chord_symbols_lib.py

# Copyright 2020 The Magenta Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""Utility functions for working with chord symbols.

The functions in this file treat a chord symbol string as having four
components:

  Root: The root pitch class of the chord, e.g. 'C#'.
  Kind: The type of chord, e.g. major, half-diminished, 13th. In the chord
      symbol figure string the chord kind is abbreviated, e.g. 'm' or '-' means
      minor, 'dim' or 'o' means diminished, '7' means dominant 7th.
  Scale degree modifications: Zero or more modifications to the scale degrees
      present in the chord. There are three different modification types:
      addition (add a new scale degree), subtraction (remove a scale degree),
      and alteration (modify a scale degree). For example, '#9' means to add a
      raised 9th, or to alter the 9th to be raised if a 9th was already present
      in the chord. Other possible modification strings include 'no3' (remove
      the 3rd scale degree), 'add2' (add the 2nd scale degree), 'b5' (flatten
      the 5th scale degree), etc.
  Bass: The bass pitch class of the chord. If missing, the bass pitch class is
      assumed to be the same as the root pitch class.

Before doing any other operations, the functions in this file attempt to
split the chord symbol figure string into these four components; if that
attempt fails a ChordSymbolError is raised.

After that, some operations leave some of the components unexamined, e.g.
transposition only modifies the root and bass, leaving the chord kind and scale
degree modifications unchanged.
"""

import itertools
import re

import constants

# Chord quality enum.
CHORD_QUALITY_MAJOR = 0
CHORD_QUALITY_MINOR = 1
CHORD_QUALITY_AUGMENTED = 2
CHORD_QUALITY_DIMINISHED = 3
CHORD_QUALITY_OTHER = 4


class ChordSymbolError(Exception):
  pass


# Intervals between scale steps.
_STEPS_ABOVE = {'A': 2, 'B': 1, 'C': 2, 'D': 2, 'E': 1, 'F': 2, 'G': 2}

# Scale steps to MIDI mapping.
_STEPS_MIDI = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}

# Mapping from scale degree to offset in half steps.
_DEGREE_OFFSETS = {1: 0, 2: 2, 3: 4, 4: 5, 5: 7, 6: 9, 7: 11}

# All scale degree names within an octave, used when attempting to name a chord
# given pitches.
_SCALE_DEGREES = [
    ('1',),
    ('b2', 'b9'),
    ('2', '9'),
    ('b3', '#9'),
    ('3',),
    ('4', '11'),
    ('b5', '#11'),
    ('5',),
    ('#5', 'b13'),
    ('6', 'bb7', '13'),
    ('b7',),
    ('7',)
]

# List of chord kinds with abbreviations and scale degrees. Scale degrees are
# represented as strings here a) for human readability, and b) because the
# number of semitones is insufficient when the chords have scale degree
# modifications.
_CHORD_KINDS = [
    # major triad
    (['', 'maj', 'M'],
     ['1', '3', '5']),

    # minor triad
    (['m', 'min', '-'],
     ['1', 'b3', '5']),

    # augmented triad
    (['+', 'aug'],
     ['1', '3', '#5']),

    # diminished triad
    (['o', 'dim'],
     ['1', 'b3', 'b5']),

    # dominant 7th
    (['7'],
     ['1', '3', '5', 'b7']),

    # major 7th
    (['maj7', 'M7'],
     ['1', '3', '5', '7']),

    # minor 7th
    (['m7', 'min7', '-7'],
     ['1', 'b3', '5', 'b7']),

    # diminished 7th
    (['o7', 'dim7'],
     ['1', 'b3', 'b5', 'bb7']),

    # augmented 7th
    (['+7', 'aug7'],
     ['1', '3', '#5', 'b7']),

    # half-diminished
    (['m7b5', '-7b5', '/o', '/o7'],
     ['1', 'b3', 'b5', 'b7']),

    # minor triad with major 7th
    (['mmaj7', 'mM7', 'minmaj7', 'minM7', '-maj7', '-M7',
      'm(maj7)', 'm(M7)', 'min(maj7)', 'min(M7)', '-(maj7)', '-(M7)'],
     ['1', 'b3', '5', '7']),

