def __init__(self, interval_class_token=None):
from abjad.tools import pitchtools
if isinstance(interval_class_token, type(self)):
number = interval_class_token.number
elif isinstance(interval_class_token, numbers.Number):
if not 0 <= interval_class_token <= 6:
message = 'must be between 0 and 6, inclusive.'
raise ValueError(message)
number = interval_class_token
elif hasattr(interval_class_token, 'semitones'):
number = interval_class_token.semitones
number %= 12
if 6 < number:
number = 12 - number
elif interval_class_token is None:
number = 0
elif isinstance(interval_class_token, str):
number = float(interval_class_token)
if mathtools.is_integer_equivalent_expr(number):
number = int(number)
else:
message = 'can not initialize {}: {!r}.'
message = message.format(type(self).__name__, interval_class_token)
raise TypeError(message)
self._number = number
def _get_nth_component_in_time_order_from(self, n):
assert mathtools.is_integer_equivalent_expr(n)
def next(component):
if component is not None:
for parent in component._get_parentage(include_self=True):
next_sibling = parent._get_sibling(1)
if next_sibling is not None:
return next_sibling
def previous(component):
if component is not None:
for parent in component._get_parentage(include_self=True):
next_sibling = parent._get_sibling(-1)
if next_sibling is not None:
return next_sibling
result = self
if 0 < n:
for i in range(n):
result = next(result)
elif n < 0:
for i in range(abs(n)):
result = previous(result)
return result
def __init__(self, interval_class_token=None):
from abjad.tools import pitchtools
if isinstance(interval_class_token, type(self)):
number = interval_class_token.number
elif isinstance(interval_class_token, numbers.Number):
if not 0 <= interval_class_token <= 6:
message = 'must be between 0 and 6, inclusive.'
raise ValueError(message)
number = interval_class_token
elif hasattr(interval_class_token, 'semitones'):
number = interval_class_token.semitones
number %= 12
if 6 < number:
number = 12 - number
elif interval_class_token is None:
number = 0
elif isinstance(interval_class_token, str):
number = float(interval_class_token)
if mathtools.is_integer_equivalent_expr(number):
number = int(number)
else:
message = 'can not initialize {}: {!r}.'
message = message.format(type(self).__name__, interval_class_token)
raise TypeError(message)
self._number = number
def _handle_main_menu_result(self, result):
if not isinstance(result, str):
raise TypeError('result must be string.')
if result in self._user_input_to_action:
self._user_input_to_action[result]()
elif mathtools.is_integer_equivalent_expr(result):
self.edit_item(result)
else:
super(ListEditor, self)._handle_main_menu_result(result)
def _handle_main_menu_result(self, result):
assert isinstance(result, str)
if result in self.user_input_to_action:
self.user_input_to_action[result](self)
elif mathtools.is_integer_equivalent_expr(result):
self.interactively_edit_user_input_wrapper_at_number(
result, include_newline=False)
else:
raise ValueError(result)
def _format_repeat_tremolo_command(self):
tremolo = inspect_(self).get_indicator(indicatortools.Tremolo)
reattack_duration = self._get_tremolo_reattack_duration()
repeat_count = self.written_duration / reattack_duration / 2
if not mathtools.is_integer_equivalent_expr(repeat_count):
message = 'can not tremolo duration {} with {} beams.'
message = message.format(self.written_duration, tremolo.beam_count)
raise Exception(message)
repeat_count = int(repeat_count)
command = r'\repeat tremolo {}'.format(repeat_count)
return command
def _format_repeat_tremolo_command(self):
tremolo = inspect_(self).get_indicator(indicatortools.Tremolo)
reattack_duration = self._get_tremolo_reattack_duration()
repeat_count = self.written_duration / reattack_duration / 2
if not mathtools.is_integer_equivalent_expr(repeat_count):
message = 'can not tremolo duration {} with {} beams.'
message = message.format(self.written_duration, tremolo.beam_count)
raise Exception(message)
repeat_count = int(repeat_count)
command = r'\repeat tremolo {}'.format(repeat_count)
return command
def _handle_input(self, result):
assert isinstance(result, str), repr(result)
if result.endswith('!') and 1 < len(result):
self._session._is_autoadding = True
result = result.strip('!')
