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You're reading an old version of this documentation. If you want up-to-date information, please have a look at 0.10.2.
Source code for librosa.beat
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Beat and tempo
==============
.. autosummary::
:toctree: generated/
beat_track
plp
"""
import numpy as np
import scipy
import scipy.stats
from ._cache import cache
from . import core
from . import onset
from . import util
from .feature import tempogram, fourier_tempogram
from .feature import tempo as _tempo
from .util.exceptions import ParameterError
from .util.decorators import moved
from typing import Any, Callable, Optional, Tuple
__all__ = ["beat_track", "tempo", "plp"]
tempo = moved(moved_from="librosa.beat.tempo", version="0.10.0", version_removed="1.0")(
_tempo
)
[docs]def beat_track(
*,
y: Optional[np.ndarray] = None,
sr: float = 22050,
onset_envelope: Optional[np.ndarray] = None,
hop_length: int = 512,
start_bpm: float = 120.0,
tightness: float = 100,
trim: bool = True,
bpm: Optional[float] = None,
prior: Optional[scipy.stats.rv_continuous] = None,
units: str = "frames",
) -> Tuple[float, np.ndarray]:
r"""Dynamic programming beat tracker.
Beats are detected in three stages, following the method of [#]_:
1. Measure onset strength
2. Estimate tempo from onset correlation
3. Pick peaks in onset strength approximately consistent with estimated
tempo
.. [#] Ellis, Daniel PW. "Beat tracking by dynamic programming."
Journal of New Music Research 36.1 (2007): 51-60.
http://labrosa.ee.columbia.edu/projects/beattrack/
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
sr : number > 0 [scalar]
sampling rate of ``y``
onset_envelope : np.ndarray [shape=(n,)] or None
(optional) pre-computed onset strength envelope.
hop_length : int > 0 [scalar]
number of audio samples between successive ``onset_envelope`` values
start_bpm : float > 0 [scalar]
initial guess for the tempo estimator (in beats per minute)
tightness : float [scalar]
tightness of beat distribution around tempo
trim : bool [scalar]
trim leading/trailing beats with weak onsets
bpm : float [scalar]
(optional) If provided, use ``bpm`` as the tempo instead of
estimating it from ``onsets``.
prior : scipy.stats.rv_continuous [optional]
An optional prior distribution over tempo.
If provided, ``start_bpm`` will be ignored.
units : {'frames', 'samples', 'time'}
The units to encode detected beat events in.
By default, 'frames' are used.
Returns
-------
tempo : float [scalar, non-negative]
estimated global tempo (in beats per minute)
beats : np.ndarray [shape=(m,)]
estimated beat event locations in the specified units
(default is frame indices)
.. note::
If no onset strength could be detected, beat_tracker estimates 0 BPM
and returns an empty list.
Raises
------
ParameterError
if neither ``y`` nor ``onset_envelope`` are provided,
or if ``units`` is not one of 'frames', 'samples', or 'time'
See Also
--------
librosa.onset.onset_strength
Examples
--------
Track beats using time series input
>>> y, sr = librosa.load(librosa.ex('choice'), duration=10)
>>> tempo, beats = librosa.beat.beat_track(y=y, sr=sr)
>>> tempo
135.99917763157896
Print the frames corresponding to beats
>>> beats
array([ 3, 21, 40, 59, 78, 96, 116, 135, 154, 173, 192, 211,
230, 249, 268, 287, 306, 325, 344, 363])
Or print them as timestamps
>>> librosa.frames_to_time(beats, sr=sr)
array([0.07 , 0.488, 0.929, 1.37 , 1.811, 2.229, 2.694, 3.135,
3.576, 4.017, 4.458, 4.899, 5.341, 5.782, 6.223, 6.664,
7.105, 7.546, 7.988, 8.429])
Track beats using a pre-computed onset envelope
>>> onset_env = librosa.onset.onset_strength(y=y, sr=sr,
... aggregate=np.median)
>>> tempo, beats = librosa.beat.beat_track(onset_envelope=onset_env,
... sr=sr)
>>> tempo
135.99917763157896
>>> beats
array([ 3, 21, 40, 59, 78, 96, 116, 135, 154, 173, 192, 211,
230, 249, 268, 287, 306, 325, 344, 363])
Plot the beat events against the onset strength envelope
>>> import matplotlib.pyplot as plt
>>> hop_length = 512
>>> fig, ax = plt.subplots(nrows=2, sharex=True)
>>> times = librosa.times_like(onset_env, sr=sr, hop_length=hop_length)
>>> M = librosa.feature.melspectrogram(y=y, sr=sr, hop_length=hop_length)
>>> librosa.display.specshow(librosa.power_to_db(M, ref=np.max),
... y_axis='mel', x_axis='time', hop_length=hop_length,
... ax=ax[0])
>>> ax[0].label_outer()
>>> ax[0].set(title='Mel spectrogram')
>>> ax[1].plot(times, librosa.util.normalize(onset_env),
... label='Onset strength')
>>> ax[1].vlines(times[beats], 0, 1, alpha=0.5, color='r',
... linestyle='--', label='Beats')
>>> ax[1].legend()
"""
# First, get the frame->beat strength profile if we don't already have one
if onset_envelope is None:
if y is None:
raise ParameterError("y or onset_envelope must be provided")
onset_envelope = onset.onset_strength(
y=y, sr=sr, hop_length=hop_length, aggregate=np.median
)