    # major 6th
    (['6'],
     ['1', '3', '5', '6']),

    # minor 6th
    (['m6', 'min6', '-6'],
     ['1', 'b3', '5', '6']),

    # dominant 9th
    (['9'],
     ['1', '3', '5', 'b7', '9']),

    # major 9th
    (['maj9', 'M9'],
     ['1', '3', '5', '7', '9']),

    # minor 9th
    (['m9', 'min9', '-9'],
     ['1', 'b3', '5', 'b7', '9']),

    # augmented 9th
    (['+9', 'aug9'],
     ['1', '3', '#5', 'b7', '9']),

    # 6/9 chord
    (['6/9'],
     ['1', '3', '5', '6', '9']),

    # dominant 11th
    (['11'],
     ['1', '3', '5', 'b7', '9', '11']),

    # major 11th
    (['maj11', 'M11'],
     ['1', '3', '5', '7', '9', '11']),

    # minor 11th
    (['m11', 'min11', '-11'],
     ['1', 'b3', '5', 'b7', '9', '11']),

    # dominant 13th
    (['13'],
     ['1', '3', '5', 'b7', '9', '11', '13']),

    # major 13th
    (['maj13', 'M13'],
     ['1', '3', '5', '7', '9', '11', '13']),

    # minor 13th
    (['m13', 'min13', '-13'],
     ['1', 'b3', '5', 'b7', '9', '11', '13']),

    # suspended 2nd
    (['sus2'],
     ['1', '2', '5']),

    # suspended 4th
    (['sus', 'sus4'],
     ['1', '4', '5']),

    # suspended 4th with dominant 7th
    (['sus7', '7sus'],
     ['1', '4', '5', 'b7']),

    # pedal point
    (['ped'],
     ['1']),

    # power chord
    (['5'],
     ['1', '5'])
]

# Dictionary mapping chord kind abbreviations to names and scale degrees.
_CHORD_KINDS_BY_ABBREV = dict((abbrev, degrees)
                              for abbrevs, degrees in _CHORD_KINDS
                              for abbrev in abbrevs)


# Function to add a scale degree.
def _add_scale_degree(degrees, degree, alter):
  if degree in degrees:
    raise ChordSymbolError('Scale degree already in chord: %d' % degree)
  if degree == 7:
    alter -= 1
  degrees[degree] = alter


# Function to remove a scale degree.
def _subtract_scale_degree(degrees, degree, unused_alter):
  if degree not in degrees:
    raise ChordSymbolError('Scale degree not in chord: %d' % degree)
  del degrees[degree]


# Function to alter (or add) a scale degree.
def _alter_scale_degree(degrees, degree, alter):
  if degree in degrees:
    degrees[degree] += alter
  else:
    degrees[degree] = alter


# Scale degree modifications. There are three basic types of modifications:
# addition, subtraction, and alteration. These have been expanded into six types
# to aid in parsing, as each of the three basic operations has its own
# requirements on the scale degree operand:
#
#  - Addition can accept altered and unaltered scale degrees.
#  - Subtraction can only accept unaltered scale degrees.
#  - Alteration can only accept altered scale degrees.

_DEGREE_MODIFICATIONS = {
    'add': (_add_scale_degree, 0),
    'add#': (_add_scale_degree, 1),
    'addb': (_add_scale_degree, -1),
    'no': (_subtract_scale_degree, 0),
    '#': (_alter_scale_degree, 1),
    'b': (_alter_scale_degree, -1)
}

# Regular expression for chord root.
# Examples: 'C', 'G#', 'Ab', 'D######'
_ROOT_PATTERN = r'[A-G](?:#*|b*)(?![#b])'

# Regular expression for chord kind (abbreviated).
# Examples: '', 'm7b5', 'min', '-13', '+', 'm(M7)', 'dim', '/o7', 'sus2'
_CHORD_KIND_PATTERN = '|'.join(re.escape(abbrev)
                               for abbrev in _CHORD_KINDS_BY_ABBREV)

# Regular expression for scale degree modifications. (To keep the regex simpler,
# parentheses are not required to match here, e.g. '(#9', 'add2)', '(b5(#9)',
# and 'no5)(b9' will all match.)
# Examples: '#9', 'add6add9', 'no5(b9)', '(add2b5no3)', '(no5)(b9)'
_MODIFICATIONS_PATTERN = r'(?:\(?(?:%s)[0-9]+\)?)*' % '|'.join(
    re.escape(mod) for mod in _DEGREE_MODIFICATIONS)