if result in self._command_to_method:
self._command_to_method[result]()
elif mathtools.is_integer_equivalent_expr(result):
if self.allow_item_edit:
self.edit_item(result)
else:
superclass = super(CollectionAutoeditor, self)
superclass._handle_input(result)
def __init__(
self,
leaf_count=None,
is_diminution=True,
beam_each_cell=True,
beam_cells_together=False,
):
assert mathtools.is_integer_equivalent_expr(leaf_count)
RhythmMaker.__init__(self,
beam_each_cell=beam_each_cell,
beam_cells_together=beam_cells_together
)
leaf_count = int(leaf_count)
self._leaf_count = leaf_count
self._is_diminution = is_diminution
def __init__(self, item=None):
from abjad.tools import pitchtools
if isinstance(item, numbers.Number):
sign = mathtools.sign(item)
abs_token = abs(item)
if abs_token % 12 == 0 and 12 <= abs_token:
number = 12
else:
number = abs_token % 12
number *= sign
elif isinstance(item, pitchtools.Interval):
number = item.semitones
sign = mathtools.sign(number)
abs_number = abs(number)
if abs_number % 12 == 0 and 12 <= abs_number:
number = 12
else:
number = abs_number % 12
number *= sign
elif isinstance(item, pitchtools.IntervalClass):
number = item.number
sign = mathtools.sign(number)
abs_number = abs(number)
if abs_number % 12 == 0 and 12 <= abs_number:
number = 12
else:
number = abs_number % 12
number *= sign
elif item is None:
number = 0
elif isinstance(item, str):
number = float(item)
if mathtools.is_integer_equivalent_expr(number):
number = int(number)
sign = mathtools.sign(number)
abs_token = abs(number)
if abs_token % 12 == 0 and 12 <= abs_token:
number = 12
else:
number = abs_token % 12
number *= sign
else:
message = 'can not initialize {}: {!r}.'
message = message.format(type(self).__name__, item)
raise ValueError(message)
self._number = number
def __init__(self, item=None):
from abjad.tools import pitchtools
if isinstance(item, numbers.Number):
sign = mathtools.sign(item)
abs_token = abs(item)
if abs_token % 12 == 0 and 12 <= abs_token:
number = 12
else:
number = abs_token % 12
number *= sign
elif isinstance(item, pitchtools.Interval):
number = item.semitones
sign = mathtools.sign(number)
abs_number = abs(number)
if abs_number % 12 == 0 and 12 <= abs_number:
number = 12
else:
number = abs_number % 12
number *= sign
elif isinstance(item, pitchtools.IntervalClass):
number = item.number
sign = mathtools.sign(number)
abs_number = abs(number)
if abs_number % 12 == 0 and 12 <= abs_number:
number = 12
else:
number = abs_number % 12
number *= sign
elif item is None:
number = 0
elif isinstance(item, str):
number = float(item)
if mathtools.is_integer_equivalent_expr(number):
number = int(number)
sign = mathtools.sign(number)
abs_token = abs(number)
if abs_token % 12 == 0 and 12 <= abs_token:
number = 12
else:
number = abs_token % 12
number *= sign
else:
message = 'can not initialize {}: {!r}.'
