.realizeTermini(pitchReference=pitchReference, nodeId=nodeId, alteredDegrees=alteredDegrees) # note: in some cases this range may need to be extended low = low.transpose(-12) high = high.transpose(12) post, postNodeId = self.realizeAscending( pitchReference=pitchReference, nodeId=nodeId, alteredDegrees=alteredDegrees, minPitch=low, maxPitch=high, fillMinMaxIfNone=False) # avoid recursion by setting false pre, preNodeId = self.realizeDescending( pitchReference=pitchReference, nodeId=nodeId, minPitch=low, maxPitch=high, alteredDegrees=alteredDegrees, includeFirst=True, fillMinMaxIfNone=False) # avoid recursion by setting false # environLocal.printDebug(['realizeMinMax()', 'post', post, 'postNodeId', postNodeId]) postPairs = [] collect = False for i, nId in enumerate(postNodeId): p = post[i] # if first id is a terminus, skip if i == 0 and nId in (Terminus.LOW, Terminus.HIGH): continue # turn off collection after finding next terminus elif nId in (Terminus.LOW, Terminus.HIGH) and collect is True: postPairs.append((p, nId)) break elif nId in (Terminus.LOW, Terminus.HIGH) and collect is False: collect = True if collect: postPairs.append((p, nId)) # environLocal.printDebug(['realizeMinMax()', 'postPairs', postPairs]) prePairs = [] collect = False for i, nId in enumerate(preNodeId): p = pre[i] # if first id is a terminus, skip if i == 0 and nId in (Terminus.LOW, Terminus.HIGH): continue # turn off collection after finding next terminus elif nId in (Terminus.LOW, Terminus.HIGH) and collect is True: prePairs.append((p, nId)) break elif nId in (Terminus.LOW, Terminus.HIGH) and collect is False: collect = True if collect: prePairs.append((p, nId)) # environLocal.printDebug(['realizeMinMax()', 'prePairs', prePairs]) # now, we have pairs that are one span, from each terminus; need to # now find lowest and highest pitch minPitch = post[-1] maxPitch = post[0] for p, nId in postPairs + prePairs: if p.ps < minPitch.ps: minPitch = p if p.ps > maxPitch.ps: maxPitch = p # may not be first or last to get min/max return minPitch, maxPitch def realizePitchByDegree( self, pitchReference: pitch.Pitch|str, nodeId: Node|int|Terminus|None = None, nodeDegreeTargets=(1,), minPitch: pitch.Pitch|str|None = None, maxPitch: pitch.Pitch|str|None = None, direction: Direction = Direction.ASCENDING, alteredDegrees=None, ): # noinspection PyShadowingNames ''' Realize the native nodes of this network based on a pitch assigned to a valid `nodeId`, where `nodeId` can be specified by integer (starting from 1) or key (a tuple of origin, destination keys). The `nodeDegreeTargets` specifies the degrees to be included within the specified range. Example: build a network of the Major scale: >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork() >>> net.fillBiDirectedEdges(edgeList) Now for every "scale" where G is the 3rd degree, give me the tonic if that note is between C2 and C3. (There's only one such note: E-2). >>> net.realizePitchByDegree('G', 3, [1], 'c2', 'c3') [] But between c2 and f3 there are two, E-2 and E-3 (it doesn't matter that the G which is scale degree 3 for E-3 is above F3): >>> net.realizePitchByDegree('G', 3, [1], 'c2', 'f3') [, ] Give us nodes 1, 2, and 5 for scales where G is node 5 (e.g., C major's dominant) where any pitch is between C2 and F4 >>> pitchList = net.realizePitchByDegree('G', 5, [1, 2, 5], 'c2', 'f4') >>> print(' '.join([str(p) for p in