# Regular expression for chord bass.
# Examples: '', '/C', '/Bb', '/F##', '/Dbbbb'
_BASS_PATTERN = '|/%s' % _ROOT_PATTERN

# Regular expression for full chord symbol.
_CHORD_SYMBOL_PATTERN = ''.join('(%s)' % pattern for pattern in [
    _ROOT_PATTERN,            # root pitch class
    _CHORD_KIND_PATTERN,      # chord kind
    _MODIFICATIONS_PATTERN,   # scale degree modifications
    _BASS_PATTERN]) + '$'     # bass pitch class
_CHORD_SYMBOL_REGEX = re.compile(_CHORD_SYMBOL_PATTERN)

# Regular expression for a single pitch class.
# Examples: 'C', 'G#', 'Ab', 'D######'
_PITCH_CLASS_PATTERN = r'([A-G])(#*|b*)$'
_PITCH_CLASS_REGEX = re.compile(_PITCH_CLASS_PATTERN)

# Regular expression for a single scale degree.
# Examples: '1', '7', 'b3', '#5', 'bb7', '13'
_SCALE_DEGREE_PATTERN = r'(#*|b*)([0-9]+)$'
_SCALE_DEGREE_REGEX = re.compile(_SCALE_DEGREE_PATTERN)

# Regular expression for a single scale degree modification. (To keep the regex
# simpler, parentheses are not required to match here, so open or closing paren
# could be missing, e.g. '(#9' and 'add2)' will both match.)
# Examples: '#9', 'add6', 'no5', '(b5)', '(add9)'
_MODIFICATION_PATTERN = r'\(?(%s)([0-9]+)\)?' % '|'.join(
    re.escape(mod) for mod in _DEGREE_MODIFICATIONS)
_MODIFICATION_REGEX = re.compile(_MODIFICATION_PATTERN)


def _parse_pitch_class(pitch_class_str):
  """Parse pitch class from string, returning scale step and alteration."""
  match = re.match(_PITCH_CLASS_REGEX, pitch_class_str)
  step, alter = match.groups()
  return step, len(alter) * (1 if '#' in alter else -1)


def _parse_root(root_str):
  """Parse chord root from string."""
  return _parse_pitch_class(root_str)


def _parse_degree(degree_str):
  """Parse scale degree from string (from internal kind representation)."""
  match = _SCALE_DEGREE_REGEX.match(degree_str)
  alter, degree = match.groups()
  return int(degree), len(alter) * (1 if '#' in alter else -1)


def _parse_kind(kind_str):
  """Parse chord kind from string, returning a scale degree dictionary."""
  degrees = _CHORD_KINDS_BY_ABBREV[kind_str]
  # Here we make the assumption that each scale degree can be present in a chord
  # at most once. This is not generally true, as e.g. a chord could contain both
  # b9 and #9.
  return dict(_parse_degree(degree_str) for degree_str in degrees)


def _parse_modifications(modifications_str):
  """Parse scale degree modifications from string.

  This returns a list of function-degree-alteration triples. The function, when
  applied to the list of scale degrees, the degree to modify, and the
  alteration, performs the modification.

  Args:
    modifications_str: A string containing the scale degree modifications to
        apply to a chord, in standard chord symbol format.

  Returns:
    A Python list of scale degree modification tuples, each of which contains a)
    a function that applies the modification, b) the integer scale degree to
    which to apply the modifications, and c) the number of semitones in the
    modification.
  """
  modifications = []
  while modifications_str:
    match = _MODIFICATION_REGEX.match(modifications_str)
    type_str, degree_str = match.groups()
    mod_fn, alter = _DEGREE_MODIFICATIONS[type_str]
    modifications.append((mod_fn, int(degree_str), alter))
    modifications_str = modifications_str[match.end():]
    assert match.end() > 0
  return modifications


def _parse_bass(bass_str):
  """Parse bass, returning scale step and alteration or None if no bass."""
  if bass_str:
    return _parse_pitch_class(bass_str[1:])
  else:
    return None


def _apply_modifications(degrees, modifications):
  """Apply scale degree modifications to a scale degree dictionary."""
  for mod_fn, degree, alter in modifications:
    mod_fn(degrees, degree, alter)


def _split_chord_symbol(figure):
  """Split a chord symbol into root, kind, degree modifications, and bass."""
  match = _CHORD_SYMBOL_REGEX.match(figure)
  if not match:
    raise ChordSymbolError('Unable to parse chord symbol: %s' % figure)
  root_str, kind_str, modifications_str, bass_str = match.groups()
  return root_str, kind_str, modifications_str, bass_str


def _parse_chord_symbol(figure):
  """Parse a chord symbol string.

