def is_pitch_class_unique(self):
r'''Is true when pitch set is pitch-class-unique. Otherwise false.
.. container:: example
>>> set_ = abjad.PitchSet(
... items=[-2, -1.5, 6, 7, -1.5, 7],
... item_class=abjad.NumberedPitch,
... )
>>> set_.is_pitch_class_unique
True
.. container:: example
>>> set_ = abjad.PitchSet(
... items=[-2, -1.5, 6, 7, 10.5, 7],
... item_class=abjad.NumberedPitch,
... )
>>> set_.is_pitch_class_unique
False
Returns true or false.
'''
from abjad.tools import pitchtools
numbered_pitch_class_set = pitchtools.PitchClassSet(
self, item_class=pitchtools.NumberedPitchClass)
return len(self) == len(numbered_pitch_class_set)
def duplicate_pitch_classes(self):
r'''Gets duplicate pitch-classes in pitch set.
.. container:: example
>>> set_ = abjad.PitchSet(
... items=[-2, -1.5, 6, 7, -1.5, 7],
... item_class=abjad.NumberedPitch,
... )
>>> set_.duplicate_pitch_classes
PitchClassSet([])
>>> set_ = abjad.PitchSet(
... items=[-2, -1.5, 6, 7, 10.5, 7],
... item_class=abjad.NumberedPitch,
... )
>>> set_.duplicate_pitch_classes
PitchClassSet([10.5])
Returns pitch-class set.
'''
from abjad.tools import pitchtools
pitch_classes = []
duplicate_pitch_classes = []
for pitch in self:
pitch_class = pitchtools.NumberedPitchClass(pitch)
if pitch_class in pitch_classes:
duplicate_pitch_classes.append(pitch_class)
pitch_classes.append(pitch_class)
return pitchtools.PitchClassSet(
duplicate_pitch_classes,
item_class=pitchtools.NumberedPitchClass,
)
def is_pitch_class_unique(self):
r'''Is true when pitch set is pitch-class-unique. Otherwise false.
Returns true or false.
'''
from abjad.tools import pitchtools
numbered_pitch_class_set = pitchtools.PitchClassSet(
self, item_class=pitchtools.NumberedPitchClass)
return len(self) == len(numbered_pitch_class_set)
def inventory_aggregate_subsets():
'''Inventory aggregate subsets:
::
>>> U_star = pitchtools.inventory_aggregate_subsets()
>>> len(U_star)
4096
>>> for pcset in U_star[:20]:
... pcset
PitchClassSet([])
PitchClassSet([0])
PitchClassSet([1])
PitchClassSet([0, 1])
PitchClassSet([2])
PitchClassSet([0, 2])
PitchClassSet([1, 2])
PitchClassSet([0, 1, 2])
PitchClassSet([3])
PitchClassSet([0, 3])
PitchClassSet([1, 3])
PitchClassSet([0, 1, 3])
PitchClassSet([2, 3])
PitchClassSet([0, 2, 3])
PitchClassSet([1, 2, 3])
PitchClassSet([0, 1, 2, 3])
PitchClassSet([4])
PitchClassSet([0, 4])
PitchClassSet([1, 4])
PitchClassSet([0, 1, 4])
There are 4096 subsets of the aggregate.
This is ``U*`` in [Morris 1987].
Returns list of numbered pitch-class sets.
'''
from abjad.tools import pitchtools
def _helper(binary_string):
result = zip(binary_string, range(len(binary_string)))
result = [x[1] for x in result if x[0] == '1']
return result
result = []
for x in range(4096):
subset = ''.join(
list(reversed(mathtools.integer_to_binary_string(x).zfill(12))))
subset = _helper(subset)
subset = pitchtools.PitchClassSet(
subset,
item_class=pitchtools.NumberedPitchClass,
)
result.append(subset)
return result
def _analyze_incomplete_chord(expr):
from abjad.tools import tonalanalysistools
pitches = pitchtools.PitchSegment.from_selection(expr)
npcset = pitchtools.PitchClassSet(
pitches, item_class=pitchtools.NamedPitchClass)
dicv = pitchtools.IntervalClassVector(
items=npcset,
item_class=pitchtools.NamedInversionEquivalentIntervalClass,
)
# TODO: eliminate code duplication #
if dicv == TonalAnalysisAgent._make_dicv('c', 'ef'):
model_npcs = ['c', 'ef']
quality, extent = 'minor', 'triad'
elif dicv == TonalAnalysisAgent._make_dicv('c', 'e'):
model_npcs = ['c', 'e']
quality, extent = 'major', 'triad'
elif dicv == TonalAnalysisAgent._make_dicv('c', 'ef', 'bff'):
model_npcs = ['c', 'ef', 'bff']
quality, extent = 'diminished', 'seventh'
elif dicv == TonalAnalysisAgent._make_dicv('c', 'ef', 'bf'):
model_npcs = ['c', 'ef', 'bf']
quality, extent = 'minor', 'seventh'
elif dicv == TonalAnalysisAgent._make_dicv('c', 'e', 'bf'):
model_npcs = ['c', 'e', 'bf']
quality, extent = 'dominant', 'seventh'
elif dicv == TonalAnalysisAgent._make_dicv('c', 'e', 'b'):
model_npcs = ['c', 'e', 'b']
quality, extent = 'major', 'seventh'
else:
message = 'can not identify incomplete tertian chord.'