pitchList])) C2 D2 G2 C3 D3 G3 C4 D4 There are no networks based on the major scale's edge-list where with node 1 (i.e. "tonic") between C2 and F2 where G is scale degree 7 >>> net.realizePitchByDegree('G', 7, [1], 'c2', 'f2') [] ''' realizedPitch, realizedNode = self.realize( pitchReference=pitchReference, nodeId=nodeId, minPitch=minPitch, maxPitch=maxPitch, direction=direction, alteredDegrees=alteredDegrees) # take modulus of all nodeDegreeTargetsModulus = [self.degreeModulus(s) for s in nodeDegreeTargets] # environLocal.printDebug(['realizePitchByDegree(); nodeDegreeTargets', nodeDegreeTargets]) post = [] for i, p in enumerate(realizedPitch): # get the node n = self.nodes[realizedNode[i]] # environLocal.printDebug(['realizePitchByDegree(); p', p, n.degree]) if self.degreeModulus(n.degree) in nodeDegreeTargetsModulus: post.append(p) return post def getNetworkxGraph(self): ''' Create a networkx graph from the raw Node representation. Return a networks Graph object representing a realized version of this IntervalNetwork if networkx is installed ''' # noinspection PyPackageRequirements import networkx # type: ignore # pylint: disable=import-error weight = 1 style = 'solid' def sortTerminusLowThenIntThenTerminusHigh(a): ''' return a two-tuple where the first element is -1 if 'Terminus.LOW', 0 if an int, and 1 if 'Terminus.HIGH' or another string, and the second element is the value itself. ''' sortFirst = 0 if isinstance(a, str): if a.upper() == 'Terminus.LOW': sortFirst = -1 else: sortFirst = 1 return (sortFirst, a) # g = networkx.DiGraph() g = networkx.MultiDiGraph() for unused_eId, e in self.edges.items(): if e.direction == Direction.ASCENDING: weight = 0.9 # these values are just for display style = 'solid' elif e.direction == Direction.DESCENDING: weight = 0.6 style = 'solid' elif e.direction == Direction.BI: weight = 1.0 style = 'solid' for src, dst in e.connections: g.add_edge(src, dst, weight=weight, style=style) # set positions of all nodes based on degree, where y value is degree # and x is count of values at that degree degreeCount = OrderedDict() # degree, count pairs # sorting nodes will help, but not insure, proper positioning nKeys = list(self.nodes.keys()) nKeys.sort(key=sortTerminusLowThenIntThenTerminusHigh) for nId in nKeys: n = self.nodes[nId] if n.degree not in degreeCount: degreeCount[n.degree] = 0 g.node[nId]['pos'] = (degreeCount[n.degree], n.degree) degreeCount[n.degree] += 1 environLocal.printDebug(['got degree count', degreeCount]) return g def plot(self, **keywords): ''' Given a method and keyword configuration arguments, create and display a plot. Requires `networkx` to be installed. * Changed in v8: other parameters were unused and removed. ''' # # >>> s = corpus.parse('bach/bwv324.xml') #_DOCS_HIDE # >>> s.plot('pianoroll', doneAction=None) #_DOCS_HIDE # >>> #_DOCS_SHOW s = corpus.parse('bach/bwv57.8') # >>> #_DOCS_SHOW s.plot('pianoroll') # # .. image:: images/PlotHorizontalBarPitchSpaceOffset.