  This converts the chord symbol string to a tuple representation with the
  following components:

    Root: A tuple containing scale step and alteration.
    Degrees: A dictionary where the keys are integer scale degrees, and values
        are integer alterations. For example, if 9 -> -1 is in the dictionary,
        the chord contains a b9.
    Bass: A tuple containins scale step and alteration. If bass is unspecified,
        the chord root is used.

  Args:
    figure: A chord symbol figure string.

  Returns:
    A tuple containing the chord root pitch class, scale degrees, and bass pitch
    class.
  """
  root_str, kind_str, modifications_str, bass_str = _split_chord_symbol(figure)

  root = _parse_root(root_str)
  degrees = _parse_kind(kind_str)
  modifications = _parse_modifications(modifications_str)
  bass = _parse_bass(bass_str)

  # Apply scale degree modifications.
  _apply_modifications(degrees, modifications)

  return root, degrees, bass or root


def _transpose_pitch_class(step, alter, transpose_amount):
  """Transposes a chord symbol figure string by the given amount."""
  transpose_amount %= 12

  # Transpose up as many steps as we can.
  while transpose_amount >= _STEPS_ABOVE[step]:
    transpose_amount -= _STEPS_ABOVE[step]
    step = chr(ord('A') + (ord(step) - ord('A') + 1) % 7)

  if transpose_amount > 0:
    if alter >= 0:
      # Transpose up one more step and remove sharps (or add flats).
      alter -= _STEPS_ABOVE[step] - transpose_amount
      step = chr(ord('A') + (ord(step) - ord('A') + 1) % 7)
    else:
      # Remove flats.
      alter += transpose_amount

  return step, alter


def _pitch_class_to_string(step, alter):
  """Convert a pitch class scale step and alteration to string."""
  return step + abs(alter) * ('#' if alter >= 0 else 'b')


def _pitch_class_to_midi(step, alter):
  """Convert a pitch class scale step and alteration to MIDI note."""
  return (_STEPS_MIDI[step] + alter) % 12


def _largest_chord_kind_from_degrees(degrees):
  """Find the largest chord that is contained in a set of scale degrees."""
  best_chord_abbrev = None
  best_chord_degrees = []
  for chord_abbrevs, chord_degrees in _CHORD_KINDS:
    if len(chord_degrees) <= len(best_chord_degrees):
      continue
    if not set(chord_degrees) - set(degrees):
      best_chord_abbrev, best_chord_degrees = chord_abbrevs[0], chord_degrees
  return best_chord_abbrev


def _largest_chord_kind_from_relative_pitches(relative_pitches):
  """Find the largest chord contained in a set of relative pitches."""
  scale_degrees = [_SCALE_DEGREES[pitch] for pitch in relative_pitches]
  best_chord_abbrev = None
  best_degrees = []
  for degrees in itertools.product(*scale_degrees):
    degree_steps = [_parse_degree(degree_str)[0]
                    for degree_str in degrees]
    if len(degree_steps) > len(set(degree_steps)):
      # This set of scale degrees has duplicates, which we do not currently
      # allow.
      continue
    chord_abbrev = _largest_chord_kind_from_degrees(degrees)
    if best_chord_abbrev is None or (
        len(_CHORD_KINDS_BY_ABBREV[chord_abbrev]) >
        len(_CHORD_KINDS_BY_ABBREV[best_chord_abbrev])):
      # We store the chord kind with the most matches, and the scale degrees
      # representation that led to those matches (since a set of relative
      # pitches can be interpreted as scale degrees in multiple ways).
      best_chord_abbrev, best_degrees = chord_abbrev, degrees
  return best_chord_abbrev, best_degrees