# Do we have any onsets to grab?
if not onset_envelope.any():
return (0, np.array([], dtype=int))
# Estimate BPM if one was not provided
if bpm is None:
bpm = _tempo(
onset_envelope=onset_envelope,
sr=sr,
hop_length=hop_length,
start_bpm=start_bpm,
prior=prior,
)[0]
# Then, run the tracker
beats = __beat_tracker(onset_envelope, bpm, float(sr) / hop_length, tightness, trim)
if units == "frames":
return (bpm, beats)
elif units == "samples":
return (bpm, core.frames_to_samples(beats, hop_length=hop_length))
elif units == "time":
return (bpm, core.frames_to_time(beats, hop_length=hop_length, sr=sr))
else:
raise ParameterError(f"Invalid unit type: {units}")
[docs]def plp(
*,
y: Optional[np.ndarray] = None,
sr: float = 22050,
onset_envelope: Optional[np.ndarray] = None,
hop_length: int = 512,
win_length: int = 384,
tempo_min: Optional[float] = 30,
tempo_max: Optional[float] = 300,
prior: Optional[scipy.stats.rv_continuous] = None,
) -> np.ndarray:
"""Predominant local pulse (PLP) estimation. [#]_
The PLP method analyzes the onset strength envelope in the frequency domain
to find a locally stable tempo for each frame. These local periodicities
are used to synthesize local half-waves, which are combined such that peaks
coincide with rhythmically salient frames (e.g. onset events on a musical time grid).
The local maxima of the pulse curve can be taken as estimated beat positions.
This method may be preferred over the dynamic programming method of `beat_track`
when either the tempo is expected to vary significantly over time. Additionally,
since `plp` does not require the entire signal to make predictions, it may be
preferable when beat-tracking long recordings in a streaming setting.
.. [#] Grosche, P., & Muller, M. (2011).
"Extracting predominant local pulse information from music recordings."
IEEE Transactions on Audio, Speech, and Language Processing, 19(6), 1688-1701.
Parameters
----------
y : np.ndarray [shape=(..., n)] or None
audio time series. Multi-channel is supported.
sr : number > 0 [scalar]
sampling rate of ``y``
onset_envelope : np.ndarray [shape=(..., n)] or None
(optional) pre-computed onset strength envelope
hop_length : int > 0 [scalar]
number of audio samples between successive ``onset_envelope`` values
win_length : int > 0 [scalar]
number of frames to use for tempogram analysis.
By default, 384 frames (at ``sr=22050`` and ``hop_length=512``) corresponds
to about 8.9 seconds.
tempo_min, tempo_max : numbers > 0 [scalar], optional
Minimum and maximum permissible tempo values. ``tempo_max`` must be at least
``tempo_min``.
Set either (or both) to `None` to disable this constraint.
prior : scipy.stats.rv_continuous [optional]
A prior distribution over tempo (in beats per minute).
By default, a uniform prior over ``[tempo_min, tempo_max]`` is used.
Returns
-------
pulse : np.ndarray, shape=[(..., n)]
The estimated pulse curve. Maxima correspond to rhythmically salient
points of time.
If input is multi-channel, one pulse curve per channel is computed.
See Also
--------
beat_track
librosa.onset.onset_strength
librosa.feature.fourier_tempogram
Examples
--------
Visualize the PLP compared to an onset strength envelope.
Both are normalized here to make comparison easier.