message = message.format(type(self).__name__, item)
raise ValueError(message)
self._number = number
def _scale_taleas(self, divisions, talea_denominator, taleas):
talea_denominator = talea_denominator or 1
dummy_division = (1, talea_denominator)
divisions.append(dummy_division)
Duration = durationtools.Duration
divisions = Duration.durations_to_nonreduced_fractions(divisions)
dummy_division = divisions.pop()
lcd = dummy_division.denominator
multiplier = lcd / talea_denominator
assert mathtools.is_integer_equivalent_expr(multiplier), repr(multiplier)
multiplier = int(multiplier)
scaled_taleas = []
for talea in taleas:
talea = [multiplier * _ for _ in talea]
talea = datastructuretools.CyclicTuple(talea)
scaled_taleas.append(talea)
result = [divisions, lcd]
result.extend(scaled_taleas)
return tuple(result)
def _scale_taleas(self, divisions, talea_denominator, taleas):
talea_denominator = talea_denominator or 1
dummy_division = (1, talea_denominator)
divisions.append(dummy_division)
Duration = durationtools.Duration
divisions = Duration.durations_to_nonreduced_fractions(divisions)
dummy_division = divisions.pop()
lcd = dummy_division.denominator
multiplier = lcd / talea_denominator
assert mathtools.is_integer_equivalent_expr(multiplier), repr(
multiplier)
multiplier = int(multiplier)
scaled_taleas = []
for talea in taleas:
talea = [multiplier * _ for _ in talea]
talea = datastructuretools.CyclicTuple(talea)
scaled_taleas.append(talea)
result = [divisions, lcd]
result.extend(scaled_taleas)
return tuple(result)
def __init__(
self,
leaf_count=1,
is_diminution=True,
beam_cells_together=False,
beam_each_cell=True,
decrease_durations_monotonically=True,
forbidden_written_duration=None,
):
RhythmMaker.__init__(
self,
beam_cells_together=beam_cells_together,
beam_each_cell=beam_each_cell,
decrease_durations_monotonically=decrease_durations_monotonically,
forbidden_written_duration=forbidden_written_duration,
)
assert mathtools.is_integer_equivalent_expr(leaf_count)
leaf_count = int(leaf_count)
self._leaf_count = leaf_count
self._is_diminution = is_diminution
def is_integer_equivalent_singleton(expr):
r'''Is true when `expr` is a singleton of integer-equivalent expressions.
::
>>> mathtools.is_integer_equivalent_singleton((2.0,))
True
Otherwise false:
::
>>> mathtools.is_integer_equivalent_singleton((2.5,))
False
Returns boolean.
'''
from abjad.tools import mathtools
return isinstance(expr, tuple) and len(expr) == 1 and \
all(mathtools.is_integer_equivalent_expr(x) for x in expr)
def is_integer_equivalent_pair(expr):
r'''Is true when `expr` is a pair of integer-equivalent expressions.
::
>>> mathtools.is_integer_equivalent_pair((2.0, '3'))
True
Otherwise false:
::
>>> mathtools.is_integer_equivalent_pair((2.5, '3'))
False
Returns boolean.
'''
from abjad.tools import mathtools
return isinstance(expr, tuple) and len(expr) == 2 and \
all(mathtools.is_integer_equivalent_expr(x) for x in expr)
def is_integer_equivalent_pair(expr):
r'''Is true when `expr` is a pair of integer-equivalent expressions.
::
>>> mathtools.is_integer_equivalent_pair((2.0, '3'))
True
Otherwise false:
::
>>> mathtools.is_integer_equivalent_pair((2.5, '3'))
False
Returns true or false.
'''
from abjad.tools import mathtools
return isinstance(expr, tuple) and len(expr) == 2 and \
all(mathtools.is_integer_equivalent_expr(x) for x in expr)
def is_integer_equivalent_n_tuple(expr, n):
r'''Is true when `expr` is a tuple of `n` integer-equivalent expressions.
::
>>> mathtools.is_integer_equivalent_n_tuple((2.0, '3', Fraction(4, 1)), 3)
True
Otherwise false:
::
>>> mathtools.is_integer_equivalent_n_tuple((2.5, '3', Fraction(4, 1)), 3)
False
Returns boolean.
'''
from abjad.tools import mathtools
return isinstance(expr, tuple) and len(expr) == n and \
all(mathtools.is_integer_equivalent_expr(x) for x in expr)
def is_integer_equivalent_n_tuple(expr, n):
r'''Is true when `expr` is a tuple of `n` integer-equivalent expressions.
::
>>> mathtools.is_integer_equivalent_n_tuple((2.0, '3', Fraction(4, 1)), 3)
True
Otherwise false:
::
>>> mathtools.is_integer_equivalent_n_tuple((2.5, '3', Fraction(4, 1)), 3)
False
Returns true or false.
'''
from abjad.tools import mathtools
return isinstance(expr, tuple) and len(expr) == n and \
all(mathtools.is_integer_equivalent_expr(x) for x in expr)
def is_integer_equivalent_singleton(expr):
r'''Is true when `expr` is a singleton of integer-equivalent expressions.
