packages/notation.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Music notation utilities"""

import re
import numpy as np
from numba import jit
from .intervals import INTERVALS
from .._cache import cache
from ..util.exceptions import ParameterError
from typing import Dict, List, Union, overload
from ..util.decorators import vectorize
from .._typing import _ScalarOrSequence, _FloatLike_co, _SequenceLike


__all__ = [
    "key_to_degrees",
    "key_to_notes",
    "mela_to_degrees",
    "mela_to_svara",
    "thaat_to_degrees",
    "list_mela",
    "list_thaat",
    "fifths_to_note",
    "interval_to_fjs",
]

THAAT_MAP = dict(
    bilaval=[0, 2, 4, 5, 7, 9, 11],
    khamaj=[0, 2, 4, 5, 7, 9, 10],
    kafi=[0, 2, 3, 5, 7, 9, 10],
    asavari=[0, 2, 3, 5, 7, 8, 10],
    bhairavi=[0, 1, 3, 5, 7, 8, 10],
    kalyan=[0, 2, 4, 6, 7, 9, 11],
    marva=[0, 1, 4, 6, 7, 9, 11],
    poorvi=[0, 1, 4, 6, 7, 8, 11],
    todi=[0, 1, 3, 6, 7, 8, 11],
    bhairav=[0, 1, 4, 5, 7, 8, 11],
)

# Enumeration will start from 1
MELAKARTA_MAP = {
    k: i
    for i, k in enumerate(
        [
            "kanakangi",
            "ratnangi",
            "ganamurthi",
            "vanaspathi",
            "manavathi",
            "tanarupi",
            "senavathi",
            "hanumathodi",
            "dhenuka",
            "natakapriya",
            "kokilapriya",
            "rupavathi",
            "gayakapriya",
            "vakulabharanam",
            "mayamalavagaula",
            "chakravakom",
            "suryakantham",
            "hatakambari",
            "jhankaradhwani",
            "natabhairavi",
            "keeravani",
            "kharaharapriya",
            "gaurimanohari",
            "varunapriya",
            "mararanjini",
            "charukesi",
            "sarasangi",
            "harikambhoji",
            "dheerasankarabharanam",
            "naganandini",
            "yagapriya",
            "ragavardhini",
            "gangeyabhushani",
            "vagadheeswari",
            "sulini",
            "chalanatta",
            "salagam",
            "jalarnavam",
            "jhalavarali",
            "navaneetham",
            "pavani",
            "raghupriya",
            "gavambodhi",
            "bhavapriya",
            "subhapanthuvarali",
            "shadvidhamargini",
            "suvarnangi",
            "divyamani",
            "dhavalambari",
            "namanarayani",
            "kamavardhini",
            "ramapriya",
            "gamanasrama",
            "viswambhari",
            "syamalangi",
            "shanmukhapriya",
            "simhendramadhyamam",
            "hemavathi",
            "dharmavathi",
            "neethimathi",
            "kanthamani",
            "rishabhapriya",
            "latangi",
            "vachaspathi",
            "mechakalyani",
            "chitrambari",
            "sucharitra",
            "jyotisvarupini",
            "dhatuvardhini",
            "nasikabhushani",
            "kosalam",
            "rasikapriya",
        ],
        1,
    )
}


# Pre-compiled regular expressions for note and key parsing
NOTE_RE = re.compile(
    r"^(?P<note>[A-Ga-g])"
    r"(?P<accidental>[#♯𝄪b!♭𝄫♮]*)"
    r"(?P<octave>[+-]?\d+)?"
    r"(?P<cents>[+-]\d+)?$"
)

KEY_RE = re.compile(
    r"^(?P<tonic>[A-Ga-g])" r"(?P<accidental>[#♯b!♭]?)" r":(?P<scale>(maj|min)(or)?)$"
)


def thaat_to_degrees(thaat: str) -> np.ndarray:
    """Construct the svara indices (degrees) for a given thaat

    Parameters
    ----------
    thaat : str
        The name of the thaat

    Returns
    -------
    indices : np.ndarray
        A list of the seven svara indices (starting from 0=Sa)
        contained in the specified thaat

    See Also
    --------
    key_to_degrees
    mela_to_degrees
    list_thaat

    Examples
    --------
    >>> librosa.thaat_to_degrees('bilaval')
    array([ 0,  2,  4,  5,  7,  9, 11])