* # :width: 600 # import is here to avoid import of matplotlib problems from music21 import graph # first ordered arg can be method type g = graph.primitives.GraphNetworkxGraph( networkxGraph=self.getNetworkxGraph()) g.process() def getRelativeNodeId( self, pitchReference: pitch.Pitch|str, nodeId: Node|int|Terminus|None, pitchTarget: pitch.Pitch|note.Note|str, *, comparisonAttribute: str = 'ps', direction: Direction = Direction.ASCENDING, alteredDegrees=None ): ''' Given a reference pitch assigned to node id, determine the relative node id of pitchTarget, even if displaced over multiple octaves The `nodeId` parameter may be a :class:`~music21.scale.intervalNetwork.Node` object, a node degree, a terminus string, or a None (indicating Terminus.LOW). Returns None if no match. If `getNeighbor` is True, or direction, the nearest node will be returned. If more than one node defines the same pitch, Node weights are used to select a single node. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork(edgeList) >>> net.getRelativeNodeId('a', 1, 'a4') Terminus.LOW >>> net.getRelativeNodeId('a', 1, 'b4') 0 >>> net.getRelativeNodeId('a', 1, 'c#4') 1 >>> net.getRelativeNodeId('a', 1, 'c4', comparisonAttribute='step') 1 >>> net.getRelativeNodeId('a', 1, 'c', comparisonAttribute='step') 1 >>> net.getRelativeNodeId('a', 1, 'b-4') is None True ''' # TODO: this always takes the first: need to add weighted selection nodeObj: Node if nodeId is None: # assume first nodeObj = self.terminusLowNodes[0] else: nodeObj = self.nodeNameToNodes(nodeId)[0] # environLocal.printDebug(['getRelativeNodeId', 'result of nodeNameToNodes', # self.nodeNameToNodes(nodeName)]) if isinstance(pitchTarget, str): pitchTargetObj = pitch.Pitch(pitchTarget) elif isinstance(pitchTarget, note.Note): pitchTargetObj = pitchTarget.pitch else: pitchTargetObj = pitchTarget saveOctave = pitchTargetObj.octave if saveOctave is None: pitchTargetObj.octave = pitchTargetObj.implicitOctave # try an octave spread first # if a scale degree is larger than an octave this will fail minPitch = pitchTargetObj.transpose(-12, inPlace=False) maxPitch = pitchTargetObj.transpose(12, inPlace=False) realizedPitches, realizedNodes = self.realize(pitchReference, nodeObj, minPitch=minPitch, maxPitch=maxPitch, direction=direction, alteredDegrees=alteredDegrees) # environLocal.printDebug(['getRelativeNodeId()', 'nodeObj', nodeObj, # 'realizedPitch', realizedPitch, 'realizedNode', realizedNode]) post = [] # collect more than one for realizedPitch, realizedNode in zip(realizedPitches, realizedNodes): # environLocal.printDebug(['getRelativeNodeId', 'comparing', # realizedPitch[i], realizedNode[i]]) # comparison of attributes, not object if (getattr(pitchTargetObj, comparisonAttribute) == getattr(realizedPitch, comparisonAttribute)): if realizedNode not in post: # may be more than one match post.append(realizedNode) if saveOctave is None: pitchTargetObj.octave = None if not post: return None elif len(post) == 1: return post[0] else: # do a weighted selection # environLocal.printDebug(['getRelativeNodeId()', 'got multiple matches', post]) # use node keys stored in post, get node, and collect weights return common.weightedSelection(post, [self.nodes[x].weight for x in post]) def getNeighborNodeIds( self, pitchReference: pitch.Pitch|str, nodeName: Node|int|Terminus|None, pitchTarget: pitch.Pitch|str, direction: Direction = Direction.ASCENDING, alteredDegrees=None, ): ''' Given a reference pitch assigned to a node id, determine the node ids that neighbor this pitch. Returns None if an exact match. