def test_mathtools_difference_series_01():
r'''Returns generator of differences l_i+1 - l_i for l_i in list l.
'''
t = [1, 1, 2, 3, 5, 5, 6]
d = mathtools.difference_series(t)
assert list(d) == [0, 1, 1, 2, 0, 1]
def test_mathtools_difference_series_01():
r'''Returns generator of differences l_i+1 - l_i for l_i in list l.
'''
t = [1, 1, 2, 3, 5, 5, 6]
d = mathtools.difference_series(t)
assert list(d) == [0, 1, 1, 2, 0, 1]
def from_selection(
cls,
selection,
item_class=None,
custom_identifier=None,
):
r'''Makes interval segment from component `selection`.
::
>>> staff = Staff("c'8 d'8 e'8 f'8 g'8 a'8 b'8 c''8")
>>> pitchtools.IntervalSegment.from_selection(
... staff, item_class=pitchtools.NumberedInterval)
IntervalSegment([2, 2, 1, 2, 2, 2, 1])
Returns interval segment.
'''
from abjad.tools import pitchtools
pitch_segment = pitchtools.PitchSegment.from_selection(selection)
intervals = (-x for x in mathtools.difference_series(pitch_segment))
return cls(
tokens=intervals,
item_class=item_class,
custom_identifier=custom_identifier,
)
def merge_duration_sequences(*sequences):
r'''Merge duration `sequences`:
::
>>> sequencetools.merge_duration_sequences([10, 10, 10], [7])
[7, 3, 10, 10]
Merge more duration sequences:
::
>>> sequencetools.merge_duration_sequences([10, 10, 10], [10, 10])
[10, 10, 10]
The idea is that each sequence element represents a duration.
Returns list.
'''
from abjad.tools import sequencetools
offset_lists = []
for sequence in sequences:
offset_list = mathtools.cumulative_sums(sequence, start=None)
offset_lists.append(offset_list)
all_offsets = sequencetools.join_subsequences(offset_lists)
all_offsets = list(sorted(set(all_offsets)))
all_offsets.insert(0, 0)
all_durations = mathtools.difference_series(all_offsets)
return all_durations
def _get_composite_offset_difference_series_from_leaves_in_expr(expr):
offsets = []
for leaf in iterate(expr).by_class(scoretools.Leaf):
start_offset = leaf._get_timespan().start_offset
if start_offset not in offsets:
offsets.append(start_offset)
stop_offset = leaf._get_timespan().stop_offset
if stop_offset not in offsets:
offsets.append(stop_offset)
offsets.sort()
return list(mathtools.difference_series(offsets))
def _get_leaf_offsets(expr):
from abjad.tools import scoretools
offsets = []
for leaf in iterate(expr).by_class(scoretools.Leaf):
start_offset = leaf._get_timespan().start_offset
if start_offset not in offsets:
offsets.append(start_offset)
stop_offset = leaf._get_timespan().stop_offset
if stop_offset not in offsets:
offsets.append(stop_offset)
offsets.sort()
return list(mathtools.difference_series(offsets))
def _get_composite_offset_difference_series_from_leaves_in_expr(expr):
from abjad.tools import scoretools
offsets = []
for leaf in iterate(expr).by_class(scoretools.Leaf):
start_offset = leaf._get_timespan().start_offset
if start_offset not in offsets:
offsets.append(start_offset)
stop_offset = leaf._get_timespan().stop_offset
if stop_offset not in offsets:
offsets.append(stop_offset)
offsets.sort()
return list(mathtools.difference_series(offsets))
def _get_composite_offset_difference_series_from_leaves_in_expr(expr):
from abjad.tools import iterationtools
offsets = []
for leaf in iterationtools.iterate_leaves_in_expr(expr):
start_offset = leaf._get_timespan().start_offset
if start_offset not in offsets:
offsets.append(start_offset)
stop_offset = leaf._get_timespan().stop_offset
if stop_offset not in offsets:
offsets.append(stop_offset)
offsets.sort()
return list(mathtools.difference_series(offsets))
def _make_timespans(
self,
layer=None,
music_specifiers=None,
target_timespan=None,
timespan_inventory=None,
):
import consort
new_timespans = abjad.TimespanList()
if not self.voice_names and not self.labels:
return new_timespans
rotation_indices = self.rotation_indices or (0,)
rotation_indices = abjad.CyclicTuple(rotation_indices)
context_counter = collections.Counter()
preexisting_timespans = self._collect_preexisting_timespans(
target_timespan=target_timespan,
timespan_inventory=timespan_inventory,
)
partitioned_timespans = self._partition_preexisting_timespans(
preexisting_timespans)
for group_index, group in enumerate(partitioned_timespans):
rotation_index = rotation_indices[group_index]
offsets = set()
offsets.add(group.start_offset)
offsets.add(group.stop_offset)
for timespan in group:
if self.include_inner_starts:
offsets.add(timespan.start_offset)
if self.include_inner_stops:
offsets.add(timespan.stop_offset)
offsets = tuple(sorted(offsets))
durations = mathtools.difference_series(offsets)
durations = consort.rotate(durations, rotation_index)
start_offset = offsets[0]
for context_name, music_specifier in music_specifiers.items():
context_seed = context_counter[context_name]
timespans = music_specifier(
durations=durations,
layer=layer,
division_masks=self.division_masks,
padding=self.padding,
seed=context_seed,
start_offset=start_offset,
timespan_specifier=self.timespan_specifier,
voice_name=context_name,
)
context_counter[context_name] += 1
new_timespans.extend(timespans)
return new_timespans
def from_selection(class_, selection, item_class=None):
r'''Initialize interval-class segment from component selection:
::
>>> staff_1 = Staff("c'4 <d' fs' a'>4 b2")
>>> staff_2 = Staff("c4. r8 g2")
>>> selection = select((staff_1, staff_2))
>>> pitchtools.IntervalClassSegment.from_selection(selection)
IntervalClassSegment(['-M2', '-M3', '-m3', '+m7', '+M7', '-P5'])
Returns interval-class segment.