::
>>> mathtools.is_integer_equivalent_singleton((2.0,))
True
Otherwise false:
::
>>> mathtools.is_integer_equivalent_singleton((2.5,))
False
Returns true or false.
'''
from abjad.tools import mathtools
return isinstance(expr, tuple) and len(expr) == 1 and \
all(mathtools.is_integer_equivalent_expr(x) for x in expr)
def all_are_integer_equivalent_exprs(expr):
"""True when `expr` is a sequence and all elements in `expr` are integer-equivalent expressions:
::
>>> sequencetools.all_are_integer_equivalent_exprs([1, '2', 3.0, Fraction(4, 1)])
True
Otherwise false:
::
>>> sequencetools.all_are_integer_equivalent_exprs([1, '2', 3.5, 4])
False
Returns boolean.
"""
try:
return all(mathtools.is_integer_equivalent_expr(x) for x in expr)
except TypeError:
return False
def all_are_integer_equivalent_exprs(expr):
'''Is true when `expr` is a sequence and all elements in `expr` are
integer-equivalent expressions.
::
>>> mathtools.all_are_integer_equivalent_exprs([1, '2', 3.0, Fraction(4, 1)])
True
Otherwise false:
::
>>> mathtools.all_are_integer_equivalent_exprs([1, '2', 3.5, 4])
False
Returns true or false.
'''
from abjad.tools import mathtools
try:
return all(mathtools.is_integer_equivalent_expr(x) for x in expr)
except TypeError:
return False
def _get_nth_component_in_time_order_from(self, n):
assert mathtools.is_integer_equivalent_expr(n)
def next(component):
if component is not None:
for parent in component._get_parentage(include_self=True):
next_sibling = parent._get_sibling(1)
if next_sibling is not None:
return next_sibling
def previous(component):
if component is not None:
for parent in component._get_parentage(include_self=True):
next_sibling = parent._get_sibling(-1)
if next_sibling is not None:
return next_sibling
result = self
if 0 < n:
for i in range(n):
result = next(result)
elif n < 0:
for i in range(abs(n)):
result = previous(result)
return result
def test_mathtools_is_integer_equivalent_expr_02():
assert not mathtools.is_integer_equivalent_expr('foo')
assert not mathtools.is_integer_equivalent_expr('12.0')
assert not mathtools.is_integer_equivalent_expr(1.5)
assert not mathtools.is_integer_equivalent_expr(-1.5)
def test_mathtools_is_integer_equivalent_expr_01():
assert mathtools.is_integer_equivalent_expr(12)
assert mathtools.is_integer_equivalent_expr('12')
assert mathtools.is_integer_equivalent_expr(-1)
assert mathtools.is_integer_equivalent_expr('-1')
def list_related_tempos(
self,
maximum_numerator=None,
maximum_denominator=None,
):
r'''Lists tempos related to this tempo.
Returns list of tempo / ratio pairs.
Each new tempo equals not less than half of this tempo
and not more than twice this tempo.
.. container:: example
Rewrites tempo ``58`` MM by ratios of the form ``n:d`` such that
``1 <= n <= 8`` and ``1 <= d <= 8``:
...
::
>>> tempo = Tempo(Duration(1, 4), 58)
>>> pairs = tempo.list_related_tempos(
... maximum_numerator=8,
... maximum_denominator=8,
... )
::
>>> for tempo, ratio in pairs:
... string = '{!s}\t{!s}'.format(tempo, ratio)
... print(string)
4=29 1:2
4=58 1:1
4=87 3:2
4=116 2:1
.. container:: example
Rewrites tempo ``58`` MM by ratios of the form ``n:d`` such that
``1 <= n <= 30`` and ``1 <= d <= 30``:
::
>>> tempo = Tempo(Duration(1, 4), 58)
>>> pairs = tempo.list_related_tempos(
... maximum_numerator=30,
... maximum_denominator=30,
... )
::
>>> for tempo, ratio in pairs:
... string = '{!s}\t{!s}'.format(tempo, ratio)
... print(string)
...