def _degrees_to_modifications(chord_degrees, target_chord_degrees):
  """Find scale degree modifications to turn chord into target chord."""
  degrees = dict(_parse_degree(degree_str) for degree_str in chord_degrees)
  target_degrees = dict(_parse_degree(degree_str)
                        for degree_str in target_chord_degrees)
  modifications_str = ''
  for degree in target_degrees:
    if degree not in degrees:
      # Add a scale degree.
      alter = target_degrees[degree]
      alter_str = abs(alter) * ('#' if alter >= 0 else 'b')
      if alter and degree > 7:
        modifications_str += '(%s%d)' % (alter_str, degree)
      else:
        modifications_str += '(add%s%d)' % (alter_str, degree)
    elif degrees[degree] != target_degrees[degree]:
      # Alter a scale degree. We shouldn't be altering to natural, that's a sign
      # that we've chosen the wrong chord kind.
      alter = target_degrees[degree]
      assert alter != 0
      alter_str = abs(alter) * ('#' if alter >= 0 else 'b')
      modifications_str += '(%s%d)' % (alter_str, degree)
  for degree in degrees:
    if degree not in target_degrees:
      # Subtract a scale degree.
      modifications_str += '(no%d)' % degree
  return modifications_str


def transpose_chord_symbol(figure, transpose_amount):
  """Transposes a chord symbol figure string by the given amount.

  Args:
    figure: The chord symbol figure string to transpose.
    transpose_amount: The integer number of half steps to transpose.

  Returns:
    The transposed chord symbol figure string.

  Raises:
    ChordSymbolError: If the given chord symbol cannot be interpreted.
  """
  # Split chord symbol into root, kind, modifications, and bass.
  root_str, kind_str, modifications_str, bass_str = _split_chord_symbol(figure)

  # Parse and transpose the root.
  root_step, root_alter = _parse_root(root_str)
  transposed_root_step, transposed_root_alter = _transpose_pitch_class(
      root_step, root_alter, transpose_amount)
  transposed_root_str = _pitch_class_to_string(
      transposed_root_step, transposed_root_alter)

  # Parse bass.
  bass = _parse_bass(bass_str)

  if bass:
    # Bass exists, transpose it.
    bass_step, bass_alter = bass  # pylint: disable=unpacking-non-sequence
    transposed_bass_step, transposed_bass_alter = _transpose_pitch_class(
        bass_step, bass_alter, transpose_amount)
    transposed_bass_str = '/' + _pitch_class_to_string(
        transposed_bass_step, transposed_bass_alter)
  else:
    # No bass.
    transposed_bass_str = bass_str

  return '%s%s%s%s' % (transposed_root_str, kind_str, modifications_str,
                       transposed_bass_str)


def pitches_to_chord_symbol(pitches):
  """Converts a set of pitches to a chord symbol.

  This is quite a complicated function and certainly imperfect, even apart from
  the inherent ambiguity and context-dependence of chord naming. The basic logic
  is as follows:

  Consider that each pitch may be the root of the chord. For each potential
  root, convert the other pitch classes to scale degrees (note that a single
  pitch class may map to multiple scale degrees, e.g. b3 is the same as #9) and
  find the chord kind that covers as many of these scale degrees as possible
  while not including any extras. Then add any remaining scale degrees as
  modifications.

  This will not always return the most natural name for a chord, but it should
  do something reasonable in most cases.

  Args:
    pitches: A python list of integer pitch values.

  Returns:
    A chord symbol figure string representing the chord containing the specified
    pitches.

  Raises:
    ChordSymbolError: If no known chord symbol corresponds to the provided
        pitches.
  """
  if not pitches:
    return constants.NO_CHORD

  # Convert to pitch classes and dedupe.
  pitch_classes = set(pitch % 12 for pitch in pitches)

  # Try using the bass note as root first.
  bass = min(pitches) % 12
  pitch_classes = [bass] + list(pitch_classes - set([bass]))

  # Try each pitch class in turn as root.
  best_root = None
  best_abbrev = None
  best_degrees = []
  for root in pitch_classes:
    relative_pitches = set((pitch - root) % 12 for pitch in pitch_classes)
    abbrev, degrees = _largest_chord_kind_from_relative_pitches(
        relative_pitches)
    if abbrev is not None:
      if best_abbrev is None or (
          len(_CHORD_KINDS_BY_ABBREV[abbrev]) >
          len(_CHORD_KINDS_BY_ABBREV[best_abbrev])):
        best_root = root
        best_abbrev = abbrev
        best_degrees = degrees

  if best_root is None:
    raise ChordSymbolError(
        'Unable to determine chord symbol from pitches: %s' % str(pitches))

  root_str = _pitch_class_to_string(*_transpose_pitch_class('C', 0, best_root))
  kind_str = best_abbrev

