Inversion

class abjad.pitch.Inversion.Inversion(*, axis=None)

Inversion operator.

>>> abjad.Inversion()
Inversion()

>>> abjad.Inversion(axis=15)
Inversion(axis=NamedPitch("ef''"))

Object model of twelve-tone inversion operator.

---

Attributes Summary

__add__	Composes inversion and operator.
__call__	Calls inversion on argument.
__radd__	Right-addition not defined on inversion.
__str__	Gets string representation of operator.
axis	Gets axis of inversion.

---

Special methods

__add__(operator)

Composes inversion and operator.

Example segment:

>>> items = [0, 2, 4, 5]
>>> segment = abjad.PitchClassSegment(items=items)
>>> abjad.show(segment) 

Example operators:

>>> inversion = abjad.Inversion()
>>> transposition = abjad.Transposition(n=3)

Transposition followed by inversion:

>>> operator = inversion + transposition
>>> str(operator)
'IT3'

>>> segment_ = operator(segment)
>>> abjad.show(segment_) 

Inversion followed by transposition:

>>> operator = transposition + inversion
>>> str(operator)
'T3I'

>>> segment_ = operator(segment)
>>> abjad.show(segment_) 

Returns compound operator:

>>> abjad.f(operator)
abjad.CompoundOperator(
    operators=[
        abjad.Inversion(),
        abjad.Transposition(
            n=3,
            ),
        ],
    )

__call__(argument)

Calls inversion on argument.

Inverts numbered pitch-class:

>>> inversion = abjad.Inversion()
>>> pitch_class = abjad.NumberedPitchClass(1)
>>> inversion(pitch_class)
NumberedPitchClass(11)

Inverts numbered pitch:

>>> inversion = abjad.Inversion()
>>> pitch = abjad.NumberedPitch(15)
>>> inversion(pitch)
NumberedPitch(-15)

Inverts named pitch:

>>> inversion = abjad.Inversion()
>>> pitch = abjad.NamedPitch("d'")
>>> inversion(pitch)
NamedPitch('bf')

Inverts named pitch class:

>>> inversion = abjad.Inversion()
>>> pitch_class = abjad.NamedPitchClass('d')
>>> inversion(pitch_class)
NamedPitchClass('bf')

Inverts pitch segment:

>>> inversion = abjad.Inversion()
>>> segment = abjad.PitchSegment("c' d' e'")
>>> inversion(segment)
PitchSegment("c' bf af")

Inverts pitch class segment:

>>> inversion = abjad.Inversion()
>>> segment = abjad.PitchClassSegment("c d e")
>>> inversion(segment)
PitchClassSegment("c bf af")

Inverts pitch class set:

>>> inversion = abjad.Inversion()
>>> setting = abjad.PitchClassSet("c d e")
>>> inversion(setting)
PitchClassSet(['c', 'af', 'bf'])

Returns new object with type equal to that of argument.

(AbjadValueObject).__copy__(*arguments)

Copies Abjad value object.

Returns new Abjad value object.

(AbjadValueObject).__eq__(argument)

Is true when all initialization values of Abjad value object equal the initialization values of argument.

Returns true or false.

(AbjadObject).__format__(format_specification='')

Formats Abjad object.

Set format_specification to '' or 'storage'. Interprets '' equal to 'storage'.

Returns string.

(AbjadValueObject).__hash__()

Hashes Abjad value object.

Returns integer.

__radd__(operator)

Right-addition not defined on inversion.

>>> abjad.Inversion().__radd__(abjad.Inversion())
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/josiah/Source/github.com/Abjad/abjad/abjad/pitch/Inversion.py", line 215, in __radd__
    raise NotImplementedError(message)
NotImplementedError: right-addition not defined on Inversion.

Raises not implemented error.

(AbjadObject).__repr__()

Gets interpreter representation of Abjad object.

Returns string.

__str__()

Gets string representation of operator.

>>> str(abjad.Inversion())
'I'

>>> str(abjad.Inversion(axis=15))
'I(Eb5)'

---

Read-only properties

axis

Gets axis of inversion.

>>> inversion = abjad.Inversion()
>>> inversion.axis is None
True

>>> inversion = abjad.Inversion(axis=15)
>>> inversion.axis
NamedPitch("ef''")

Returns named pitch or none.