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork(edgeList) >>> net.getNeighborNodeIds('c4', 1, 'b-') (4, 5) >>> net.getNeighborNodeIds('c4', 1, 'b') (5, Terminus.HIGH) ''' # TODO: this takes the first, need to add probabilistic selection if nodeName is None: # assume first nodeId = self.terminusLowNodes[0] else: nodeId = self.nodeNameToNodes(nodeName)[0] if isinstance(pitchTarget, str): pitchTargetObj = pitch.Pitch(pitchTarget) else: pitchTargetObj = pitchTarget savedOctave = pitchTargetObj.octave if savedOctave is None: # don't alter permanently, in case a Pitch object was passed in. pitchTargetObj.octave = pitchTargetObj.implicitOctave # try an octave spread first # if a scale degree is larger than an octave this will fail minPitch = pitchTargetObj.transpose(-12, inPlace=False) maxPitch = pitchTargetObj.transpose(12, inPlace=False) realizedPitches, realizedNodes = self.realize(pitchReference, nodeId, minPitch=minPitch, maxPitch=maxPitch, direction=direction, alteredDegrees=alteredDegrees) lowNeighbor = None highNeighbor = None for realizedPitch, realizedNode in zip(realizedPitches, realizedNodes): if pitchTargetObj.ps < realizedPitch.ps: highNeighbor = realizedNode # low neighbor may be a previously-encountered pitch return lowNeighbor, highNeighbor lowNeighbor = realizedNode if savedOctave is None: pitchTargetObj.octave = savedOctave return None def getRelativeNodeDegree( self, pitchReference: pitch.Pitch|str, nodeId, pitchTarget: pitch.Pitch|str, comparisonAttribute='ps', direction: Direction = Direction.ASCENDING, alteredDegrees=None, ): ''' Given a reference pitch assigned to node id, determine the relative node degree of pitchTarget, even if displaced over multiple octaves Comparison Attribute determines what will be used to determine equality. Use `ps` (default) for post-tonal uses. `name` for tonal, and `step` for diatonic. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork(edgeList) >>> [str(p) for p in net.realizePitch(pitch.Pitch('e-2')) ] ['E-2', 'F2', 'G2', 'A-2', 'B-2', 'C3', 'D3', 'E-3'] >>> net.getRelativeNodeDegree('e-2', 1, 'd3') # if e- is tonic, what is d3 7 For an octave repeating network, the neither pitch's octave matters: >>> net.getRelativeNodeDegree('e-', 1, 'd5') # if e- is tonic, what is d3 7 >>> net.getRelativeNodeDegree('e-2', 1, 'd') # if e- is tonic, what is d3 7 >>> net.getRelativeNodeDegree('e3', 1, 'd5') is None True >>> net.getRelativeNodeDegree('e3', 1, 'd5', comparisonAttribute='step') 7 >>> net.getRelativeNodeDegree('e3', 1, 'd', comparisonAttribute='step') 7 >>> net.getRelativeNodeDegree('e-3', 1, 'b-3') 5 >>> net.getRelativeNodeDegree('e-3', 1, 'e-5') 1 >>> net.getRelativeNodeDegree('e-2', 1, 'f3') 2 >>> net.getRelativeNodeDegree('e-3', 1, 'b6') is None True >>> net.getRelativeNodeDegree('e-3', 1, 'e-2') 1 >>> net.getRelativeNodeDegree('e-3', 1, 'd3') 7 >>> net.getRelativeNodeDegree('e-3', 1, 'e-3') 1 >>> net.getRelativeNodeDegree('e-3', 1, 'b-1') 5 >>> edgeList = ['p4', 'p4', 'p4'] # a non octave-repeating scale >>> net = scale.intervalNetwork.IntervalNetwork(edgeList) >>> [str(p) for p in net.realizePitch('f2')] ['F2', 'B-2', 'E-3', 'A-3'] >>> [str(p) for p in net.realizePitch('f2', 1, 'f2', 'f6')] ['F2', 'B-2', 'E-3', 'A-3', 'D-4', 'G-4', 'C-5', 'F-5', 'A5', 'D6'] >>> net.getRelativeNodeDegree('f2', 1, 'a-3') # could be 4 or 1 1 >>> net.getRelativeNodeDegree('f2', 1, 'd-4') # 2 is correct 2 >>> net.getRelativeNodeDegree('f2', 1, 'g-4') # 3 is correct 3 >>> net.getRelativeNodeDegree('f2', 1, 'c-5') # could be 4 or 1 1 >>> net.getRelativeNodeDegree('f2', 1, 'e--6') # could be 4 or 1 1 >>> [str(p) for p in