  # If the bass pitch class is not one of the scale degrees in the chosen kind,
  # we don't need to include an explicit modification for it.
  best_chord_degrees = _CHORD_KINDS_BY_ABBREV[best_abbrev]
  if all(degree != bass_degree
         for degree in best_chord_degrees
         for bass_degree in _SCALE_DEGREES[bass]):
    best_degrees = [degree for degree in best_degrees
                    if all(degree != bass_degree
                           for bass_degree in _SCALE_DEGREES[bass])]
  modifications_str = _degrees_to_modifications(
      best_chord_degrees, best_degrees)

  if bass == best_root:
    return '%s%s%s' % (root_str, kind_str, modifications_str)
  else:
    bass_str = _pitch_class_to_string(*_transpose_pitch_class('C', 0, bass))
    return '%s%s%s/%s' % (root_str, kind_str, modifications_str, bass_str)


def chord_symbol_pitches(figure):
  """Return the pitch classes contained in a chord.

  This will generally include the root pitch class, but not the bass if it is
  not otherwise one of the pitches in the chord.

  Args:
    figure: The chord symbol figure string for which pitches are computed.

  Returns:
    A python list of integer pitch class values.

  Raises:
    ChordSymbolError: If the given chord symbol cannot be interpreted.
  """
  root, degrees, _ = _parse_chord_symbol(figure)
  root_step, root_alter = root
  root_pitch = _pitch_class_to_midi(root_step, root_alter)
  normalized_degrees = [((degree - 1) % 7 + 1, alter)
                        for degree, alter in degrees.items()]
  return [(root_pitch + _DEGREE_OFFSETS[degree] + alter) % 12
          for degree, alter in normalized_degrees]


def chord_symbol_root(figure):
  """Return the root pitch class of a chord.

  Args:
    figure: The chord symbol figure string for which the root is computed.

  Returns:
    The pitch class of the chord root, an integer between 0 and 11 inclusive.

  Raises:
    ChordSymbolError: If the given chord symbol cannot be interpreted.
  """
  root_str, _, _, _ = _split_chord_symbol(figure)
  root_step, root_alter = _parse_root(root_str)
  return _pitch_class_to_midi(root_step, root_alter)


def chord_symbol_bass(figure):
  """Return the bass pitch class of a chord.

  Args:
    figure: The chord symbol figure string for which the bass is computed.

  Returns:
    The pitch class of the chord bass, an integer between 0 and 11 inclusive.

  Raises:
    ChordSymbolError: If the given chord symbol cannot be interpreted.
  """
  root_str, _, _, bass_str = _split_chord_symbol(figure)
  bass = _parse_bass(bass_str)
  if bass:
    bass_step, bass_alter = bass  # pylint: disable=unpacking-non-sequence
  else:
    # Bass is the same as root.
    bass_step, bass_alter = _parse_root(root_str)
  return _pitch_class_to_midi(bass_step, bass_alter)


def chord_symbol_quality(figure):
  """Return the quality (major, minor, dimished, augmented) of a chord.

  Args:
    figure: The chord symbol figure string for which quality is computed.

  Returns:
    One of CHORD_QUALITY_MAJOR, CHORD_QUALITY_MINOR, CHORD_QUALITY_AUGMENTED,
    CHORD_QUALITY_DIMINISHED, or CHORD_QUALITY_OTHER.

  Raises:
    ChordSymbolError: If the given chord symbol cannot be interpreted.
  """
  _, degrees, _ = _parse_chord_symbol(figure)
  if 1 not in degrees or 3 not in degrees or 5 not in degrees:
    return CHORD_QUALITY_OTHER
  triad = degrees[1], degrees[3], degrees[5]
  if triad == (0, 0, 0):
    return CHORD_QUALITY_MAJOR
  elif triad == (0, -1, 0):
    return CHORD_QUALITY_MINOR
  elif triad == (0, 0, 1):
    return CHORD_QUALITY_AUGMENTED
  elif triad == (0, -1, -1):
    return CHORD_QUALITY_DIMINISHED
  else:
    return CHORD_QUALITY_OTHER