    >>> librosa.thaat_to_degrees('todi')
    array([ 0,  1,  3,  6,  7,  8, 11])
    """
    return np.asarray(THAAT_MAP[thaat.lower()])


def mela_to_degrees(mela: Union[str, int]) -> np.ndarray:
    """Construct the svara indices (degrees) for a given melakarta raga

    Parameters
    ----------
    mela : str or int
        Either the name or integer index ([1, 2, ..., 72]) of the melakarta raga

    Returns
    -------
    degrees : np.ndarray
        A list of the seven svara indices (starting from 0=Sa)
        contained in the specified raga

    See Also
    --------
    thaat_to_degrees
    key_to_degrees
    list_mela

    Examples
    --------
    Melakarta #1 (kanakangi):

    >>> librosa.mela_to_degrees(1)
    array([0, 1, 2, 5, 7, 8, 9])

    Or using a name directly:

    >>> librosa.mela_to_degrees('kanakangi')
    array([0, 1, 2, 5, 7, 8, 9])
    """

    if isinstance(mela, str):
        index = MELAKARTA_MAP[mela.lower()] - 1
    elif 0 < mela <= 72:
        index = mela - 1
    else:
        raise ParameterError(f"mela={mela} must be in range [1, 72]")

    # always have Sa [0]
    degrees = [0]

    # Fill in Ri and Ga
    lower = index % 36
    if 0 <= lower < 6:
        # Ri1, Ga1
        degrees.extend([1, 2])
    elif 6 <= lower < 12:
        # Ri1, Ga2
        degrees.extend([1, 3])
    elif 12 <= lower < 18:
        # Ri1, Ga3
        degrees.extend([1, 4])
    elif 18 <= lower < 24:
        # Ri2, Ga2
        degrees.extend([2, 3])
    elif 24 <= lower < 30:
        # Ri2, Ga3
        degrees.extend([2, 4])
    else:
        # Ri3, Ga3
        degrees.extend([3, 4])

    # Determine Ma
    if index < 36:
        # Ma1
        degrees.append(5)
    else:
        # Ma2
        degrees.append(6)

    # always have Pa [7]
    degrees.append(7)

    # Determine Dha and Ni
    upper = index % 6
    if upper == 0:
        # Dha1, Ni1
        degrees.extend([8, 9])
    elif upper == 1:
        # Dha1, Ni2
        degrees.extend([8, 10])
    elif upper == 2:
        # Dha1, Ni3
        degrees.extend([8, 11])
    elif upper == 3:
        # Dha2, Ni2
        degrees.extend([9, 10])
    elif upper == 4:
        # Dha2, Ni3
        degrees.extend([9, 11])
    else:
        # Dha3, Ni3
        degrees.extend([10, 11])

    return np.array(degrees)


@cache(level=10)
def mela_to_svara(
    mela: Union[str, int], *, abbr: bool = True, unicode: bool = True
) -> List[str]:
    """Spell the Carnatic svara names for a given melakarta raga

    This function exists to resolve enharmonic equivalences between
    pitch classes:

        - Ri2 / Ga1
        - Ri3 / Ga2
        - Dha2 / Ni1
        - Dha3 / Ni2

    For svara outside the raga, names are chosen to preserve orderings
    so that all Ri precede all Ga, and all Dha precede all Ni.

    Parameters
    ----------
    mela : str or int
        the name or numerical index of the melakarta raga

    abbr : bool
        If `True`, use single-letter svara names: S, R, G, ...

        If `False`, use full names: Sa, Ri, Ga, ...

    unicode : bool
        If `True`, use unicode symbols for numberings, e.g., Ri\u2081

        If `False`, use low-order ASCII, e.g., Ri1.

    Returns
    -------
    svara : list of strings

        The svara names for each of the 12 pitch classes.

    See Also
    --------
    key_to_notes
    mela_to_degrees
    list_mela

    Examples
    --------
    Melakarta #1 (Kanakangi) uses R1, G1, D1, N1

    >>> librosa.mela_to_svara(1)
    ['S', 'R₁', 'G₁', 'G₂', 'G₃', 'M₁', 'M₂', 'P', 'D₁', 'N₁', 'N₂', 'N₃']

    #19 (Jhankaradhwani) uses R2 and G2 so the third svara are Ri:

    >>> librosa.mela_to_svara(19)
    ['S', 'R₁', 'R₂', 'G₂', 'G₃', 'M₁', 'M₂', 'P', 'D₁', 'N₁', 'N₂', 'N₃']

