def order_by(self, segment):
"""
Orders pitch-class set by pitch-class `segment`.
.. container:: example
>>> set_ = abjad.PitchClassSet(['c', 'e', 'b'])
>>> segment = abjad.PitchClassSegment(['e', 'a', 'f'])
>>> set_.order_by(segment)
PitchClassSegment("b e c")
Returns pitch-class segment.
"""
import abjad
if not len(self) == len(segment):
message = "set and segment must be on equal length."
raise ValueError(message)
enumerator = Enumerator(self)
for pitch_classes in enumerator.yield_permutations():
candidate = abjad.PitchClassSegment(pitch_classes)
if candidate._is_equivalent_under_transposition(segment):
return candidate
message = "{!s} can not order by {!s}."
message = message.format(self, segment)
raise ValueError(message)
def order_by(self, segment):
"""
Orders pitch-class set by pitch-class `segment`.
.. container:: example
>>> set_ = abjad.PitchClassSet(['c', 'e', 'b'])
>>> segment = abjad.PitchClassSegment(['e', 'a', 'f'])
>>> set_.order_by(segment)
PitchClassSegment("b e c")
Returns pitch-class segment.
"""
import abjad
if not len(self) == len(segment):
message = 'set and segment must be on equal length.'
raise ValueError(message)
enumerator = Enumerator(self)
for pitch_classes in enumerator.yield_permutations():
candidate = abjad.PitchClassSegment(pitch_classes)
if candidate._is_equivalent_under_transposition(segment):
return candidate
message = '{!s} can not order by {!s}.'
message = message.format(self, segment)
raise ValueError(message)
def __init__(self, items=None, item_class=None):
import abjad
prototype = (
abjad.PitchClassSegment,
abjad.PitchClassSet,
abjad.PitchSegment,
abjad.PitchSet,
)
if isinstance(items, prototype):
items = list(items)
enumerator = Enumerator(items)
pairs = enumerator.yield_pairs()
items = [second - first for first, second in pairs]
Set.__init__(self, items=items, item_class=item_class)
def __init__(self, items=None, item_class=None):
import abjad
prototype = (
abjad.PitchSegment,
abjad.PitchSet,
abjad.PitchClassSegment,
abjad.PitchClassSet,
)
if isinstance(items, prototype):
intervals = []
items = tuple(items)
enumerator = Enumerator(items)
pairs = enumerator.yield_pairs()
for first, second in pairs:
intervals.append(second - first)
items = intervals
Vector.__init__(self, items=items, item_class=item_class)
def __init__(self, items=None, item_class=None):
import abjad
prototype = (
abjad.PitchSegment,
abjad.PitchSet,
abjad.PitchClassSegment,
abjad.PitchClassSet,
)
if isinstance(items, prototype):
intervals = []
items = tuple(items)
enumerator = Enumerator(items)
pairs = enumerator.yield_pairs()
for first, second in pairs:
intervals.append(second - first)
items = intervals
Vector.__init__(self, items=items, item_class=item_class)
def from_selection(class_, selection, item_class=None):
"""
Initializes interval set 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))
>>> intervals = abjad.IntervalSet.from_selection(selection)
>>> for interval in sorted(intervals):
... interval
...
NamedInterval('-M6')
NamedInterval('-P5')
NamedInterval('-A4')
NamedInterval('-M3')
NamedInterval('-m3')
NamedInterval('-M2')
NamedInterval('+m2')
NamedInterval('+m3')
NamedInterval('+M3')
NamedInterval('+P4')
NamedInterval('+P5')
NamedInterval('+m7')
NamedInterval('+M7')
NamedInterval('+P8')
NamedInterval('+M9')
NamedInterval('+A11')
NamedInterval('+M13')
Returns interval set.
"""
import abjad
pitch_segment = abjad.PitchSegment.from_selection(selection)
enumerator = Enumerator(pitch_segment)
pairs = enumerator.yield_pairs()
intervals = [second - first for first, second in pairs]
return class_(
items=intervals,
item_class=item_class,
)
def list_related_tempos(
self,
maximum_numerator=None,
maximum_denominator=None,
integer_tempos_only=False,
) -> typing.List[typing.Tuple["MetronomeMark", "Ratio"]]:
r"""
Lists related tempos.
.. container:: example
Rewrites tempo ``4=58`` by ratios ``n:d`` such that ``1 <= n <= 8``
and ``1 <= d <= 8``.
>>> mark = abjad.MetronomeMark((1, 4), 58)
>>> pairs = mark.list_related_tempos(
... maximum_numerator=8,
... maximum_denominator=8,
... )
>>> for tempo, ratio in pairs:
... string = f'{tempo!s}\t{ratio!s}'
... print(string)
4=29 1:2
4=33+1/7 4:7
4=34+4/5 3:5
4=36+1/4 5:8
4=38+2/3 2:3
4=41+3/7 5:7
4=43+1/2 3:4
4=46+2/5 4:5
4=48+1/3 5:6
4=49+5/7 6:7
4=50+3/4 7:8
4=58 1:1
4=66+2/7 8:7
4=67+2/3 7:6
4=69+3/5 6:5
4=72+1/2 5:4
4=77+1/3 4:3
4=81+1/5 7:5
4=87 3:2
4=92+4/5 8:5
4=96+2/3 5:3
4=101+1/2 7:4
4=116 2:1
.. container:: example
Integer-valued tempos only:
>>> mark = abjad.MetronomeMark((1, 4), 58)
>>> pairs = mark.list_related_tempos(
... maximum_numerator=16,
... maximum_denominator=16,
... integer_tempos_only=True,
... )
>>> for tempo, ratio in pairs:
... string = f'{tempo!s}\t{ratio!s}'
... print(string)
4=29 1:2
4=58 1:1
4=87 3:2
4=116 2:1
Constrains ratios such that ``1:2 <= n:d <= 2:1``.
"""
allowable_numerators = range(1, maximum_numerator + 1)
allowable_denominators = range(1, maximum_denominator + 1)
numbers = [allowable_numerators, allowable_denominators]
enumerator = Enumerator(numbers)
pairs = enumerator.yield_outer_product()
multipliers = [Multiplier(_) for _ in pairs]
multipliers = [_ for _ in multipliers if Fraction(1, 2) <= _ <= Fraction(2)]
multipliers.sort()
multipliers = sequence(multipliers).remove_repeats()
pairs = []
for multiplier in multipliers:
new_units_per_minute = multiplier * self.units_per_minute
if integer_tempos_only and not mathtools.is_integer_equivalent_number(
new_units_per_minute
):
continue
metronome_mark = type(self)(
reference_duration=self.reference_duration,
units_per_minute=new_units_per_minute,
)
ratio = Ratio(multiplier.pair)
pair = (metronome_mark, ratio)
pairs.append(pair)
return pairs