.. _abjadext--microtones--utilities:

utilities
=========

.. automodule:: abjadext.microtones.utilities

.. currentmodule:: abjadext.microtones.utilities

.. container:: svg-container

   .. inheritance-diagram:: abjadext
      :lineage: abjadext.microtones.utilities

.. raw:: html

   <hr/>

.. rubric:: Classes
   :class: section-header

.. autosummary::
   :nosignatures:

   ~PitchClassSegment
   ~PitchClassSet
   ~PitchSegment
   ~PitchSet
   ~RatioClassSegment
   ~RatioClassSet
   ~RatioSegment
   ~RatioSet

.. autoclass:: PitchClassSegment

   .. raw:: html

      <hr/>

   .. rubric:: Attributes Summary
      :class: class-header

   .. autosummary::
      :nosignatures:

      __add__
      __contains__
      __getitem__
      __iter__
      __len__
      __repr__
      __str__
      complement
      invert
      multiply
      retrograde
      rotate
      sorted
      transpose

   .. raw:: html

      <hr/>

   .. rubric:: Special methods
      :class: class-header

   .. automethod:: PitchClassSegment.__add__

   .. automethod:: PitchClassSegment.__contains__

   .. automethod:: PitchClassSegment.__getitem__

   .. automethod:: PitchClassSegment.__iter__

   .. automethod:: PitchClassSegment.__len__

   .. automethod:: PitchClassSegment.__repr__

   .. automethod:: PitchClassSegment.__str__

   .. raw:: html

      <hr/>

   .. rubric:: Methods
      :class: class-header

   .. automethod:: PitchClassSegment.complement

   .. automethod:: PitchClassSegment.invert

   .. automethod:: PitchClassSegment.multiply

   .. automethod:: PitchClassSegment.retrograde

   .. automethod:: PitchClassSegment.rotate

   .. automethod:: PitchClassSegment.sorted

   .. automethod:: PitchClassSegment.transpose

.. autoclass:: PitchClassSet

   .. raw:: html

      <hr/>

   .. rubric:: Attributes Summary
      :class: class-header

   .. autosummary::
      :nosignatures:

      __add__
      __contains__
      __getitem__
      __iter__
      __len__
      __repr__
      __str__
      complement
      invert
      multiply
      normal_order
      prime_form
      sorted
      transpose

   .. raw:: html

      <hr/>

   .. rubric:: Special methods
      :class: class-header

   .. automethod:: PitchClassSet.__add__

   .. automethod:: PitchClassSet.__contains__

   .. automethod:: PitchClassSet.__getitem__

   .. automethod:: PitchClassSet.__iter__

   .. automethod:: PitchClassSet.__len__

   .. automethod:: PitchClassSet.__repr__

   .. automethod:: PitchClassSet.__str__

   .. raw:: html

      <hr/>

   .. rubric:: Methods
      :class: class-header

   .. automethod:: PitchClassSet.complement

   .. automethod:: PitchClassSet.invert

   .. automethod:: PitchClassSet.multiply

   .. automethod:: PitchClassSet.normal_order

   .. automethod:: PitchClassSet.prime_form

   .. automethod:: PitchClassSet.sorted

   .. automethod:: PitchClassSet.transpose

.. autoclass:: PitchSegment

   .. raw:: html

      <hr/>

   .. rubric:: Attributes Summary
      :class: class-header

   .. autosummary::
      :nosignatures:

      __add__
      __contains__
      __getitem__
      __iter__
      __len__
      __repr__
      __setitem__
      __str__
      complement
      invert
      multiply
      retrograde
      rotate
      sorted
      transpose

   .. raw:: html

      <hr/>

   .. rubric:: Special methods
      :class: class-header

   .. automethod:: PitchSegment.__add__

   .. automethod:: PitchSegment.__contains__

   .. automethod:: PitchSegment.__getitem__

   .. automethod:: PitchSegment.__iter__

   .. automethod:: PitchSegment.__len__

   .. automethod:: PitchSegment.__repr__

   .. automethod:: PitchSegment.__setitem__

   .. automethod:: PitchSegment.__str__

   .. raw:: html

      <hr/>

   .. rubric:: Methods
      :class: class-header

   .. automethod:: PitchSegment.complement

   .. automethod:: PitchSegment.invert

   .. automethod:: PitchSegment.multiply

   .. automethod:: PitchSegment.retrograde

   .. automethod:: PitchSegment.rotate

   .. automethod:: PitchSegment.sorted

   .. automethod:: PitchSegment.transpose

.. autoclass:: PitchSet

   .. raw:: html

      <hr/>

   .. rubric:: Attributes Summary
      :class: class-header

   .. autosummary::
      :nosignatures:

      __add__
      __contains__
      __getitem__
      __iter__
      __len__
      __repr__
      __str__
      complement
      invert
      multiply
      sorted
      transpose