    #31 (Yagapriya) uses R3 and G3, so third and fourth svara are Ri:

    >>> librosa.mela_to_svara(31)
    ['S', 'R₁', 'R₂', 'R₃', 'G₃', 'M₁', 'M₂', 'P', 'D₁', 'N₁', 'N₂', 'N₃']

    #34 (Vagadheeswari) uses D2 and N2, so Ni1 becomes Dha2:

    >>> librosa.mela_to_svara(34)
    ['S', 'R₁', 'R₂', 'R₃', 'G₃', 'M₁', 'M₂', 'P', 'D₁', 'D₂', 'N₂', 'N₃']

    #36 (Chalanatta) uses D3 and N3, so Ni2 becomes Dha3:

    >>> librosa.mela_to_svara(36)
    ['S', 'R₁', 'R₂', 'R₃', 'G₃', 'M₁', 'M₂', 'P', 'D₁', 'D₂', 'D₃', 'N₃']

    # You can also query by raga name instead of index:

    >>> librosa.mela_to_svara('chalanatta')
    ['S', 'R₁', 'R₂', 'R₃', 'G₃', 'M₁', 'M₂', 'P', 'D₁', 'D₂', 'D₃', 'N₃']
    """

    # The following will be constant for all ragas
    svara_map = [
        "Sa",
        "Ri\u2081",
        "",  # Ri2/Ga1
        "",  # Ri3/Ga2
        "Ga\u2083",
        "Ma\u2081",
        "Ma\u2082",
        "Pa",
        "Dha\u2081",
        "",  # Dha2/Ni1
        "",  # Dha3/Ni2
        "Ni\u2083",
    ]

    if isinstance(mela, str):
        mela_idx = MELAKARTA_MAP[mela.lower()] - 1
    elif 0 < mela <= 72:
        mela_idx = mela - 1
    else:
        raise ParameterError(f"mela={mela} must be in range [1, 72]")

    # Determine Ri2/Ga1
    lower = mela_idx % 36
    if lower < 6:
        # First six will have Ri1/Ga1
        svara_map[2] = "Ga\u2081"
    else:
        # All others have either Ga2/Ga3
        # So we'll call this Ri2
        svara_map[2] = "Ri\u2082"

    # Determine Ri3/Ga2
    if lower < 30:
        # First thirty should get Ga2
        svara_map[3] = "Ga\u2082"
    else:
        # Only the last six have Ri3
        svara_map[3] = "Ri\u2083"

    upper = mela_idx % 6

    # Determine Dha2/Ni1
    if upper == 0:
        # these are the only ones with Ni1
        svara_map[9] = "Ni\u2081"
    else:
        # Everyone else has Dha2
        svara_map[9] = "Dha\u2082"

    # Determine Dha3/Ni2
    if upper == 5:
        # This one has Dha3
        svara_map[10] = "Dha\u2083"
    else:
        # Everyone else has Ni2
        svara_map[10] = "Ni\u2082"

    if abbr:
        t_abbr = str.maketrans({"a": "", "h": "", "i": ""})
        svara_map = [s.translate(t_abbr) for s in svara_map]

    if not unicode:
        t_uni = str.maketrans({"\u2081": "1", "\u2082": "2", "\u2083": "3"})
        svara_map = [s.translate(t_uni) for s in svara_map]

    return list(svara_map)


def list_mela() -> Dict[str, int]:
    """List melakarta ragas by name and index.

    Melakarta raga names are transcribed from [#]_, with the exception of #45
    (subhapanthuvarali).

    .. [#] Bhagyalekshmy, S. (1990).
        Ragas in Carnatic music.
        South Asia Books.

    Returns
    -------
    mela_map : dict
        A dictionary mapping melakarta raga names to indices (1, 2, ..., 72)

    Examples
    --------
    >>> librosa.list_mela()
    {'kanakangi': 1,
     'ratnangi': 2,
     'ganamurthi': 3,
     'vanaspathi': 4,
     ...}

    See Also
    --------
    mela_to_degrees
    mela_to_svara
    list_thaat
    """
    return MELAKARTA_MAP.copy()


def list_thaat() -> List[str]:
    """List supported thaats by name.

