def _from_number(self, argument):
direction = mathtools.sign(argument)
number = self._to_nearest_quarter_tone(abs(argument))
pc_number = number % 12
if pc_number == 0 and number:
pc_number = 12
self._number = pc_number * direction
def direction_number(self):
"""
Gets direction number of named interval.
.. container:: example
>>> abjad.NamedInterval('+M9').direction_number
1
>>> abjad.NamedInterval('+dim2').direction_number
1
>>> abjad.NamedInterval('+A1').direction_number
1
>>> abjad.NamedInterval('P1').direction_number
0
>>> abjad.NamedInterval('-m3').direction_number
-1
Returns ``-1``, ``0`` or ``1``.
"""
if self.quality == "P" and abs(self.number) == 1:
return 0
return mathtools.sign(self.number)
def _from_interval_or_interval_class(self, argument):
try:
quality = argument.quality
diatonic_number = abs(argument.number)
direction = mathtools.sign(argument.number)
except AttributeError:
direction, quality, diatonic_number = self._numbered_to_named(
argument)
self._from_named_parts(direction, quality, diatonic_number)
def _from_interval_or_interval_class(self, argument):
try:
quality = argument.quality
diatonic_number = abs(argument.number)
direction = mathtools.sign(argument.number)
except AttributeError:
direction, quality, diatonic_number = self._numbered_to_named(
argument
)
self._from_named_parts(direction, quality, diatonic_number)
def __str__(self):
"""
String representation of numbered interval.
Returns string.
"""
direction_symbol = constants._direction_number_to_direction_symbol[
mathtools.sign(self.number)
]
return "{}{}".format(direction_symbol, abs(self.number))
def _from_number(self, argument):
import abjad
number = self._to_nearest_quarter_tone(argument)
direction = mathtools.sign(number)
octaves = 0
pc_number = abs(number)
while pc_number > 12:
pc_number -= 12
octaves += 1
self._octaves = octaves
self._interval_class = abjad.NumberedIntervalClass(pc_number *
direction)
def test_init(input_, semitones, name):
class_ = NamedInterval
if (
isinstance(semitones, type) and
issubclass(semitones, Exception)
):
with pytest.raises(semitones):
class_(input_)
return
instance = class_(input_)
assert float(instance) == semitones
assert instance.name == name
NamedInterval(instance)
NumberedInterval(instance)
NamedIntervalClass(instance)
NumberedIntervalClass(instance)
if isinstance(input_, str):
group_dict = constants._interval_name_abbreviation_regex.match(
input_).groupdict()
inflected_up = class_('{}{}{}{}'.format(
group_dict['direction'] or '',
group_dict['quality'],
'+',
group_dict['number'],
))
inflected_down = class_('{}{}{}{}'.format(
group_dict['direction'] or '',
group_dict['quality'],
'~',
group_dict['number'],
))
if (
(mathtools.sign(float(instance)) == instance.direction_number) and
abs(instance.number) != 1
):
direction = mathtools.sign(float(instance))
assert float(inflected_up) == (abs(float(instance)) + 0.5) * direction
assert float(inflected_down) == (abs(float(instance)) - 0.5) * direction
def _from_number(self, argument):
import abjad
number = self._to_nearest_quarter_tone(argument)
direction = mathtools.sign(number)
octaves = 0
pc_number = abs(number)
while pc_number > 12:
pc_number -= 12
octaves += 1
self._octaves = octaves
self._interval_class = abjad.NumberedIntervalClass(
pc_number * direction
)
def _numbered_to_named(cls, number):
number = cls._to_nearest_quarter_tone(float(number))
direction = mathtools.sign(number)
octaves, semitones = divmod(abs(number), 12)
quartertone = ""
if semitones % 1:
semitones -= 0.5
quartertone = "+"
quality, diatonic_number = constants._semitones_to_quality_and_diatonic_number[
semitones]
quality += quartertone
diatonic_number += octaves * 7
diatonic_number = cls._to_nearest_quarter_tone(diatonic_number)
return direction, quality, diatonic_number
def number(self):
"""
Gets number of named interval.
.. container:: example
>>> abjad.NamedInterval('+M9').number
9
Returns nonnegative number.