net.realizePitch('f6', 1, 'f2', 'f6')] ['G#2', 'C#3', 'F#3', 'B3', 'E4', 'A4', 'D5', 'G5', 'C6', 'F6'] >>> net.getRelativeNodeDegree('f6', 1, 'd5') 1 >>> net.getRelativeNodeDegree('f6', 1, 'g5') 2 >>> net.getRelativeNodeDegree('f6', 1, 'a4') 3 >>> net.getRelativeNodeDegree('f6', 1, 'e4') 2 >>> net.getRelativeNodeDegree('f6', 1, 'b3') 1 ''' nId = self.getRelativeNodeId( pitchReference=pitchReference, nodeId=nodeId, pitchTarget=pitchTarget, comparisonAttribute=comparisonAttribute, alteredDegrees=alteredDegrees, direction=direction) if nId is None: return None else: return self.nodeIdToDegree(nId) def getPitchFromNodeDegree( self, pitchReference: pitch.Pitch|str, nodeName: Node|int|Terminus|None, nodeDegreeTarget, direction: Direction = Direction.ASCENDING, minPitch=None, maxPitch=None, alteredDegrees=None, equateTermini=True, ): ''' Given a reference pitch assigned to node id, determine the pitch for the target node degree. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork(edgeList) >>> [str(p) for p in net.realizePitch(pitch.Pitch('e-2')) ] ['E-2', 'F2', 'G2', 'A-2', 'B-2', 'C3', 'D3', 'E-3'] >>> net.getPitchFromNodeDegree('e4', 1, 1) >>> net.getPitchFromNodeDegree('e4', 1, 7) # seventh scale degree >>> net.getPitchFromNodeDegree('e4', 1, 8) >>> net.getPitchFromNodeDegree('e4', 1, 9) >>> net.getPitchFromNodeDegree('e4', 1, 3, minPitch='c2', maxPitch='c3') This will always get the lowest pitch: >>> net.getPitchFromNodeDegree('e4', 1, 3, minPitch='c2', maxPitch='c10') >>> net.fillMelodicMinor() >>> net.getPitchFromNodeDegree('c', 1, 5) >>> net.getPitchFromNodeDegree('c', 1, 6, scale.Direction.ASCENDING) >>> net.getPitchFromNodeDegree('c', 1, 6, scale.Direction.DESCENDING) ''' # these are the reference node -- generally one except for bidirectional # scales. nodeListForNames = self.nodeNameToNodes(nodeName) # environLocal.printDebug(['getPitchFromNodeDegree()', 'node reference', # nodeId, 'node degree', nodeId.degree, # 'pitchReference', pitchReference, 'alteredDegrees', alteredDegrees]) # here, we give a node degree, and may return 1 or more valid nodes; # need to select the node that is appropriate to the directed # realization nodeTargetId = None nodeTargetIdList = self.nodeNameToNodes(nodeDegreeTarget, permitDegreeModuli=True, equateTermini=equateTermini) # environLocal.printDebug(['getPitchFromNodeDegree()', # 'result of nodeNameToNodes', nodeTargetIdList, # 'nodeDegreeTarget', nodeDegreeTarget]) if len(nodeTargetIdList) == 1: nodeTargetId = nodeTargetIdList[0] # easy case # case where we equate terminals and get both min and max elif [n.id for n in nodeTargetIdList] == [Terminus.LOW, Terminus.HIGH]: # get first, terminus low nodeTargetId = nodeTargetIdList[0] # easy case else: # have more than one node that is defined for a given degree for nId in nodeTargetIdList: dirList = self.nodeIdToEdgeDirections(nId) # environLocal.printDebug(['getPitchFromNodeDegree()', # 'comparing dirList', dirList]) # for now, simply find the nId that has the requested # direction. a more sophisticated matching may be needed if direction in dirList: nodeTargetId = nId break if nodeTargetId is None: # environLocal.printDebug(['getPitchFromNodeDegree()', # 'cannot select node based on direction', nodeTargetIdList]) nodeTargetId = nodeTargetIdList[0] # easy case # environLocal.printDebug(['getPitchFromNodeDegree()', 'nodeTargetId', nodeTargetId]) # get