def __sub__(self, argument):
r'''Subtracts `argument` from numbered pitch-class.
Subtraction is defined against both numbered intervals
and against other pitch-classes.
.. container:: example
::
>>> abjad.NumberedPitchClass(6) - abjad.NumberedPitchClass(6)
NumberedInversionEquivalentIntervalClass(0)
::
>>> abjad.NumberedPitchClass(6) - abjad.NumberedPitchClass(7)
NumberedInversionEquivalentIntervalClass(1)
::
>>> abjad.NumberedPitchClass(7) - abjad.NumberedPitchClass(6)
NumberedInversionEquivalentIntervalClass(1)
.. container:: example
::
>>> abjad.NumberedPitchClass(6) - abjad.NumberedInterval(-1)
NumberedPitchClass(5)
::
>>> abjad.NumberedPitchClass(6) - abjad.NumberedInterval(0)
NumberedPitchClass(6)
::
>>> abjad.NumberedPitchClass(6) - abjad.NumberedInterval(1)
NumberedPitchClass(5)
Returns numbered inversion-equivalent interval-class.
'''
from abjad.tools import pitchtools
if isinstance(argument, type(self)):
interval_class_number = abs(
self.number - argument.number
)
if 6 < interval_class_number:
interval_class_number = 12 - interval_class_number
return pitchtools.NumberedInversionEquivalentIntervalClass(
interval_class_number)
interval_class = pitchtools.NumberedInversionEquivalentIntervalClass(
argument)
return type(self)(self.number - interval_class.number % 12)
def __sub__(self, expr):
r'''Subtracts `expr` from numbered pitch-class.
Subtraction defined against both numbered intervals
and against other pitch-classes.
Returns numbered inversion-equivalent interval-class.
'''
from abjad.tools import pitchtools
if isinstance(expr, type(self)):
interval_class_number = abs(self.pitch_class_number -
expr.pitch_class_number)
if 6 < interval_class_number:
interval_class_number = 12 - interval_class_number
return pitchtools.NumberedInversionEquivalentIntervalClass(
interval_class_number)
interval_class = pitchtools.NumberedInversionEquivalentIntervalClass(
expr)
return type(self)(self.pitch_class_number - interval_class.number % 12)
def label_leaves_in_expr_with_numbered_inversion_equivalent_interval_classes(
expr, markup_direction=Up):
r"""Label leaves in `expr` with numbered inversion-equivalent interval classes:
::
>>> notes = scoretools.make_notes(
... [0, 25, 11, -4, -14, -13, 9, 10, 6, 5],
... [Duration(1, 8)],
... )
>>> staff = Staff(notes)
>>> labeltools.label_leaves_in_expr_with_numbered_inversion_equivalent_interval_classes(
... staff)
.. doctest::
>>> print(format(staff))
\new Staff {
c'8 ^ \markup { 1 }
cs'''8 ^ \markup { 2 }
b'8 ^ \markup { 3 }
af8 ^ \markup { 2 }
bf,8 ^ \markup { 1 }
b,8 ^ \markup { 2 }
a'8 ^ \markup { 1 }
bf'8 ^ \markup { 4 }
fs'8 ^ \markup { 1 }
f'8
}
::
>>> show(staff) # doctest: +SKIP
Returns none.
"""
for note in iterate(expr).by_class(scoretools.Note):
logical_voice_iterator = iterate(note).by_logical_voice_from_component(
scoretools.Leaf, )
try:
next(logical_voice_iterator)
next_leaf = next(logical_voice_iterator)
if isinstance(next_leaf, scoretools.Note):
mdi = note.written_pitch - next_leaf.written_pitch
iecic = \
pitchtools.NumberedInversionEquivalentIntervalClass(mdi)
markup = markuptools.Markup(iecic, markup_direction)
attach(markup, note)
except StopIteration:
pass
def instantiate_pitch_and_interval_test_collection():
r'''Instantiate pitch and interval test collection:
::
>>> for x in pitchtools.instantiate_pitch_and_interval_test_collection(): x
...
