Source code for librosa.core.notation

#!/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 ..util.decorators import vectorize

__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)?)$"
)


[docs]def thaat_to_degrees(thaat): """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()])
[docs]def mela_to_degrees(mela): """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("mela={} must be in range [1, 72]".format(mela)) # 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)
[docs]@cache(level=10) def mela_to_svara(mela, *, abbr=True, unicode=True): """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", None, # Ri2/Ga1 None, # Ri3/Ga2 "Ga\u2083", "Ma\u2081", "Ma\u2082", "Pa", "Dha\u2081", None, # Dha2/Ni1 None, # 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("mela={} must be in range [1, 72]".format(mela)) # 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: svara_map = [ s.translate(str.maketrans({"a": "", "h": "", "i": ""})) for s in svara_map ] if not unicode: svara_map = [ s.translate(str.maketrans({"\u2081": "1", "\u2082": "2", "\u2083": "3"})) for s in svara_map ] return list(svara_map)
[docs]def list_mela(): """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()
[docs]def list_thaat(): """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())
[docs]@cache(level=10) def key_to_notes(key, *, unicode=True): """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("Improper key format: {:s}".format(key)) 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
[docs]def key_to_degrees(key): """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("Improper key format: {:s}".format(key)) 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
[docs]@cache(level=10) def fifths_to_note(*, unison, fifths, unicode=True): """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=True) 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=True) 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=True) 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")
[docs]@vectorize(otypes="U", excluded=set(["unison", "tolerance", "unicode"])) def interval_to_fjs(interval, *, unison="C", tolerance=65.0 / 63, unicode=True): """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') """ if interval <= 0: 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