a realization to find the node # pass direction as well when getting realization # TODO: need a way to force that we get a realization that # may goes through a particular node; we could start at that node? # brute force approach might make multiple attempts to realize # TODO: BUG: Does not work with bidirectional scales. # TODO: possibly cache results for unused_counter in range(10): realizedPitch, realizedNode = self.realize( pitchReference=pitchReference, nodeId=nodeListForNames[0], minPitch=minPitch, maxPitch=maxPitch, direction=direction, alteredDegrees=alteredDegrees) # environLocal.printDebug(['getPitchFromNodeDegree()', # 'realizedPitch', realizedPitch, 'realizedNode', realizedNode, # 'nodeTargetId', nodeTargetId,]) # get the pitch when we have a node id to match for i, nId in enumerate(realizedNode): # environLocal.printDebug(['comparing', nId, 'nodeTargetId', nodeTargetId]) if nId == nodeTargetId.id: return realizedPitch[i] # NOTE: this condition may be too generous, and was added to solve # a non-tracked problem. # only match this generously if we are equating termini if equateTermini: if ((nId in (Terminus.HIGH, Terminus.LOW)) and (nodeTargetId.id in (Terminus.HIGH, Terminus.LOW))): return realizedPitch[i] # environLocal.printDebug(['getPitchFromNodeDegree() on trial', trial, ', # failed to find node', nodeTargetId]) @staticmethod def filterPitchList( pitchTarget: t.Union[list[str], list[pitch.Pitch], str, pitch.Pitch] ) -> tuple[list[pitch.Pitch], pitch.Pitch, pitch.Pitch]: ''' Given a list or one pitch, check if all are pitch objects; convert if necessary. Return a 3-tuple: a list of all pitches, the min value and the max value. >>> Net = scale.intervalNetwork.IntervalNetwork >>> Net.filterPitchList(['c#4', 'f5', 'd3']) ([, , ], , ) A single string or pitch can be given. >>> Net.filterPitchList('c#') ([], , ) Empty lists raise value errors: >>> Net.filterPitchList([]) Traceback (most recent call last): ValueError: There must be at least one pitch given. * Changed in v8: staticmethod. Raise value error on empty ''' pitchList: list[pitch.Pitch] if not isinstance(pitchTarget, (list, tuple)): pitchObj: pitch.Pitch if isinstance(pitchTarget, str): pitchObj = pitch.Pitch(pitchTarget) else: pitchObj = pitchTarget pitchList = [pitchObj] else: # convert a list of string into pitch objects pitchList = [] for p in pitchTarget: if isinstance(p, str): pitchList.append(pitch.Pitch(p)) else: pitchList.append(p) if not pitchList: raise ValueError('There must be at least one pitch given.') # automatically derive a min and max from the supplied pitch sortList = [(pitch.ps, i) for i, pitch in enumerate(pitchList)] sortList.sort() minPitch = pitchList[sortList[0][1]] # first index maxPitch = pitchList[sortList[-1][1]] # last index return pitchList, minPitch, maxPitch def match(self, pitchReference: pitch.Pitch|str, nodeId, pitchTarget, comparisonAttribute='pitchClass', alteredDegrees=None): # noinspection PyShadowingNames ''' Given one or more pitches in `pitchTarget`, return a tuple of a list of matched pitches, and a list of unmatched pitches. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork(edgeList) >>> [str(p) for p in net.realizePitch('e-2')] ['E-2', 'F2', 'G2', 'A-2', 'B-2', 'C3', 'D3', 'E-3'] >>> net.match('e-2', 1, 'c3') # if e- is tonic, is 'c3' in the scale? ([], []) >>> net.match('e-2', 1, 'd3') ([], []) >>> net.match('e-2', 1, 'd#3') ([], []) >>> net.match('e-2', 1, 'e3') ([], []) >>> pitchTarget = [pitch.Pitch('b-2'), pitch.Pitch('b2'), pitch.Pitch('c3')] >>> net.match('e-2', 1, pitchTarget) ([, ], []) >>> pitchTarget = ['b-2', 'b2', 'c3', 'e-3', 'e#3', 'f2', 'e--2'] >>> (matched, unmatched) = net.match('e-2', 1, pitchTarget) >>> [str(p) for p in matched] ['B-2', 'C3', 'E-3', 'E#3', 'F2', 'E--2'] >>> unmatched [] ''' # these return a Node, not a nodeId # TODO: just getting first if nodeId is None: # assume first nodeId = self.terminusLowNodes[0] else: nodeId = self.nodeNameToNodes(nodeId)[0] pitchTarget, minPitch, maxPitch = self.filterPitchList(pitchTarget) # TODO: need to do both directions nodesRealized = self.realizePitch(pitchReference, nodeId, minPitch, maxPitch, alteredDegrees=alteredDegrees) matched = [] noMatch = [] # notFound = [] for target in pitchTarget: found = False for p in nodesRealized: # enharmonic switch here match = False if getattr(p, comparisonAttribute) == getattr(target, comparisonAttribute): match = True if match: matched.append(target) found = True break if not found: noMatch.append(target) return matched, noMatch def findMissing(self, pitchReference: pitch.Pitch|str, nodeId, pitchTarget, comparisonAttribute='pitchClass', minPitch=None, maxPitch=None, direction: Direction = Direction.ASCENDING, alteredDegrees=None): # noinspection PyShadowingNames ''' Find all pitches in the realized scale that are not in the pitch target network based on the comparison attribute. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork(edgeList) >>> [str(p) for p in net.realizePitch('G3')] ['G3', 'A3', 'B3', 'C4', 'D4', 'E4', 'F#4', 'G4'] >>> net.findMissing('g', 1, ['g', 'a', 'b', 'd', 'f#']) [, ] ''' # these return a Node, not a nodeId if nodeId is None: # assume first nodeId = self.terminusLowNodes[0] else: nodeId = self.nodeNameToNodes(nodeId)[0] # TODO: need to do both directions nodesRealized = self.realizePitch(pitchReference, nodeId, minPitch=minPitch, maxPitch=maxPitch, alteredDegrees=alteredDegrees) # note: reassigns min and max pitchTarget, minPitch, maxPitch = self.filterPitchList(pitchTarget) # environLocal.printDebug(['nodesRealized:', nodesRealized,]) post = [] for target in nodesRealized: match = False for p in pitchTarget: # enharmonic switch here if getattr(p, comparisonAttribute) == getattr(target, comparisonAttribute): match = True break # environLocal.printDebug(['looking at:', target, p, 'match', match]) if not match: post.append(target) return post _SCALE_STARTS: tuple[str, ...] = ( 'C', 'C#', 'D-', 'D', 'D#', 'E-', 'E', 'F', 'F#', 'G', 'G#', 'A', 'B-', 'B', 'C-', ) def find(self, pitchTarget, resultsReturned=4, comparisonAttribute='pitchClass', alteredDegrees=None): ''' Given a collection of pitches, test all transpositions of a realized version of this network, and return the number of matches in each for each pitch assigned to the first node. >>> edgeList = ['M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2'] >>> net = scale.intervalNetwork.IntervalNetwork(edgeList) a network built on G or D as >>> net.find(['g', 'a', 'b', 'd', 'f#']) [(5, ), (5, ), (4, ), (4, )] >>> net.find(['g', 'a', 'b', 'c', 'd', 'e', 'f#']) [(7, ), (6, ), (6, ), (5, )] If resultsReturned is None then return every such scale. ''' nodeId = self.terminusLowNodes[0] sortList = [] # pitch strings in _SCALE_STARTS are converted to