raise ValueError(message)
bass = min(pitches).named_pitch_class
try:
npcseg = npcset.order_by(
pitchtools.PitchClassSegment(
model_npcs,
item_class=pitchtools.NamedPitchClass,
))
except ValueError:
message = 'can not identify incomplete tertian chord.'
raise ValueError(message)
inversion = npcseg.index(bass)
root = npcseg[0]
return tonalanalysistools.RootedChordClass(
root,
quality,
extent,
inversion,
)
def duplicate_pitch_classes(self):
r'''Duplicate pitch-classes in pitch set.
Returns pitch-class set.
'''
from abjad.tools import pitchtools
pitch_classes = []
duplicate_pitch_classes = []
for pitch in self:
pitch_class = pitchtools.NumberedPitchClass(pitch)
if pitch_class in pitch_classes:
duplicate_pitch_classes.append(pitch_class)
pitch_classes.append(pitch_class)
return pitchtools.PitchClassSet(
duplicate_pitch_classes,
item_class=pitchtools.NumberedPitchClass,
)
def has_duplicates(self):
r'''True if segment contains duplicate items:
::
>>> pitch_class_segment = pitchtools.PitchClassSegment(
... items=[-2, -1.5, 6, 7, -1.5, 7],
... )
>>> pitch_class_segment.has_duplicates
True
::
>>> pitch_class_segment = pitchtools.PitchClassSegment(
... items="c d e f g a b",
... )
>>> pitch_class_segment.has_duplicates
False
Returns true or false.
'''
from abjad.tools import pitchtools
return len(pitchtools.PitchClassSet(self)) < len(self)
def _analyze_chord(expr):
from abjad.tools import tonalanalysistools
pitches = pitchtools.PitchSegment.from_selection(expr)
npcset = pitchtools.PitchClassSet(
pitches,
item_class=pitchtools.NamedPitchClass,
)
ordered_npcs = []
letters = ('c', 'e', 'g', 'b', 'd', 'f', 'a')
for letter in letters:
for npc in npcset:
if npc.diatonic_pitch_class_name == letter:
ordered_npcs.append(npc)
ordered_npcs = pitchtools.PitchClassSegment(
ordered_npcs, item_class=pitchtools.NamedPitchClass)
for x in range(len(ordered_npcs)):
ordered_npcs = ordered_npcs.rotate(1)
segment = \
pitchtools.IntervalClassSegment(
items=mathtools.difference_series(ordered_npcs),
item_class=pitchtools.NamedInversionEquivalentIntervalClass,
)
if segment.is_tertian:
break
else:
return None
root = ordered_npcs[0]
class_ = tonalanalysistools.RootlessChordClass
rootless_chord_class = class_.from_interval_class_segment(segment)
bass = min(pitches).named_pitch_class
inversion = ordered_npcs.index(bass)
return tonalanalysistools.RootedChordClass(
root,
rootless_chord_class.quality_string,
rootless_chord_class.extent,
inversion,
)
def yield_all_pitch_class_sets():
'''Yields all pitch-class sets.
.. container:: example
::
>>> all_pitch_class_sets = pitchtools.yield_all_pitch_class_sets()
>>> len(all_pitch_class_sets)
4096
::
>>> for pitch_class_set in all_pitch_class_sets[:20]:
... pitch_class_set
PitchClassSet([])
PitchClassSet([0])
PitchClassSet([1])
PitchClassSet([0, 1])
PitchClassSet([2])
PitchClassSet([0, 2])
PitchClassSet([1, 2])
PitchClassSet([0, 1, 2])
PitchClassSet([3])
PitchClassSet([0, 3])
PitchClassSet([1, 3])
PitchClassSet([0, 1, 3])
PitchClassSet([2, 3])
PitchClassSet([0, 2, 3])
PitchClassSet([1, 2, 3])
PitchClassSet([0, 1, 2, 3])
PitchClassSet([4])
PitchClassSet([0, 4])
PitchClassSet([1, 4])
PitchClassSet([0, 1, 4])
There are 4096 pitch-class sets.
This is ``U*`` in [Morris 1987].
Returns list of numbered pitch-class sets.
'''
from abjad.tools import pitchtools
def _helper(binary_string):
result = zip(binary_string, range(len(binary_string)))
result = [x[1] for x in result if x[0] == '1']
return result
result = []
for x in range(4096):
string = mathtools.integer_to_binary_string(x).zfill(12)
subset = ''.join(list(reversed(string)))
subset = _helper(subset)
subset = pitchtools.PitchClassSet(
subset,
item_class=pitchtools.NumberedPitchClass,
)
result.append(subset)
return result