    Returns
    -------
    thaats : list
        A list of supported thaats

    Examples
    --------
    >>> librosa.list_thaat()
    ['bilaval',
     'khamaj',
     'kafi',
     'asavari',
     'bhairavi',
     'kalyan',
     'marva',
     'poorvi',
     'todi',
     'bhairav']

    See Also
    --------
    list_mela
    thaat_to_degrees
    """
    return list(THAAT_MAP.keys())


@cache(level=10)
def key_to_notes(key: str, *, unicode: bool = True) -> List[str]:
    """Lists all 12 note names in the chromatic scale, as spelled according to
    a given key (major or minor).

    This function exists to resolve enharmonic equivalences between different
    spellings for the same pitch (e.g. C♯ vs D♭), and is primarily useful when producing
    human-readable outputs (e.g. plotting) for pitch content.

    Note names are decided by the following rules:

    1. If the tonic of the key has an accidental (sharp or flat), that accidental will be
       used consistently for all notes.

    2. If the tonic does not have an accidental, accidentals will be inferred to minimize
       the total number used for diatonic scale degrees.

    3. If there is a tie (e.g., in the case of C:maj vs A:min), sharps will be preferred.

    Parameters
    ----------
    key : string
        Must be in the form TONIC:key.  Tonic must be upper case (``CDEFGAB``),
        key must be lower-case (``maj`` or ``min``).

        Single accidentals (``b!♭`` for flat, or ``#♯`` for sharp) are supported.

        Examples: ``C:maj, Db:min, A♭:min``.

    unicode : bool
        If ``True`` (default), use Unicode symbols (♯𝄪♭𝄫)for accidentals.

        If ``False``, Unicode symbols will be mapped to low-order ASCII representations::

            ♯ -> #, 𝄪 -> ##, ♭ -> b, 𝄫 -> bb

    Returns
    -------
    notes : list
        ``notes[k]`` is the name for semitone ``k`` (starting from C)
        under the given key.  All chromatic notes (0 through 11) are
        included.

    See Also
    --------
    midi_to_note

    Examples
    --------
    `C:maj` will use all sharps

    >>> librosa.key_to_notes('C:maj')
    ['C', 'C♯', 'D', 'D♯', 'E', 'F', 'F♯', 'G', 'G♯', 'A', 'A♯', 'B']

    `A:min` has the same notes

    >>> librosa.key_to_notes('A:min')
    ['C', 'C♯', 'D', 'D♯', 'E', 'F', 'F♯', 'G', 'G♯', 'A', 'A♯', 'B']

    `A♯:min` will use sharps, but spell note 0 (`C`) as `B♯`

    >>> librosa.key_to_notes('A#:min')
    ['B♯', 'C♯', 'D', 'D♯', 'E', 'E♯', 'F♯', 'G', 'G♯', 'A', 'A♯', 'B']

    `G♯:maj` will use a double-sharp to spell note 7 (`G`) as `F𝄪`:

    >>> librosa.key_to_notes('G#:maj')
    ['B♯', 'C♯', 'D', 'D♯', 'E', 'E♯', 'F♯', 'F𝄪', 'G♯', 'A', 'A♯', 'B']

    `F♭:min` will use double-flats

    >>> librosa.key_to_notes('Fb:min')
    ['D𝄫', 'D♭', 'E𝄫', 'E♭', 'F♭', 'F', 'G♭', 'A𝄫', 'A♭', 'B𝄫', 'B♭', 'C♭']
    """

    # Parse the key signature
    match = KEY_RE.match(key)

    if not match:
        raise ParameterError(f"Improper key format: {key:s}")

    pitch_map = {"C": 0, "D": 2, "E": 4, "F": 5, "G": 7, "A": 9, "B": 11}
    acc_map = {"#": 1, "": 0, "b": -1, "!": -1, "♯": 1, "♭": -1}

    tonic = match.group("tonic").upper()
    accidental = match.group("accidental")
    offset = acc_map[accidental]

    scale = match.group("scale")[:3].lower()

    # Determine major or minor
    major = scale == "maj"

    # calculate how many clockwise steps we are on CoF (== # sharps)
    if major:
        tonic_number = ((pitch_map[tonic] + offset) * 7) % 12
    else:
        tonic_number = ((pitch_map[tonic] + offset) * 7 + 9) % 12

    # Decide if using flats or sharps
    # Logic here is as follows:
    #   1. respect the given notation for the tonic.
    #      Sharp tonics will always use sharps, likewise flats.
    #   2. If no accidental in the tonic, try to minimize accidentals.
    #   3. If there's a tie for accidentals, use sharp for major and flat for minor.

