# ------------------------------------------------------------------------------
# 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')
[docs]
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
[docs]
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
type 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
[docs]
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
<music21.interval.Interval M3>
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]] = []
[docs]
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}'
[docs]
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
<music21.scale.intervalNetwork.Edge Direction.ASCENDING M3 [(0, 1)]>
'''
# 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
[docs]
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
<music21.scale.intervalNetwork.Edge Direction.BI M3
[(Terminus.LOW, 1), (1, Terminus.LOW)]>
'''
# 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
[docs]
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()
[docs]
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)
[docs]
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-)
# ------------------------------------------------------------------------------
[docs]
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()
[docs]
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()
[docs]
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
[docs]
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: <music21.scale.intervalNetwork.Node id=Terminus.LOW>,
0: <music21.scale.intervalNetwork.Node id=0>,
1: <music21.scale.intervalNetwork.Node id=1>,
...
5: <music21.scale.intervalNetwork.Node id=5>,
Terminus.HIGH: <music21.scale.intervalNetwork.Node id=Terminus.HIGH>})
>>> net.edges
OrderedDict({0: <music21.scale.intervalNetwork.Edge Direction.BI M2
[(Terminus.LOW, 0), (0, Terminus.LOW)]>,
1: <music21.scale.intervalNetwork.Edge Direction.BI M2 [(0, 1), (1, 0)]>,
2: <music21.scale.intervalNetwork.Edge Direction.BI m2 [(1, 2), (2, 1)]>,
...
5: <music21.scale.intervalNetwork.Edge Direction.BI M2 [(4, 5), (5, 4)]>,
6: <music21.scale.intervalNetwork.Edge Direction.BI m2
[(5, Terminus.HIGH), (Terminus.HIGH, 5)]>})
>>> [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
[docs]
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
[docs]
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)
[<music21.pitch.Pitch C4>, <music21.pitch.Pitch D-4>, <music21.pitch.Pitch F4>]
'''
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
[docs]
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
[docs]
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
[<music21.scale.intervalNetwork.Node id=Terminus.LOW>]
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
[<music21.scale.intervalNetwork.Node id=Terminus.HIGH>]
'''
post = []
# for now, there is only one
post.append(self.nodes[Terminus.HIGH])
return post
# --------------------------------------------------------------------------
[docs]
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
[docs]
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
[docs]
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
[docs]
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
[docs]
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]
<music21.scale.intervalNetwork.Node id=Terminus.LOW>
>>> net.nodeNameToNodes(scale.Terminus.HIGH)
[<music21.scale.intervalNetwork.Node id=Terminus.HIGH>]
>>> net.nodeNameToNodes(scale.Terminus.LOW)
[<music21.scale.intervalNetwork.Node id=Terminus.LOW>]
Test using a nodeStep, or an integer nodeName
>>> net.nodeNameToNodes(1)
[<music21.scale.intervalNetwork.Node id=Terminus.LOW>,
<music21.scale.intervalNetwork.Node id=Terminus.HIGH>]
>>> net.nodeNameToNodes(1, equateTermini=False)
[<music21.scale.intervalNetwork.Node id=Terminus.LOW>]
>>> net.nodeNameToNodes(2)
[<music21.scale.intervalNetwork.Node id=0>]
With degree moduli, degree zero is the top-most non-terminal
(since terminals are redundant)
>>> net.nodeNameToNodes(0)
[<music21.scale.intervalNetwork.Node id=5>]
>>> net.nodeNameToNodes(-1)
[<music21.scale.intervalNetwork.Node id=4>]
>>> net.nodeNameToNodes(8)
[<music21.scale.intervalNetwork.Node id=Terminus.LOW>,
<music21.scale.intervalNetwork.Node id=Terminus.HIGH>]
'''
# 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}')
[docs]
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]
<music21.scale.intervalNetwork.Node id=Terminus.LOW>
'''
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
[docs]
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
[docs]
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
[docs]
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)
<music21.pitch.Pitch G5>
>>> net.nextPitch('g', 1, 'f#5', direction=scale.Direction.DESCENDING)
<music21.pitch.Pitch E5>
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)
<music21.pitch.Pitch A5>
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)
<music21.pitch.Pitch A-2>