4=30 15:29
4=32 16:29
4=34 17:29
4=36 18:29
4=38 19:29
4=40 20:29
4=42 21:29
4=44 22:29
4=46 23:29
4=48 24:29
4=50 25:29
4=52 26:29
4=54 27:29
4=56 28:29
4=58 1:1
4=60 30:29
Returns list.
'''
# assert integer tempo
assert isinstance(self.units_per_minute, int), repr(self)
# find divisors
divisors = mathtools.divisors(self.units_per_minute)
if maximum_denominator is not None:
divisors = [x for x in divisors if x <= maximum_denominator]
# make pairs
pairs = []
for divisor in divisors:
start = int(math.ceil(divisor / 2.0))
stop = 2 * divisor
numerators = range(start, stop + 1)
if maximum_numerator is not None:
numerators = [
x for x in numerators
if x <= maximum_numerator
]
for numerator in numerators:
ratio = mathtools.Ratio(numerator, divisor)
multiplier = durationtools.Multiplier(*ratio)
new_units_per_minute = multiplier * self.units_per_minute
assert mathtools.is_integer_equivalent_expr(
new_units_per_minute)
new_units_per_minute = int(new_units_per_minute)
new_tempo = type(self)(
duration=self.duration,
units_per_minute=new_units_per_minute,
)
pair = (new_tempo, ratio)
if pair not in pairs:
pairs.append(pair)
# sort pairs
pairs.sort()
# return pairs
return pairs
def list_related_tempos(
self,
maximum_numerator=None,
maximum_denominator=None,
):
r'''Lists tempos related to this tempo.
Returns list of tempo / ratio pairs.
Each new tempo equals not less than half of this tempo
and not more than twice this tempo.
.. container:: example
Rewrites tempo ``58`` MM by ratios of the form ``n:d`` such that
``1 <= n <= 8`` and ``1 <= d <= 8``:
...
::
>>> tempo = Tempo(Duration(1, 4), 58)
>>> pairs = tempo.list_related_tempos(
... maximum_numerator=8,
... maximum_denominator=8,
... )
::
>>> for tempo, ratio in pairs:
... string = '{!s}\t{!s}'.format(tempo, ratio)
... print string
4=29 1:2
4=58 1:1
4=87 3:2
4=116 2:1
.. container:: example
Rewrites tempo ``58`` MM by ratios of the form ``n:d`` such that
``1 <= n <= 30`` and ``1 <= d <= 30``:
::
>>> tempo = Tempo(Duration(1, 4), 58)
>>> pairs = tempo.list_related_tempos(
... maximum_numerator=30,
... maximum_denominator=30,
... )
::
>>> for tempo, ratio in pairs:
... string = '{!s}\t{!s}'.format(tempo, ratio)
... print string
...
4=30 15:29
4=32 16:29
4=34 17:29
4=36 18:29
4=38 19:29
4=40 20:29
4=42 21:29
4=44 22:29
4=46 23:29
4=48 24:29
4=50 25:29
4=52 26:29
4=54 27:29
4=56 28:29
4=58 1:1
4=60 30:29
Returns list.
'''
# assert integer tempo
assert isinstance(self.units_per_minute, int), repr(self)
# find divisors
divisors = mathtools.divisors(self.units_per_minute)
if maximum_denominator is not None:
divisors = [x for x in divisors if x <= maximum_denominator]
# make pairs
pairs = []
for divisor in divisors:
start = int(math.ceil(divisor / 2.0))
stop = 2 * divisor
numerators = range(start, stop + 1)
if maximum_numerator is not None:
numerators = [
x for x in numerators
if x <= maximum_numerator
]
for numerator in numerators:
ratio = mathtools.Ratio(numerator, divisor)
multiplier = durationtools.Multiplier(*ratio)
new_units_per_minute = multiplier * self.units_per_minute
assert mathtools.is_integer_equivalent_expr(
new_units_per_minute)
new_units_per_minute = int(new_units_per_minute)
new_tempo = type(self)(self.duration, new_units_per_minute)
pair = (new_tempo, ratio)
if pair not in pairs:
pairs.append(pair)
# sort pairs
pairs.sort()
# return pairs
return pairs