    if offset < 0:
        # use flats explicitly
        use_sharps = False

    elif offset > 0:
        # use sharps explicitly
        use_sharps = True

    elif 0 <= tonic_number < 6:
        use_sharps = True

    elif tonic_number > 6:
        use_sharps = False

    # Basic note sequences for simple keys
    notes_sharp = ["C", "C♯", "D", "D♯", "E", "F", "F♯", "G", "G♯", "A", "A♯", "B"]
    notes_flat = ["C", "D♭", "D", "E♭", "E", "F", "G♭", "G", "A♭", "A", "B♭", "B"]

    # These apply when we have >= 6 sharps
    sharp_corrections = [
        (5, "E♯"),
        (0, "B♯"),
        (7, "F𝄪"),
        (2, "C𝄪"),
        (9, "G𝄪"),
        (4, "D𝄪"),
        (11, "A𝄪"),
    ]

    # These apply when we have >= 6 flats
    flat_corrections = [
        (11, "C♭"),
        (4, "F♭"),
        (9, "B𝄫"),
        (2, "E𝄫"),
        (7, "A𝄫"),
        (0, "D𝄫"),
    ]  # last would be (5, 'G𝄫')

    # Apply a mod-12 correction to distinguish B#:maj from C:maj
    n_sharps = tonic_number
    if tonic_number == 0 and tonic == "B":
        n_sharps = 12

    if use_sharps:
        # This will only execute if n_sharps >= 6
        for n in range(0, n_sharps - 6 + 1):
            index, name = sharp_corrections[n]
            notes_sharp[index] = name

        notes = notes_sharp
    else:
        n_flats = (12 - tonic_number) % 12

        # This will only execute if tonic_number <= 6
        for n in range(0, n_flats - 6 + 1):
            index, name = flat_corrections[n]
            notes_flat[index] = name

        notes = notes_flat

    # Finally, apply any unicode down-translation if necessary
    if not unicode:
        translations = str.maketrans({"♯": "#", "𝄪": "##", "♭": "b", "𝄫": "bb"})
        notes = list(n.translate(translations) for n in notes)

    return notes


def key_to_degrees(key: str) -> np.ndarray:
    """Construct the diatonic scale degrees for a given key.

    Parameters
    ----------
    key : str
        Must be in the form TONIC:key.  Tonic must be upper case (``CDEFGAB``),
        key must be lower-case (``maj`` or ``min``).

        Single accidentals (``b!♭`` for flat, or ``#♯`` for sharp) are supported.

        Examples: ``C:maj, Db:min, A♭:min``.

    Returns
    -------
    degrees : np.ndarray
        An array containing the semitone numbers (0=C, 1=C#, ... 11=B)
        for each of the seven scale degrees in the given key, starting
        from the tonic.

    See Also
    --------
    key_to_notes

    Examples
    --------
    >>> librosa.key_to_degrees('C:maj')
    array([ 0,  2,  4,  5,  7,  9, 11])

    >>> librosa.key_to_degrees('C#:maj')
    array([ 1,  3,  5,  6,  8, 10,  0])

    >>> librosa.key_to_degrees('A:min')
    array([ 9, 11,  0,  2,  4,  5,  7])

    """
    notes = dict(
        maj=np.array([0, 2, 4, 5, 7, 9, 11]), min=np.array([0, 2, 3, 5, 7, 8, 10])
    )

    match = KEY_RE.match(key)

    if not match:
        raise ParameterError(f"Improper key format: {key:s}")

    pitch_map = {"C": 0, "D": 2, "E": 4, "F": 5, "G": 7, "A": 9, "B": 11}
    acc_map = {"#": 1, "": 0, "b": -1, "!": -1, "♯": 1, "♭": -1}
    tonic = match.group("tonic").upper()
    accidental = match.group("accidental")
    offset = acc_map[accidental]

    scale = match.group("scale")[:3].lower()

    return (notes[scale] + pitch_map[tonic] + offset) % 12


@cache(level=10)
def fifths_to_note(*, unison: str, fifths: int, unicode: bool = True) -> str:
    """Calculate the note name for a given number of perfect fifths
    from a specified unison.

    This function is primarily intended as a utility routine for
    Functional Just System (FJS) notation conversions.

    This function does not assume the "circle of fifths" or equal temperament,
    so 12 fifths will not generally produce a note of the same pitch class
    due to the accumulation of accidentals.