'''
from abjad.tools import pitchtools
pitch_segment = pitchtools.PitchSegment.from_selection(selection)
intervals = mathtools.difference_series(pitch_segment)
return class_(
items=intervals,
item_class=item_class,
)
def from_selection(cls, selection, item_class=None):
r'''Initialize interval-class segment from component selection:
::
>>> staff_1 = Staff("c'4 <d' fs' a'>4 b2")
>>> staff_2 = Staff("c4. r8 g2")
>>> selection = select((staff_1, staff_2))
>>> pitchtools.IntervalClassSegment.from_selection(selection)
IntervalClassSegment(['-M2', '-M3', '-m3', '+m7', '+M7', '-P5'])
Returns interval-class segment.
'''
from abjad.tools import pitchtools
pitch_segment = pitchtools.PitchSegment.from_selection(selection)
intervals = mathtools.difference_series(pitch_segment)
return cls(
items=intervals,
item_class=item_class,
)
def from_selection(cls, selection, item_class=None, name=None):
r'''Initialize interval segment from component selection:
::
>>> staff = Staff("c'8 d'8 e'8 f'8 g'8 a'8 b'8 c''8")
>>> pitchtools.IntervalSegment.from_selection(
... staff, item_class=pitchtools.NumberedInterval)
IntervalSegment([+2, +2, +1, +2, +2, +2, +1])
Returns interval segment.
'''
from abjad.tools import pitchtools
pitch_segment = pitchtools.PitchSegment.from_selection(selection)
intervals = (-x for x in mathtools.difference_series(pitch_segment))
return cls(
tokens=intervals,
item_class=item_class,
name=name,
)
def from_selection(class_, selection, item_class=None):
r'''Initializes interval-class segment from component selection.
.. container:: example
>>> staff_1 = abjad.Staff("c'4 <d' fs' a'>4 b2")
>>> staff_2 = abjad.Staff("c4. r8 g2")
>>> selection = abjad.select((staff_1, staff_2))
>>> abjad.IntervalClassSegment.from_selection(selection)
IntervalClassSegment(['-M2', '-M3', '-m3', '+m7', '+M7', '-P5'])
Returns interval-class segment.
'''
import abjad
pitch_segment = abjad.PitchSegment.from_selection(selection)
pitches = [_ for _ in pitch_segment]
intervals = mathtools.difference_series(pitches)
return class_(
items=intervals,
item_class=item_class,
)
def from_selection(
class_,
selection,
item_class=None,
):
r'''Makes interval segment from component `selection`.
::
>>> staff = Staff("c'8 d'8 e'8 f'8 g'8 a'8 b'8 c''8")
>>> pitchtools.IntervalSegment.from_selection(
... staff, item_class=pitchtools.NumberedInterval)
IntervalSegment([2, 2, 1, 2, 2, 2, 1])
Returns interval segment.
'''
from abjad.tools import pitchtools
pitch_segment = pitchtools.PitchSegment.from_selection(selection)
intervals = (-x for x in mathtools.difference_series(pitch_segment))
return class_(
items=intervals,
item_class=item_class,
)
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 _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 test_quantizationtools_QEventSequence_from_millisecond_durations_01():
r'''Test basic functionality.
'''
durations = mathtools.difference_series(
[x[0] for x in quantizationtools.make_test_time_segments()])
q_events = quantizationtools.QEventSequence.from_millisecond_durations(
durations)
assert q_events == quantizationtools.QEventSequence((
quantizationtools.PitchedQEvent(
durationtools.Offset(0, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(163, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(511, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(627, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(1208, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(1417, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(1997, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(3204, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(3297, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(4087, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(4296, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(4830, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(6362, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(6595, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(6687, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(7013, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(7245, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(7872, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(8197, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(8359, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(8638, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(8731, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(8917, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(9288, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(9404, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(10240, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(10356, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(10496, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(10890, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(11169, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(11285, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(11424, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(12307, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(12957, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(13073, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(13653, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(13979, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(14234, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(15256, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(15883, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(16022, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(16649, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(16927, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(17044, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.PitchedQEvent(
durationtools.Offset(17276, 1),
(pitchtools.NamedPitch("c'"),)
),
quantizationtools.TerminalQEvent(
durationtools.Offset(18483, 1)
)
))