>>> y, sr = librosa.load(librosa.ex('brahms'))
>>> onset_env = librosa.onset.onset_strength(y=y, sr=sr)
>>> pulse = librosa.beat.plp(onset_envelope=onset_env, sr=sr)
>>> # Or compute pulse with an alternate prior, like log-normal
>>> import scipy.stats
>>> prior = scipy.stats.lognorm(loc=np.log(120), scale=120, s=1)
>>> pulse_lognorm = librosa.beat.plp(onset_envelope=onset_env, sr=sr,
... prior=prior)
>>> melspec = librosa.feature.melspectrogram(y=y, sr=sr)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=3, sharex=True)
>>> librosa.display.specshow(librosa.power_to_db(melspec,
... ref=np.max),
... x_axis='time', y_axis='mel', ax=ax[0])
>>> ax[0].set(title='Mel spectrogram')
>>> ax[0].label_outer()
>>> ax[1].plot(librosa.times_like(onset_env),
... librosa.util.normalize(onset_env),
... label='Onset strength')
>>> ax[1].plot(librosa.times_like(pulse),
... librosa.util.normalize(pulse),
... label='Predominant local pulse (PLP)')
>>> ax[1].set(title='Uniform tempo prior [30, 300]')
>>> ax[1].label_outer()
>>> ax[2].plot(librosa.times_like(onset_env),
... librosa.util.normalize(onset_env),
... label='Onset strength')
>>> ax[2].plot(librosa.times_like(pulse_lognorm),
... librosa.util.normalize(pulse_lognorm),
... label='Predominant local pulse (PLP)')
>>> ax[2].set(title='Log-normal tempo prior, mean=120', xlim=[5, 20])
>>> ax[2].legend()
PLP local maxima can be used as estimates of beat positions.
>>> tempo, beats = librosa.beat.beat_track(onset_envelope=onset_env)
>>> beats_plp = np.flatnonzero(librosa.util.localmax(pulse))
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True)
>>> times = librosa.times_like(onset_env, sr=sr)
>>> ax[0].plot(times, librosa.util.normalize(onset_env),
... label='Onset strength')
>>> ax[0].vlines(times[beats], 0, 1, alpha=0.5, color='r',
... linestyle='--', label='Beats')
>>> ax[0].legend()
>>> ax[0].set(title='librosa.beat.beat_track')
>>> ax[0].label_outer()
>>> # Limit the plot to a 15-second window
>>> times = librosa.times_like(pulse, sr=sr)
>>> ax[1].plot(times, librosa.util.normalize(pulse),
... label='PLP')
>>> ax[1].vlines(times[beats_plp], 0, 1, alpha=0.5, color='r',
... linestyle='--', label='PLP Beats')
>>> ax[1].legend()
>>> ax[1].set(title='librosa.beat.plp', xlim=[5, 20])
>>> ax[1].xaxis.set_major_formatter(librosa.display.TimeFormatter())
"""
# Step 1: get the onset envelope
if onset_envelope is None:
onset_envelope = onset.onset_strength(
y=y, sr=sr, hop_length=hop_length, aggregate=np.median
)
if tempo_min is not None and tempo_max is not None and tempo_max <= tempo_min:
raise ParameterError(
f"tempo_max={tempo_max} must be larger than tempo_min={tempo_min}"
)
# Step 2: get the fourier tempogram
ftgram = fourier_tempogram(
onset_envelope=onset_envelope,
sr=sr,
hop_length=hop_length,
win_length=win_length,
)
# Step 3: pin to the feasible tempo range
tempo_frequencies = core.fourier_tempo_frequencies(
sr=sr, hop_length=hop_length, win_length=win_length
)
if tempo_min is not None:
ftgram[..., tempo_frequencies < tempo_min, :] = 0
if tempo_max is not None:
ftgram[..., tempo_frequencies > tempo_max, :] = 0
# reshape lengths to match dimension properly
tempo_frequencies = util.expand_to(tempo_frequencies, ndim=ftgram.ndim, axes=-2)
# Step 3: Discard everything below the peak
ftmag = np.log1p(1e6 * np.abs(ftgram))
if prior is not None:
ftmag += prior.logpdf(tempo_frequencies)
peak_values = ftmag.max(axis=-2, keepdims=True)
ftgram[ftmag < peak_values] = 0
# Normalize to keep only phase information
ftgram /= util.tiny(ftgram) ** 0.5 + np.abs(ftgram.max(axis=-2, keepdims=True))
# Step 5: invert the Fourier tempogram to get the pulse
pulse = core.istft(
ftgram, hop_length=1, n_fft=win_length, length=onset_envelope.shape[-1]
)
# Step 6: retain only the positive part of the pulse cycle
pulse = np.clip(pulse, 0, None, pulse)
# Return the normalized pulse
return util.normalize(pulse, axis=-1)
def __beat_tracker(
onset_envelope: np.ndarray, bpm: float, fft_res: float, tightness: float, trim: bool
) -> np.ndarray:
"""Internal function that tracks beats in an onset strength envelope.