"""
number = self._interval_class._number
direction = mathtools.sign(number)
number = abs(number) + (7 * self.octaves)
return number * direction
def _numbered_to_named(cls, number):
number = cls._to_nearest_quarter_tone(float(number))
direction = mathtools.sign(number)
octaves, semitones = divmod(abs(number), 12)
quartertone = ""
if semitones % 1:
semitones -= 0.5
quartertone = "+"
quality, diatonic_number = constants._semitones_to_quality_and_diatonic_number[
semitones
]
quality += quartertone
diatonic_number += octaves * 7
diatonic_number = cls._to_nearest_quarter_tone(diatonic_number)
return direction, quality, diatonic_number
def number(self):
"""
Gets number of named interval.
.. container:: example
>>> abjad.NamedInterval('+M9').number
9
Returns nonnegative number.
"""
number = self._interval_class._number
direction = mathtools.sign(number)
number = abs(number) + (7 * self.octaves)
return number * direction
def __init__(self, argument):
import abjad
if isinstance(argument, str):
match = constants._interval_name_abbreviation_regex.match(argument)
if match is None:
try:
argument = float(argument)
self._from_number(argument)
return
except ValueError:
message = 'can not initialize {} from {!r}.'
message = message.format(type(self).__name__, argument)
raise ValueError(message)
message = 'can not initialize {} from {!r}.'
message = message.format(type(self).__name__, argument)
raise ValueError(message)
group_dict = match.groupdict()
direction = group_dict['direction']
if direction == '-':
direction = -1
else:
direction = 1
quality = group_dict['quality']
diatonic_number = int(group_dict['number'])
quality = self._validate_quality_and_diatonic_number(
quality,
diatonic_number,
)
quartertone = group_dict['quartertone']
quality += quartertone
self._from_named_parts(direction, quality, diatonic_number)
elif isinstance(argument, tuple) and len(argument) == 2:
quality, number = argument
direction = mathtools.sign(number)
diatonic_number = abs(number)
quality = self._validate_quality_and_diatonic_number(
quality,
diatonic_number,
)
self._from_named_parts(direction, quality, diatonic_number)
elif isinstance(argument, numbers.Number):
self._from_number(argument)
elif isinstance(argument, (abjad.Interval, abjad.IntervalClass)):
self._from_interval_or_interval_class(argument)
else:
message = 'can not initialize {} from {!r}.'
message = message.format(type(self).__name__, argument)
raise ValueError(message)
def __init__(self, argument):
import abjad
if isinstance(argument, str):
match = constants._interval_name_abbreviation_regex.match(argument)
if match is None:
try:
argument = float(argument)
self._from_number(argument)
return
except ValueError:
message = "can not initialize {} from {!r}."
message = message.format(type(self).__name__, argument)
raise ValueError(message)
message = "can not initialize {} from {!r}."
message = message.format(type(self).__name__, argument)
raise ValueError(message)
group_dict = match.groupdict()
direction = group_dict["direction"]
if direction == "-":
direction = -1
else:
direction = 1
quality = group_dict["quality"]
diatonic_number = int(group_dict["number"])
quality = self._validate_quality_and_diatonic_number(
quality, diatonic_number
)
quartertone = group_dict["quartertone"]
quality += quartertone
self._from_named_parts(direction, quality, diatonic_number)
elif isinstance(argument, tuple) and len(argument) == 2:
quality, number = argument
direction = mathtools.sign(number)
diatonic_number = abs(number)
quality = self._validate_quality_and_diatonic_number(
quality, diatonic_number
)
self._from_named_parts(direction, quality, diatonic_number)
elif isinstance(argument, numbers.Number):
self._from_number(argument)
elif isinstance(argument, (abjad.Interval, abjad.IntervalClass)):
self._from_interval_or_interval_class(argument)
else:
message = "can not initialize {} from {!r}."
message = message.format(type(self).__name__, argument)
raise ValueError(message)
def direction_number(self):
"""
Gets direction number of numbered interval.
.. container:: example
>>> abjad.NumberedInterval(-14).direction_number
-1
>>> abjad.NumberedInterval(0).direction_number
0
>>> abjad.NumberedInterval(6).direction_number
1
Returns integer.
""" ""
return mathtools.sign(self.number)
def direction_number(self):
"""
Gets direction number of numbered interval.