>>> net.nextPitch('g', 1, 'a-2',
... direction=scale.Direction.ASCENDING,
... alteredDegrees=alteredDegrees)
<music21.pitch.Pitch B2>
'''
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,
)
[docs]
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
[docs]
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
[docs]
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
[docs]
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
[docs]
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()
[<music21.interval.Interval M2>, <music21.interval.Interval M2>,
<music21.interval.Interval m2>, <music21.interval.Interval M2>,
<music21.interval.Interval M2>, <music21.interval.Interval M2>,
<music21.interval.Interval m2>]
'''
# 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
[docs]
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'))
(<music21.pitch.Pitch G3>, <music21.pitch.Pitch G4>)
>>> net.realizeTermini(pitch.Pitch('a6'))
(<music21.pitch.Pitch A6>, <music21.pitch.Pitch A7>)
'''
# 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]
[docs]
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'))
(<music21.pitch.Pitch C4>, <music21.pitch.Pitch C6>)
>>> net.realizeMinMax(pitch.Pitch('B-5'))
(<music21.pitch.Pitch B-5>, <music21.pitch.Pitch B-7>)
Note that it might not always be two octaves apart
# s = scale.AbstractDiatonicScale('major')
# s._net.realizeMinMax(pitch.Pitch('D2'))
# (<music21.pitch.Pitch D2>, <music21.pitch.Pitch D3>)
'''
# 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: list[tuple[pitch.Pitch, Terminus|int]] = []
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: list[tuple[pitch.Pitch, Terminus|int]] = []
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
[docs]
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')
[<music21.pitch.Pitch E-2>]
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')
[<music21.pitch.Pitch E-2>, <music21.pitch.Pitch E-3>]
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
[docs]
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])
[docs]
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
[docs]
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)
[docs]
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)
<music21.pitch.Pitch E4>
>>> net.getPitchFromNodeDegree('e4', 1, 7) # seventh scale degree
<music21.pitch.Pitch D#5>
>>> net.getPitchFromNodeDegree('e4', 1, 8)
<music21.pitch.Pitch E4>
>>> net.getPitchFromNodeDegree('e4', 1, 9)
<music21.pitch.Pitch F#4>
>>> net.getPitchFromNodeDegree('e4', 1, 3, minPitch='c2', maxPitch='c3')
<music21.pitch.Pitch G#2>
This will always get the lowest pitch:
>>> net.getPitchFromNodeDegree('e4', 1, 3, minPitch='c2', maxPitch='c10')
<music21.pitch.Pitch G#2>
>>> net.fillMelodicMinor()
>>> net.getPitchFromNodeDegree('c', 1, 5)
<music21.pitch.Pitch G4>
>>> net.getPitchFromNodeDegree('c', 1, 6, scale.Direction.ASCENDING)
<music21.pitch.Pitch A4>
>>> net.getPitchFromNodeDegree('c', 1, 6, scale.Direction.DESCENDING)
<music21.pitch.Pitch A-4>
'''
# 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])
[docs]
@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'])
([<music21.pitch.Pitch C#4>, <music21.pitch.Pitch F5>, <music21.pitch.Pitch D3>],
<music21.pitch.Pitch D3>,
<music21.pitch.Pitch F5>)
A single string or pitch can be given.
>>> Net.filterPitchList('c#')
([<music21.pitch.Pitch C#>],
<music21.pitch.Pitch C#>,
<music21.pitch.Pitch 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
[docs]
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?
([<music21.pitch.Pitch C3>], [])
>>> net.match('e-2', 1, 'd3')
([<music21.pitch.Pitch D3>], [])
>>> net.match('e-2', 1, 'd#3')
([<music21.pitch.Pitch D#3>], [])
>>> net.match('e-2', 1, 'e3')
([], [<music21.pitch.Pitch E3>])
>>> pitchTarget = [pitch.Pitch('b-2'), pitch.Pitch('b2'), pitch.Pitch('c3')]
>>> net.match('e-2', 1, pitchTarget)
([<music21.pitch.Pitch B-2>, <music21.pitch.Pitch C3>], [<music21.pitch.Pitch B2>])
>>> 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
[<music21.pitch.Pitch B2>]
'''
# 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
[docs]
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#'])
[<music21.pitch.Pitch C5>, <music21.pitch.Pitch E5>]
'''
# 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-',
)
[docs]
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, <music21.pitch.Pitch G>), (5, <music21.pitch.Pitch D>),
(4, <music21.pitch.Pitch A>), (4, <music21.pitch.Pitch C>)]
>>> net.find(['g', 'a', 'b', 'c', 'd', 'e', 'f#'])
[(7, <music21.pitch.Pitch G>), (6, <music21.pitch.Pitch D>),
(6, <music21.pitch.Pitch C>), (5, <music21.pitch.Pitch A>)]
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
[docs]
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
<music21.pitch.Pitch A----4>
>>> b.transposePitchAndApplySimplification(i, p)
<music21.pitch.Pitch F#4>
'''
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
[docs]
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()