actual pitches in .realize, # and then manipulated. If they were Pitch objects already, they would get # deepcopied which is very slow. for p in self._SCALE_STARTS: # Realize scales from each pitch, and then compare to pitchTarget. # PitchTarget may be a list of pitches matched, unused_noMatch = self.match( p, nodeId, pitchTarget, comparisonAttribute=comparisonAttribute, alteredDegrees=alteredDegrees) sortList.append((len(matched), pitch.Pitch(p))) sortList.sort() sortList.reverse() # want most matches first if resultsReturned is not None: return sortList[:resultsReturned] else: return sortList def transposePitchAndApplySimplification( self, intervalObj: interval.Interval, pitchObj: pitch.Pitch ) -> pitch.Pitch: ''' transposes the pitch according to the given interval object and uses the simplification of the `pitchSimplification` property to simplify it afterwards. >>> b = scale.intervalNetwork.IntervalNetwork() >>> b.pitchSimplification # default 'maxAccidental' >>> i = interval.Interval('m2') >>> p = pitch.Pitch('C4') >>> allPitches = [] >>> for j in range(15): ... p = b.transposePitchAndApplySimplification(i, p) ... allPitches.append(p.nameWithOctave) >>> allPitches ['D-4', 'D4', 'E-4', 'F-4', 'F4', 'G-4', 'G4', 'A-4', 'A4', 'B-4', 'C-5', 'C5', 'D-5', 'D5', 'E-5'] >>> b.pitchSimplification = 'mostCommon' >>> p = pitch.Pitch('C4') >>> allPitches = [] >>> for j in range(15): ... p = b.transposePitchAndApplySimplification(i, p) ... allPitches.append(p.nameWithOctave) >>> allPitches ['C#4', 'D4', 'E-4', 'E4', 'F4', 'F#4', 'G4', 'A-4', 'A4', 'B-4', 'B4', 'C5', 'C#5', 'D5', 'E-5'] PitchSimplification can also be specified in the creation of the IntervalNetwork object >>> b = scale.intervalNetwork.IntervalNetwork(pitchSimplification=None) >>> p = pitch.Pitch('C4') >>> allPitches = [] >>> for j in range(5): ... p = b.transposePitchAndApplySimplification(i, p) ... allPitches.append(p.nameWithOctave) >>> allPitches ['D-4', 'E--4', 'F--4', 'G---4', 'A----4'] Note that beyond quadruple flats or sharps, pitchSimplification is automatic: >>> p >>> b.transposePitchAndApplySimplification(i, p) ''' pitchSimplification = self.pitchSimplification if (pitchSimplification in (None, 'none') and ((hasattr(intervalObj, 'implicitDiatonic') and intervalObj.implicitDiatonic) or (isinstance(intervalObj, interval.ChromaticInterval)))): pitchSimplification = 'mostCommon' if pitchSimplification == 'maxAccidental': pPost = intervalObj.transposePitch(pitchObj, maxAccidental=1) else: pPost = intervalObj.transposePitch(pitchObj) if pPost.accidental: if pitchSimplification == 'simplifyEnharmonic': pPost.simplifyEnharmonic(inPlace=True) elif pitchSimplification == 'mostCommon': pPost.simplifyEnharmonic(inPlace=True, mostCommon=True) elif pitchSimplification in (None, 'none'): pass else: raise IntervalNetworkException( f'unknown pitchSimplification type {pitchSimplification},' + ' allowable values are "maxAccidental" (default), "simplifyEnharmonic", ' + '"mostCommon", or None (or "none")') return pPost class BoundIntervalNetwork(IntervalNetwork): ''' This class is kept only because of the ICMC Paper. Just use IntervalNetwork instead. ''' pass # ------------------------------------------------------------------------------ # define presented order in documentation _DOC_ORDER = [IntervalNetwork, Node, Edge] if __name__ == '__main__': import music21 music21.mainTest()