.. container:: example
>>> abjad.NumberedInterval(-14).direction_number
-1
>>> abjad.NumberedInterval(0).direction_number
0
>>> abjad.NumberedInterval(6).direction_number
1
Returns integer.
""" ""
return mathtools.sign(self.number)
def direction_number(self):
"""
Gets direction number of named interval-class.
.. container:: example
>>> abjad.NamedIntervalClass('P1').direction_number
0
>>> abjad.NamedIntervalClass('+M2').direction_number
1
>>> abjad.NamedIntervalClass('-M2').direction_number
-1
Returns -1, 0 or 1.
"""
if self.quality == "P" and abs(self.number) == 1:
return 0
return mathtools.sign(self.number)
def direction_number(self):
"""
Gets direction number of named interval-class.
.. container:: example
>>> abjad.NamedIntervalClass('P1').direction_number
0
>>> abjad.NamedIntervalClass('+M2').direction_number
1
>>> abjad.NamedIntervalClass('-M2').direction_number
-1
Returns -1, 0 or 1.
"""
if self.quality == 'P' and abs(self.number) == 1:
return 0
return mathtools.sign(self.number)
def number(self):
"""
Gets number of numbered interval.
.. container:: example
>>> abjad.NumberedInterval(-14).number
-14
>>> abjad.NumberedInterval(-2).number
-2
>>> abjad.NumberedInterval(0).number
0
Returns number.
"""
number = self._interval_class._number
direction = mathtools.sign(number)
number = abs(number) + (12 * self.octaves)
return number * direction
def number(self):
"""
Gets number of numbered interval.
.. container:: example
>>> abjad.NumberedInterval(-14).number
-14
>>> abjad.NumberedInterval(-2).number
-2
>>> abjad.NumberedInterval(0).number
0
Returns number.
"""
number = self._interval_class._number
direction = mathtools.sign(number)
number = abs(number) + (12 * self.octaves)
return number * direction
def _named_to_numbered(cls, direction, quality, diatonic_number):
octave_number = 0
diatonic_pc_number = abs(diatonic_number)
while diatonic_pc_number >= 8:
diatonic_pc_number -= 7
octave_number += 1
quartertone = ""
if quality.endswith(("+", "~")):
quality, quartertone = quality[:-1], quality[-1]
base_quality = quality
if base_quality == "P" and octave_number and diatonic_pc_number == 1:
return 12 * direction
if len(quality) > 1:
base_quality = quality[0]
semitones = constants._diatonic_number_and_quality_to_semitones[
diatonic_pc_number
][base_quality]
if base_quality == "d":
semitones -= len(quality) - 1
elif base_quality == "A":
semitones += len(quality) - 1
if quartertone == "+":
semitones += 0.5
elif quartertone == "~":
semitones -= 0.5
if abs(diatonic_number) == 1:
semitones = abs(semitones)
while abs(semitones) > 12:
semitones = (abs(semitones) - 12) * mathtools.sign(semitones)
semitones *= direction
return mathtools.integer_equivalent_number_to_integer(semitones)
def _named_to_numbered(cls, direction, quality, diatonic_number):
octave_number = 0
diatonic_pc_number = abs(diatonic_number)
while diatonic_pc_number >= 8:
diatonic_pc_number -= 7
octave_number += 1
quartertone = ""
if quality.endswith(("+", "~")):
quality, quartertone = quality[:-1], quality[-1]
base_quality = quality
if base_quality == "P" and octave_number and diatonic_pc_number == 1:
return 12 * direction
if len(quality) > 1:
base_quality = quality[0]
semitones = constants._diatonic_number_and_quality_to_semitones[
diatonic_pc_number
][base_quality]
if base_quality == "d":
semitones -= len(quality) - 1
elif base_quality == "A":
semitones += len(quality) - 1
if quartertone == "+":
semitones += 0.5
elif quartertone == "~":
semitones -= 0.5
if abs(diatonic_number) == 1:
semitones = abs(semitones)
while abs(semitones) > 12:
semitones = (abs(semitones) - 12) * mathtools.sign(semitones)
semitones *= direction
return mathtools.integer_equivalent_number_to_integer(semitones)
import pytest
from abjad import mathtools
from abjad.pitch import (
NamedInterval,
NamedIntervalClass,
NumberedInterval,
NumberedIntervalClass,
)
values = []
values.extend(
(x, ((abs(x) % 12) or 12) * mathtools.sign(x)) for x in range(-48, 49)
)
values.extend(
[
("-A1", -1),
("-A10", -5),
("-A11", -6),
("-A12", -8),
("-A13", -10),
("-A14", -12),
("-A2", -3),
("-A3", -5),
("-A4", -6),
("-A5", -8),
("-A6", -10),
("-A7", -12),
("-A8", -1),
def partition_integer_by_ratio(n, ratio):
"""
Partitions positive integer-equivalent ``n`` by ``ratio``.