    Parameters
    ----------
    unison : str
        The name of the starting (unison) note, e.g., 'C' or 'Bb'.
        Unicode accidentals are supported.

    fifths : integer
        The number of perfect fifths to deviate from unison.

    unicode : bool
        If ``True`` (default), use Unicode symbols (♯𝄪♭𝄫)for accidentals.

        If ``False``, accidentals will be encoded as low-order ASCII representations::

            ♯ -> #, 𝄪 -> ##, ♭ -> b, 𝄫 -> bb

    Returns
    -------
    note : str
        The name of the requested note

    Examples
    --------
    >>> librosa.fifths_to_note(unison='C', fifths=6)
    'F♯'

    >>> librosa.fifths_to_note(unison='G', fifths=-3)
    'B♭'

    >>> librosa.fifths_to_note(unison='Eb', fifths=11, unicode=False)
    'G#'
    """
    # Starting the circle of fifths at F makes accidentals easier to count
    COFMAP = "FCGDAEB"

    acc_map = {
        "#": 1,
        "": 0,
        "b": -1,
        "!": -1,
        "♯": 1,
        "𝄪": 2,
        "♭": -1,
        "𝄫": -2,
        "♮": 0,
    }

    if unicode:
        acc_map_inv = {1: "♯", 2: "𝄪", -1: "♭", -2: "𝄫", 0: ""}
    else:
        acc_map_inv = {1: "#", 2: "##", -1: "b", -2: "bb", 0: ""}

    match = NOTE_RE.match(unison)

    if not match:
        raise ParameterError(f"Improper note format: {unison:s}")

    # Find unison in the alphabet
    pitch = match.group("note").upper()

    # Find the number of accidentals to start from
    offset = np.sum([acc_map[o] for o in match.group("accidental")])

    # Find the raw target note
    circle_idx = COFMAP.index(pitch)
    raw_output = COFMAP[(circle_idx + fifths) % 7]

    # Now how many accidentals have we accrued?
    # Equivalently, count times we cross a B<->F boundary
    acc_index = offset + (circle_idx + fifths) // 7

    # Compress multiple-accidentals as needed
    acc_str = acc_map_inv[np.sign(acc_index) * 2] * int(
        abs(acc_index) // 2
    ) + acc_map_inv[np.sign(acc_index)] * int(abs(acc_index) % 2)

    return raw_output + acc_str


@jit(nopython=True, nogil=True, cache=False)
def __o_fold(d):
    """Compute the octave-folded interval.

    This maps intervals to the range [1, 2).

    This is part of the FJS notation converter.
    It is equivalent to the `red` function described in the FJS
    documentation.
    """
    return d * (2.0 ** -np.floor(np.log2(d)))


@jit(nopython=True, nogil=True, cache=False)
def __bo_fold(d):
    """Compute the balanced, octave-folded interval.

    This maps intervals to the range [sqrt(2)/2, sqrt(2)).

    This is part of the FJS notation converter.
    It is equivalent to the `reb` function described in the FJS
    documentation, but with a simpler implementation.
    """
    return d * (2.0 ** -np.round(np.log2(d)))


@jit(nopython=True, nogil=True, cache=False)
def __fifth_search(interval, tolerance):
    """Accelerated helper function for finding the number of fifths
    to get within tolerance of a given interval.

    This implementation will give up after 32 fifths
    """
    log_tolerance = np.abs(np.log2(tolerance))
    for power in range(32):
        for sign in [1, -1]:
            if (
                np.abs(np.log2(__bo_fold(interval / 3.0 ** (power * sign))))
                <= log_tolerance
            ):
                return power * sign
        power += 1
    return power


# Translation grids for superscripts and subscripts
SUPER_TRANS = str.maketrans("0123456789", "⁰¹²³⁴⁵⁶⁷⁸⁹")
SUB_TRANS = str.maketrans("0123456789", "₀₁₂₃₄₅₆₇₈₉")


@overload
def interval_to_fjs(
    interval: _FloatLike_co,
    *,
    unison: str = ...,
    tolerance: float = ...,
    unicode: bool = ...,
) -> str:
    ...


@overload
def interval_to_fjs(
    interval: _SequenceLike[_FloatLike_co],
    *,
    unison: str = ...,
    tolerance: float = ...,
    unicode: bool = ...,
) -> np.ndarray:
    ...