NumberedInversionEquivalentIntervalClass(1)
NamedInversionEquivalentIntervalClass('+M2')
NumberedInterval(1)
NumberedIntervalClass(1)
NamedInterval('+M2')
NamedIntervalClass('+M2')
NamedPitch('c')
NamedPitchClass('c')
NumberedPitch(1)
NumberedPitchClass(1)
Use to test pitch and interval interface consistency.
Returns list.
'''
from abjad.tools import pitchtools
result = []
result.append(pitchtools.NumberedInversionEquivalentIntervalClass(1))
result.append(pitchtools.NamedInversionEquivalentIntervalClass('M2'))
result.append(pitchtools.NumberedInterval(1))
result.append(pitchtools.NumberedIntervalClass(1))
result.append(pitchtools.NamedInterval('M2'))
result.append(pitchtools.NamedIntervalClass('M2'))
result.append(pitchtools.NamedPitch('c'))
result.append(pitchtools.NamedPitchClass('c'))
result.append(pitchtools.NumberedPitch(1))
result.append(pitchtools.NumberedPitchClass(1))
return result
def list_numbered_inversion_equivalent_interval_classes_pairwise(
pitch_carriers,
wrap=False,
):
r'''Lists numbered inversion-equivalent interval-classes pairwise between
`pitch_carriers`.
::
>>> staff = Staff("c'8 d'8 e'8 f'8 g'8 a'8 b'8 c''8")
.. doctest::
>>> f(staff)
\new Staff {
c'8
d'8
e'8
f'8
g'8
a'8
b'8
c''8
}
::
>>> result = pitchtools.list_numbered_inversion_equivalent_interval_classes_pairwise(
... staff[:], wrap=False)
::
>>> for x in result: x
...
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(1)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(1)
::
>>> result = pitchtools.list_numbered_inversion_equivalent_interval_classes_pairwise(
... staff[:], wrap=True)
::
>>> for x in result: x
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(1)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(1)
NumberedInversionEquivalentIntervalClass(0)
::
>>> notes = staff[:]
>>> notes = list(reversed(notes))
::
>>> result = pitchtools.list_numbered_inversion_equivalent_interval_classes_pairwise(
... notes, wrap=False)
::
>>> for x in result: x
...
NumberedInversionEquivalentIntervalClass(1)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(1)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
::
>>> result = pitchtools.list_numbered_inversion_equivalent_interval_classes_pairwise(
... notes, wrap=True)
::
>>> for x in result: x
...
NumberedInversionEquivalentIntervalClass(1)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(1)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(2)
NumberedInversionEquivalentIntervalClass(0)
When ``wrap=False`` does not return ``pitch_carriers[-1] -
pitch_carriers[0]`` as last in series.
When ``wrap=True`` does return ``pitch_carriers[-1] - pitch_carriers[0]``
as last in series.
Returns list.
'''
from abjad.tools import pitchtools
result = []
if len(pitch_carriers) == 0:
return result
elif len(pitch_carriers) == 1:
if pitchtools.Pitch.is_pitch_carrier(pitch_carriers[0]):
return result
else:
message = 'must be pitch, note, note-head or chord.'
raise TypeError(message)
if wrap:
pairs = sequencetools.iterate_sequence_nwise(
pitch_carriers, wrapped=True)
else:
pairs = sequencetools.iterate_sequence_nwise(pitch_carriers)
for first_carrier, second_carrier in pairs:
first_pitch = pitchtools.NamedPitch.from_pitch_carrier(first_carrier)
second_pitch = pitchtools.NamedPitch.from_pitch_carrier(second_carrier)
mdi = second_pitch - first_pitch
iecic = pitchtools.NumberedInversionEquivalentIntervalClass(mdi)
result.append(iecic)
return result