.. container:: example
>>> abjad.mathtools.partition_integer_by_ratio(10, [1, 2])
[3, 7]
.. container:: example
Partitions positive integer-equivalent ``n`` by ``ratio`` with negative
parts:
>>> abjad.mathtools.partition_integer_by_ratio(10, [1, -2])
[3, -7]
.. container:: example
Partitions negative integer-equivalent ``n`` by ``ratio``:
>>> abjad.mathtools.partition_integer_by_ratio(-10, [1, 2])
[-3, -7]
.. container:: example
Partitions negative integer-equivalent ``n`` by ``ratio`` with negative
parts:
>>> abjad.mathtools.partition_integer_by_ratio(-10, [1, -2])
[-3, 7]
.. container:: example
More examples:
>>> abjad.mathtools.partition_integer_by_ratio(10, [1])
[10]
>>> abjad.mathtools.partition_integer_by_ratio(10, [1, 1])
[5, 5]
>>> abjad.mathtools.partition_integer_by_ratio(10, [1, -1, -1])
[3, -4, -3]
>>> abjad.mathtools.partition_integer_by_ratio(-10, [1, 1, 1, 1])
[-3, -2, -3, -2]
>>> abjad.mathtools.partition_integer_by_ratio(-10, [1, 1, 1, 1, 1])
[-2, -2, -2, -2, -2]
Returns result with weight equal to absolute value of ``n``.
Returns list of integers.
"""
from abjad import mathtools
if not mathtools.is_integer_equivalent_number(n):
message = "is not integer-equivalent number: {!r}."
message = message.format(n)
raise TypeError(message)
ratio = mathtools.Ratio(ratio).numbers
if not all(mathtools.is_integer_equivalent_number(part) for part in ratio):
message = "some parts in {!r} not integer-equivalent numbers."
message = message.format(ratio)
raise TypeError(message)
result = [0]
divisions = [
float(abs(n)) * abs(part) / mathtools.weight(ratio) for part in ratio
]
cumulative_divisions = mathtools.cumulative_sums(divisions, start=None)
for division in cumulative_divisions:
rounded_division = int(round(division)) - sum(result)
if division - round(division) == 0.5:
rounded_division += 1
result.append(rounded_division)
result = result[1:]
if mathtools.sign(n) == -1:
result = [-x for x in result]
ratio_signs = [mathtools.sign(x) for x in ratio]
result = [pair[0] * pair[1] for pair in zip(ratio_signs, result)]
return result
def partition_integer_by_ratio(n, ratio):
"""
Partitions positive integer-equivalent ``n`` by ``ratio``.
.. container:: example
>>> abjad.mathtools.partition_integer_by_ratio(10, [1, 2])
[3, 7]
.. container:: example
Partitions positive integer-equivalent ``n`` by ``ratio`` with negative
parts:
>>> abjad.mathtools.partition_integer_by_ratio(10, [1, -2])
[3, -7]
.. container:: example
Partitions negative integer-equivalent ``n`` by ``ratio``:
>>> abjad.mathtools.partition_integer_by_ratio(-10, [1, 2])
[-3, -7]
.. container:: example
Partitions negative integer-equivalent ``n`` by ``ratio`` with negative
parts:
>>> abjad.mathtools.partition_integer_by_ratio(-10, [1, -2])
[-3, 7]
.. container:: example
More examples:
>>> abjad.mathtools.partition_integer_by_ratio(10, [1])
[10]
>>> abjad.mathtools.partition_integer_by_ratio(10, [1, 1])
[5, 5]
>>> abjad.mathtools.partition_integer_by_ratio(10, [1, -1, -1])
[3, -4, -3]
>>> abjad.mathtools.partition_integer_by_ratio(-10, [1, 1, 1, 1])
[-3, -2, -3, -2]
>>> abjad.mathtools.partition_integer_by_ratio(-10, [1, 1, 1, 1, 1])
[-2, -2, -2, -2, -2]
Returns result with weight equal to absolute value of ``n``.