@overload
def interval_to_fjs(
    interval: _ScalarOrSequence[_FloatLike_co],
    *,
    unison: str = ...,
    tolerance: float = ...,
    unicode: bool = ...,
) -> Union[str, np.ndarray]:
    ...


@vectorize(otypes="U", excluded=set(["unison", "tolerance", "unicode"]))
def interval_to_fjs(
    interval: _ScalarOrSequence[_FloatLike_co],
    *,
    unison: str = "C",
    tolerance: float = 65.0 / 63,
    unicode: bool = True,
) -> Union[str, np.ndarray]:
    """Convert an interval to Functional Just System (FJS) notation.

    See https://misotanni.github.io/fjs/en/index.html for a thorough overview
    of the FJS notation system, and the examples below.

    FJS conversion works by identifying a Pythagorean interval which is within
    a specified tolerance of the target interval, which provides the core note
    name.  If the interval is derived from ratios other than perfect fifths,
    then the remaining factors are encoded as superscripts for otonal
    (increasing) intervals and subscripts for utonal (decreasing) intervals.

    Parameters
    ----------
    interval : float > 0 or iterable of floats
        A (just) interval to notate in FJS.

    unison : str
        The name of the unison note (corresponding to `interval=1`).

    tolerance : float
        The tolerance threshold for identifying the core note name.

    unicode : bool
        If ``True`` (default), use Unicode symbols (♯𝄪♭𝄫)for accidentals,
        and superscripts/subscripts for otonal and utonal accidentals.

        If ``False``, accidentals will be encoded as low-order ASCII representations::

            ♯ -> #, 𝄪 -> ##, ♭ -> b, 𝄫 -> bb

        Otonal and utonal accidentals will be denoted by `^##` and `_##`
        respectively (see examples below).

    Raises
    ------
    ParameterError
        If the provided interval is not positive

        If the provided interval cannot be identified with a
        just intonation prime factorization.

    Returns
    -------
    note_fjs : str or np.ndarray(dtype=str)
        The interval(s) relative to the given unison in FJS notation.

    Examples
    --------
    Pythagorean intervals appear as expected, with no otonal
    or utonal extensions:

    >>> librosa.interval_to_fjs(3/2, unison='C')
    'G'
    >>> librosa.interval_to_fjs(4/3, unison='F')
    'B♭'

    A ptolemaic major third will appear with an otonal '5':

    >>> librosa.interval_to_fjs(5/4, unison='A')
    'C♯⁵'

    And a ptolemaic minor third will appear with utonal '5':

    >>> librosa.interval_to_fjs(6/5, unison='A')
    'C₅'

    More complex intervals will have compound accidentals.
    For example:

    >>> librosa.interval_to_fjs(25/14, unison='F#')
    'E²⁵₇'
    >>> librosa.interval_to_fjs(25/14, unison='F#', unicode=False)
    'E^25_7'

    Array inputs are also supported:

    >>> librosa.interval_to_fjs([3/2, 4/3, 5/3])
    array(['G', 'F', 'A⁵'], dtype='<U2')

    """
    # suppressing the type check here because mypy won't introspect through
    # numpy vectorization
    if interval <= 0:  # type: ignore
        raise ParameterError(f"Interval={interval} must be strictly positive")

    # Find the approximate number of fifth-steps to get within tolerance
    # of the target interval
    fifths = __fifth_search(interval, tolerance)

    # determine the base note name
    note_name = fifths_to_note(unison=unison, fifths=fifths, unicode=unicode)

    # Get the prime factor expansion from the interval table
    try:
        # Balance the interval into the octave for lookup
        interval_b = __o_fold(interval)
        powers = INTERVALS[np.around(interval_b, decimals=6)]
    except KeyError as exc:
        raise ParameterError(f"Unknown interval={interval}") from exc

    # Ignore pythagorean spelling
    powers = {p: powers[p] for p in powers if p > 3}

    # Split into otonal and utonal accidentals
    otonal = np.prod([p ** powers[p] for p in powers if powers[p] > 0])
    utonal = np.prod([p ** -powers[p] for p in powers if powers[p] < 0])

    suffix = ""
    if otonal > 1:
        if unicode:
            suffix += f"{otonal:d}".translate(SUPER_TRANS)
        else:
            suffix += f"^{otonal}"

    if utonal > 1:
        if unicode:
            suffix += f"{utonal:d}".translate(SUB_TRANS)
        else:
            suffix += f"_{utonal}"

    return note_name + suffix