   .. raw:: html

      <hr/>

   .. rubric:: Special methods
      :class: class-header

   .. automethod:: PitchSet.__add__

   .. automethod:: PitchSet.__contains__

   .. automethod:: PitchSet.__getitem__

   .. automethod:: PitchSet.__iter__

   .. automethod:: PitchSet.__len__

   .. automethod:: PitchSet.__repr__

   .. automethod:: PitchSet.__str__

   .. raw:: html

      <hr/>

   .. rubric:: Methods
      :class: class-header

   .. automethod:: PitchSet.complement

   .. automethod:: PitchSet.invert

   .. automethod:: PitchSet.multiply

   .. automethod:: PitchSet.sorted

   .. automethod:: PitchSet.transpose

.. autoclass:: RatioClassSegment

   .. raw:: html

      <hr/>

   .. rubric:: Attributes Summary
      :class: class-header

   .. autosummary::
      :nosignatures:

      __add__
      __contains__
      __getitem__
      __iter__
      __len__
      __repr__
      __str__
      complement
      invert
      multiply
      retrograde
      rotate
      sorted
      transpose

   .. raw:: html

      <hr/>

   .. rubric:: Special methods
      :class: class-header

   .. automethod:: RatioClassSegment.__add__

   .. automethod:: RatioClassSegment.__contains__

   .. automethod:: RatioClassSegment.__getitem__

   .. automethod:: RatioClassSegment.__iter__

   .. automethod:: RatioClassSegment.__len__

   .. automethod:: RatioClassSegment.__repr__

   .. automethod:: RatioClassSegment.__str__

   .. raw:: html

      <hr/>

   .. rubric:: Methods
      :class: class-header

   .. automethod:: RatioClassSegment.complement

   .. automethod:: RatioClassSegment.invert

   .. automethod:: RatioClassSegment.multiply

   .. automethod:: RatioClassSegment.retrograde

   .. automethod:: RatioClassSegment.rotate

   .. automethod:: RatioClassSegment.sorted

   .. automethod:: RatioClassSegment.transpose

.. autoclass:: RatioClassSet

   .. raw:: html

      <hr/>

   .. rubric:: Attributes Summary
      :class: class-header

   .. autosummary::
      :nosignatures:

      __add__
      __contains__
      __getitem__
      __iter__
      __len__
      __repr__
      __str__
      complement
      invert
      multiply
      sorted
      transpose

   .. raw:: html

      <hr/>

   .. rubric:: Special methods
      :class: class-header

   .. automethod:: RatioClassSet.__add__

   .. automethod:: RatioClassSet.__contains__

   .. automethod:: RatioClassSet.__getitem__

   .. automethod:: RatioClassSet.__iter__

   .. automethod:: RatioClassSet.__len__

   .. automethod:: RatioClassSet.__repr__

   .. automethod:: RatioClassSet.__str__

   .. raw:: html

      <hr/>

   .. rubric:: Methods
      :class: class-header

   .. automethod:: RatioClassSet.complement

   .. automethod:: RatioClassSet.invert

   .. automethod:: RatioClassSet.multiply

   .. automethod:: RatioClassSet.sorted

   .. automethod:: RatioClassSet.transpose

.. autoclass:: RatioSegment

   .. raw:: html

      <hr/>

   .. rubric:: Attributes Summary
      :class: class-header

   .. autosummary::
      :nosignatures:

      __add__
      __contains__
      __getitem__
      __iter__
      __len__
      __repr__
      __setitem__
      __str__
      complement
      constrain_to_octave
      invert
      multiply
      retrograde
      rotate
      sorted
      transpose

   .. raw:: html

      <hr/>

   .. rubric:: Special methods
      :class: class-header

   .. automethod:: RatioSegment.__add__

   .. automethod:: RatioSegment.__contains__

   .. automethod:: RatioSegment.__getitem__

   .. automethod:: RatioSegment.__iter__

   .. automethod:: RatioSegment.__len__

   .. automethod:: RatioSegment.__repr__

   .. automethod:: RatioSegment.__setitem__

   .. automethod:: RatioSegment.__str__

   .. raw:: html

      <hr/>

   .. rubric:: Methods
      :class: class-header

   .. automethod:: RatioSegment.complement

   .. automethod:: RatioSegment.constrain_to_octave

   .. automethod:: RatioSegment.invert

   .. automethod:: RatioSegment.multiply

   .. automethod:: RatioSegment.retrograde

   .. automethod:: RatioSegment.rotate

   .. automethod:: RatioSegment.sorted

   .. automethod:: RatioSegment.transpose

.. autoclass:: RatioSet

   .. raw:: html

      <hr/>

   .. rubric:: Attributes Summary
      :class: class-header

   .. autosummary::
      :nosignatures:

      __add__
      __contains__
      __getitem__
      __iter__
      __len__
      __repr__
      __str__
      complement
      constrain_to_octave
      invert
      multiply
      sorted
      transpose

   .. raw:: html

      <hr/>

   .. rubric:: Special methods
      :class: class-header

   .. automethod:: RatioSet.__add__

   .. automethod:: RatioSet.__contains__

   .. automethod:: RatioSet.__getitem__

   .. automethod:: RatioSet.__iter__

   .. automethod:: RatioSet.__len__

   .. automethod:: RatioSet.__repr__

   .. automethod:: RatioSet.__str__

   .. raw:: html

      <hr/>

   .. rubric:: Methods
      :class: class-header

   .. automethod:: RatioSet.complement

   .. automethod:: RatioSet.constrain_to_octave

   .. automethod:: RatioSet.invert

   .. automethod:: RatioSet.multiply

   .. automethod:: RatioSet.sorted

   .. automethod:: RatioSet.transpose