Returns list of integers.
"""
from abjad import mathtools
if not mathtools.is_integer_equivalent_number(n):
message = 'is not integer-equivalent number: {!r}.'
message = message.format(n)
raise TypeError(message)
ratio = mathtools.Ratio(ratio).numbers
if not all(mathtools.is_integer_equivalent_number(part) for part in ratio):
message = 'some parts in {!r} not integer-equivalent numbers.'
message = message.format(ratio)
raise TypeError(message)
result = [0]
divisions = [
float(abs(n)) * abs(part) / mathtools.weight(ratio) for part in ratio
]
cumulative_divisions = mathtools.cumulative_sums(divisions, start=None)
for division in cumulative_divisions:
rounded_division = int(round(division)) - sum(result)
if division - round(division) == 0.5:
rounded_division += 1
result.append(rounded_division)
result = result[1:]
if mathtools.sign(n) == -1:
result = [-x for x in result]
ratio_signs = [mathtools.sign(x) for x in ratio]
result = [pair[0] * pair[1] for pair in zip(ratio_signs, result)]
return result
def _sibling(self, n):
assert n in (-1, 1), repr(n)
for parent in inspect(self).parentage():
sibling = parent.__sibling(mathtools.sign(n))
if sibling is not None:
return sibling
def from_pitch_carriers(class_, pitch_carrier_1, pitch_carrier_2):
"""
Makes named interval calculated from `pitch_carrier_1` to
`pitch_carrier_2`.
.. container:: example
>>> abjad.NamedInterval.from_pitch_carriers(
... abjad.NamedPitch(-2),
... abjad.NamedPitch(12),
... )
NamedInterval('+M9')
>>> abjad.NamedInterval.from_pitch_carriers(
... abjad.NamedPitch("css'"),
... abjad.NamedPitch("cff'"),
... )
NamedInterval('-AAAA1')
>>> abjad.NamedInterval.from_pitch_carriers("c'", "cs'''")
NamedInterval('+A15')
>>> abjad.NamedInterval.from_pitch_carriers('c', 'cqs')
NamedInterval('+P+1')
>>> abjad.NamedInterval.from_pitch_carriers("cf'", 'bs')
NamedInterval('-dd2')
>>> abjad.NamedInterval.from_pitch_carriers("cff'", 'aqs')
NamedInterval('-ddd+3')
>>> abjad.NamedInterval.from_pitch_carriers("cff'", 'atqs')
NamedInterval('-dddd+3')
Returns named interval.
"""
import abjad
pitch_1 = abjad.NamedPitch(pitch_carrier_1)
pitch_2 = abjad.NamedPitch(pitch_carrier_2)
degree_1 = pitch_1._get_diatonic_pitch_number()
degree_2 = pitch_2._get_diatonic_pitch_number()
named_sign = mathtools.sign(degree_1 - degree_2)
named_i_number = abs(degree_1 - degree_2) + 1
numbered_sign = mathtools.sign(
float(abjad.NumberedPitch(pitch_1)) -
float(abjad.NumberedPitch(pitch_2)))
numbered_i_number = abs(
float(abjad.NumberedPitch(pitch_1)) -
float(abjad.NumberedPitch(pitch_2)))
named_ic_number = named_i_number
numbered_ic_number = numbered_i_number
while named_ic_number > 8 and numbered_ic_number > 12:
named_ic_number -= 7
numbered_ic_number -= 12
# Multiply-diminished intervals can have opposite signs
if named_sign and (named_sign == -numbered_sign):
numbered_ic_number *= -1
quartertone = ""
if numbered_ic_number % 1:
quartertone = "+"
numbered_ic_number -= 0.5
mapping = {
value: key
for key, value in constants.