Parameters
----------
onset_envelope : np.ndarray [shape=(n,)]
onset strength envelope
bpm : float [scalar]
tempo estimate
fft_res : float [scalar]
resolution of the fft (sr / hop_length)
tightness : float [scalar]
how closely do we adhere to bpm?
trim : bool [scalar]
trim leading/trailing beats with weak onsets?
Returns
-------
beats : np.ndarray [shape=(n,)]
frame numbers of beat events
"""
if bpm <= 0:
raise ParameterError("bpm must be strictly positive")
# convert bpm to a sample period for searching
period = round(60.0 * fft_res / bpm)
# localscore is a smoothed version of AGC'd onset envelope
localscore = __beat_local_score(onset_envelope, period)
# run the DP
backlink, cumscore = __beat_track_dp(localscore, period, tightness)
# get the position of the last beat
beats = [__last_beat(cumscore)]
# Reconstruct the beat path from backlinks
while backlink[beats[-1]] >= 0:
beats.append(backlink[beats[-1]])
# Put the beats in ascending order
# Convert into an array of frame numbers
beats = np.array(beats[::-1], dtype=int)
# Discard spurious trailing beats
beats = __trim_beats(localscore, beats, trim)
return beats
# -- Helper functions for beat tracking
def __normalize_onsets(onsets):
"""Maps onset strength function into the range [0, 1]"""
norm = onsets.std(ddof=1)
if norm > 0:
onsets = onsets / norm
return onsets
def __beat_local_score(onset_envelope, period):
"""Construct the local score for an onset envlope and given period"""
window = np.exp(-0.5 * (np.arange(-period, period + 1) * 32.0 / period) ** 2)
return scipy.signal.convolve(__normalize_onsets(onset_envelope), window, "same")
def __beat_track_dp(localscore, period, tightness):
"""Core dynamic program for beat tracking"""
backlink = np.zeros_like(localscore, dtype=int)
cumscore = np.zeros_like(localscore)
# Search range for previous beat
window = np.arange(-2 * period, -np.round(period / 2) + 1, dtype=int)
# Make a score window, which begins biased toward start_bpm and skewed
if tightness <= 0:
raise ParameterError("tightness must be strictly positive")
txwt = -tightness * (np.log(-window / period) ** 2)
# Are we on the first beat?
first_beat = True
for i, score_i in enumerate(localscore):
# Are we reaching back before time 0?
z_pad = np.maximum(0, min(-window[0], len(window)))
# Search over all possible predecessors
candidates = txwt.copy()
candidates[z_pad:] = candidates[z_pad:] + cumscore[window[z_pad:]]
# Find the best preceding beat
beat_location = np.argmax(candidates)
# Add the local score
cumscore[i] = score_i + candidates[beat_location]
# Special case the first onset. Stop if the localscore is small
if first_beat and score_i < 0.01 * localscore.max():
backlink[i] = -1
else:
backlink[i] = window[beat_location]
first_beat = False
# Update the time range
window = window + 1
return backlink, cumscore
def __last_beat(cumscore):
"""Get the last beat from the cumulative score array"""
maxes = util.localmax(cumscore)
med_score = np.median(cumscore[np.argwhere(maxes)])
# The last of these is the last beat (since score generally increases)
return np.argwhere((cumscore * maxes * 2 > med_score)).max()
def __trim_beats(localscore: np.ndarray, beats: np.ndarray, trim: bool) -> np.ndarray:
"""Final post-processing: throw out spurious leading/trailing beats"""
smooth_boe = scipy.signal.convolve(localscore[beats], scipy.signal.hann(5), "same")
if trim:
threshold = 0.5 * ((smooth_boe**2).mean() ** 0.5)
else:
threshold = 0.0
valid = np.argwhere(smooth_boe > threshold)
return beats[valid.min() : valid.max()]