_diatonic_number_and_quality_to_semitones[named_ic_number].items()
}
quality = ""
while numbered_ic_number > max(mapping):
numbered_ic_number -= 1
quality += "A"
while numbered_ic_number < min(mapping):
numbered_ic_number += 1
quality += "d"
quality += mapping[numbered_ic_number]
quality += quartertone
direction = 1
if pitch_2 < pitch_1:
direction = -1
return class_((quality, named_i_number * direction))
def partition_integer_into_canonic_parts(n, decrease_parts_monotonically=True):
"""
Partitions integer ``n`` into canonic parts.
.. container:: example
Returns all parts positive on positive ``n``:
>>> for n in range(1, 11):
... print(n, abjad.mathtools.partition_integer_into_canonic_parts(n))
...
1 (1,)
2 (2,)
3 (3,)
4 (4,)
5 (4, 1)
6 (6,)
7 (7,)
8 (8,)
9 (8, 1)
10 (8, 2)
.. container:: example
Returns all parts negative on negative ``n``:
>>> for n in reversed(range(-20, -10)):
... print(n, abjad.mathtools.partition_integer_into_canonic_parts(n))
...
-11 (-8, -3)
-12 (-12,)
-13 (-12, -1)
-14 (-14,)
-15 (-15,)
-16 (-16,)
-17 (-16, -1)
-18 (-16, -2)
-19 (-16, -3)
-20 (-16, -4)
.. container:: example
Returns parts that increase monotonically:
>>> for n in range(11, 21):
... print(n, abjad.mathtools.partition_integer_into_canonic_parts(n,
... decrease_parts_monotonically=False))
...
11 (3, 8)
12 (12,)
13 (1, 12)
14 (14,)
15 (15,)
16 (16,)
17 (1, 16)
18 (2, 16)
19 (3, 16)
20 (4, 16)
Returns tuple with parts that decrease monotonically.
Returns tuple of integers.
"""
from abjad import mathtools
assert isinstance(n, int), repr(n)
assert isinstance(decrease_parts_monotonically, bool)
if n == 0:
return (0,)
result = []
previous_empty = True
binary_n = mathtools.integer_to_binary_string(abs(n))
binary_length = len(binary_n)
for i, character in enumerate(binary_n):
if character == "1":
place_value = 2 ** (binary_length - i - 1)
if previous_empty:
result.append(place_value)
else:
result[-1] += place_value
previous_empty = False
else:
previous_empty = True
sign_n = mathtools.sign(n)
if mathtools.sign(n) == -1:
result = [sign_n * _ for _ in result]
if decrease_parts_monotonically:
return tuple(result)
else:
return tuple(reversed(result))
def from_pitch_carriers(class_, pitch_carrier_1, pitch_carrier_2):
"""
Makes named interval calculated from `pitch_carrier_1` to
`pitch_carrier_2`.
.. container:: example
>>> abjad.NamedInterval.from_pitch_carriers(
... abjad.NamedPitch(-2),
... abjad.NamedPitch(12),
... )
NamedInterval('+M9')
>>> abjad.NamedInterval.from_pitch_carriers(
... abjad.NamedPitch("css'"),
... abjad.NamedPitch("cff'"),
... )
NamedInterval('-AAAA1')
>>> abjad.NamedInterval.from_pitch_carriers("c'", "cs'''")
NamedInterval('+A15')
>>> abjad.NamedInterval.from_pitch_carriers('c', 'cqs')
NamedInterval('+P+1')
>>> abjad.NamedInterval.from_pitch_carriers("cf'", 'bs')
NamedInterval('-dd2')
>>> abjad.NamedInterval.from_pitch_carriers("cff'", 'aqs')
NamedInterval('-ddd+3')
>>> abjad.NamedInterval.from_pitch_carriers("cff'", 'atqs')
NamedInterval('-dddd+3')
Returns named interval.
"""
import abjad
pitch_1 = abjad.NamedPitch(pitch_carrier_1)
pitch_2 = abjad.NamedPitch(pitch_carrier_2)
degree_1 = pitch_1._get_diatonic_pitch_number()
degree_2 = pitch_2._get_diatonic_pitch_number()
named_sign = mathtools.sign(degree_1 - degree_2)
named_i_number = abs(degree_1 - degree_2) + 1
numbered_sign = mathtools.sign(
float(abjad.NumberedPitch(pitch_1))
- float(abjad.NumberedPitch(pitch_2))
)
numbered_i_number = abs(
float(abjad.NumberedPitch(pitch_1))
- float(abjad.NumberedPitch(pitch_2))
)
named_ic_number = named_i_number
numbered_ic_number = numbered_i_number
while named_ic_number > 8 and numbered_ic_number > 12:
named_ic_number -= 7
numbered_ic_number -= 12
# Multiply-diminished intervals can have opposite signs
if named_sign and (named_sign == -numbered_sign):
numbered_ic_number *= -1
quartertone = ""
if numbered_ic_number % 1:
quartertone = "+"
numbered_ic_number -= 0.5
mapping = {
value: key
for key, value in constants._diatonic_number_and_quality_to_semitones[
named_ic_number
].items()
}
quality = ""
while numbered_ic_number > max(mapping):
numbered_ic_number -= 1
quality += "A"
while numbered_ic_number < min(mapping):
numbered_ic_number += 1
quality += "d"
quality += mapping[numbered_ic_number]
quality += quartertone
direction = 1
if pitch_2 < pitch_1:
direction = -1
return class_((quality, named_i_number * direction))
def partition_integer_into_canonic_parts(n, decrease_parts_monotonically=True):
"""
Partitions integer ``n`` into canonic parts.
.. container:: example
Returns all parts positive on positive ``n``:
>>> for n in range(1, 11):
... print(n, abjad.mathtools.partition_integer_into_canonic_parts(n))
...
1 (1,)
2 (2,)
3 (3,)
4 (4,)
5 (4, 1)
6 (6,)
7 (7,)
8 (8,)
9 (8, 1)
10 (8, 2)
.. container:: example
Returns all parts negative on negative ``n``:
>>> for n in reversed(range(-20, -10)):
... print(n, abjad.mathtools.partition_integer_into_canonic_parts(n))
...
-11 (-8, -3)
-12 (-12,)
-13 (-12, -1)
-14 (-14,)
-15 (-15,)
-16 (-16,)
-17 (-16, -1)
-18 (-16, -2)
-19 (-16, -3)
-20 (-16, -4)
.. container:: example
Returns parts that increase monotonically:
>>> for n in range(11, 21):
... print(n, abjad.mathtools.partition_integer_into_canonic_parts(n,
... decrease_parts_monotonically=False))
...
11 (3, 8)
12 (12,)
13 (1, 12)
14 (14,)
15 (15,)
16 (16,)
17 (1, 16)
18 (2, 16)
19 (3, 16)
20 (4, 16)
Returns tuple with parts that decrease monotonically.
Returns tuple of integers.
"""
from abjad import mathtools
assert isinstance(n, int), repr(n)
assert isinstance(decrease_parts_monotonically, bool)
if n == 0:
return (0, )
result = []
previous_empty = True
binary_n = mathtools.integer_to_binary_string(abs(n))
binary_length = len(binary_n)
for i, character in enumerate(binary_n):
if character == '1':
place_value = 2**(binary_length - i - 1)
if previous_empty:
result.append(place_value)
else:
result[-1] += place_value
previous_empty = False
else:
previous_empty = True
sign_n = mathtools.sign(n)
if mathtools.sign(n) == -1:
result = [sign_n * _ for _ in result]
if decrease_parts_monotonically:
return tuple(result)
else:
return tuple(reversed(result))
def _sibling(self, n):
assert n in (-1, 1), repr(n)
for parent in inspect(self).parentage():
sibling = parent.__sibling(mathtools.sign(n))
if sibling is not None:
return sibling
import pytest
from abjad import mathtools
from abjad.pitch import (
NamedInterval,
NamedIntervalClass,
NumberedInterval,
NumberedIntervalClass,
)
values = []
values.extend(
(x, ((abs(x) % 12) or 12) * mathtools.sign(x)) for x in range(-48, 49))
values.extend([
('-A1', -1),
('-A10', -5),
('-A11', -6),
('-A12', -8),
('-A13', -10),
('-A14', -12),
('-A2', -3),
('-A3', -5),
('-A4', -6),
('-A5', -8),
('-A6', -10),
('-A7', -12),
('-A8', -1),
('-A9', -3),
('-AA1', -2),
('-AA10', -6),
