.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plot_dynamic_beat.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_plot_dynamic_beat.py: ===================================== Beat tracking with time-varying tempo ===================================== This notebook demonstrates how to use the beat tracker in situations where the tempo may change over time. By default, the beat tracking algorithm [1]_ estimates a single tempo for the entire signal, though it does tolerate small amounts of fluctuation around that tempo. This is well suited for songs that have an approximately constant tempo, but where individual beats may not be exactly spaced accordingly. It is not well suited for songs that have radical shifts in tempo, e.g., entire sections that speed up or slow down, or gradual accelerations over long periods of time. The implementation in librosa (``librosa.beat.beat_track``) extends this algorithm to support different tempo estimates at each time point in the signal, as demonstrated below. .. [1] Ellis, Daniel PW. "Beat tracking by dynamic programming." Journal of New Music Research 36, no. 1 (2007): 51-60. http://labrosa.ee.columbia.edu/projects/beattrack/ .. GENERATED FROM PYTHON SOURCE LINES 25-34 .. code-block:: Python # Code source: Brian McFee # License: ISC import numpy as np import librosa import matplotlib.pyplot as plt from IPython.display import Audio .. GENERATED FROM PYTHON SOURCE LINES 35-40 ------------------------------ A recording with dynamic tempo ------------------------------ The example recording included in this notebook consists of a drum beat that gradually increases in tempo from 30 BPM to 240 BPM over a 30-second time interval. .. GENERATED FROM PYTHON SOURCE LINES 40-43 .. code-block:: Python y, sr = librosa.load('audio/snare-accelerate.ogg') .. GENERATED FROM PYTHON SOURCE LINES 44-47 We can visualize the spectrogram of this recording and listen to it. From the spectrogram, we can see that the spacing between drum beats becomes smaller over time, indicating a gradual increase of tempo. .. GENERATED FROM PYTHON SOURCE LINES 47-55 .. code-block:: Python fig, ax = plt.subplots() melspec = librosa.power_to_db(librosa.feature.melspectrogram(y=y, sr=sr), ref=np.max) librosa.display.specshow(melspec, y_axis='mel', x_axis='time', ax=ax) ax.set(title='Mel spectrogram') Audio(data=y, rate=sr) .. image-sg:: /auto_examples/images/sphx_glr_plot_dynamic_beat_001.png :alt: Mel spectrogram :srcset: /auto_examples/images/sphx_glr_plot_dynamic_beat_001.png :class: sphx-glr-single-img .. raw:: html

.. GENERATED FROM PYTHON SOURCE LINES 56-66 -------------------------- Static tempo beat tracking -------------------------- If we run the beat tracker on this signal directly and sonify the result as a click track, we can see that it does not follow particularly well. This is because the beat tracker is assuming a single (average) tempo across the entire signal. Note: by default, `beat_track` assumes that there is silence at the end of the signal, and trims last beats to avoid false detections. Here, there is no silence at the end, so we set `trim=False` to avoid this effect. .. GENERATED FROM PYTHON SOURCE LINES 66-74 .. code-block:: Python tempo, beats_static = librosa.beat.beat_track(y=y, sr=sr, units='time', trim=False) click_track = librosa.clicks(times=beats_static, sr=sr, click_freq=660, click_duration=0.25, length=len(y)) print(f"Tempo estimate: {tempo[0]:.2f} BPM") Audio(data=y+click_track, rate=sr) .. rst-class:: sphx-glr-script-out .. code-block:: none Tempo estimate: 107.67 BPM .. raw:: html

.. GENERATED FROM PYTHON SOURCE LINES 75-81 ------------- Dynamic tempo ------------- Instead of estimating an aggregated tempo for the whole signal, we now estimate a time-varying tempo. For this purpose, we pass `aggregate=None` to `librosa.feature.tempo`. The return value tempo_dynamic, is an array: .. GENERATED FROM PYTHON SOURCE LINES 81-83 .. code-block:: Python tempo_dynamic = librosa.feature.tempo(y=y, sr=sr, aggregate=None, std_bpm=4) .. GENERATED FROM PYTHON SOURCE LINES 84-89 The parameter `std_bpm` is the standard deviation of the tempo estimator and has a default value of 1. Here, we have increased `std_bpm` to 4. This is to account for the broad range of tempo drift in this particular recording (30 BPM to 240 BPM). We can plot the dynamic and static tempo estimates to see how they differ. .. GENERATED FROM PYTHON SOURCE LINES 89-97 .. code-block:: Python fig, ax = plt.subplots() times = librosa.times_like(tempo_dynamic, sr=sr) ax.plot(times, tempo_dynamic, label='Dynamic tempo estimate') ax.axhline(tempo, label='Static tempo estimate', color='r') ax.legend() ax.set(xlabel='Time (s)', ylabel='Tempo (BPM)') .. image-sg:: /auto_examples/images/sphx_glr_plot_dynamic_beat_002.png :alt: plot dynamic beat :srcset: /auto_examples/images/sphx_glr_plot_dynamic_beat_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 98-105 `librosa.feature.tempo` estimates tempo over a sliding window whose duration `ac_size` is equal to 8 seconds by default. In this example, the result is not perfect: `tempo_dynamic` contains jagged and nonuniform steps. However, it does provide a rough picture of how tempo is changing over time. We can now use this dynamic tempo in the beat tracker directly: .. GENERATED FROM PYTHON SOURCE LINES 105-114 .. code-block:: Python tempo, beats_dynamic = librosa.beat.beat_track(y=y, sr=sr, units='time', bpm=tempo_dynamic, trim=False) click_dynamic = librosa.clicks(times=beats_dynamic, sr=sr, click_freq=660, click_duration=0.25, length=len(y)) Audio(data=y+click_dynamic, rate=sr) .. raw:: html

.. GENERATED FROM PYTHON SOURCE LINES 115-120 (Note that since we're providing the tempo estimates as input to the beat tracker, we can ignore the first return value (`tempo`) which will simply be a copy of the input (`tempo_dynamic`).) We can visualize the difference in estimated beat timings as follows: .. GENERATED FROM PYTHON SOURCE LINES 120-128 .. code-block:: Python fig, ax = plt.subplots() librosa.display.waveshow(y=y, sr=sr, ax=ax, color='k', alpha=0.7) ax.vlines(beats_static, 0.75, 1., label='Static tempo beat estimates', color='r') ax.vlines(beats_dynamic, -1, -0.75, label='Dynamic tempo beat estimates', color='b', linestyle='--') ax.legend() .. image-sg:: /auto_examples/images/sphx_glr_plot_dynamic_beat_003.png :alt: plot dynamic beat :srcset: /auto_examples/images/sphx_glr_plot_dynamic_beat_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 129-135 In the figure above, we observe that `beats_dynamic`, the beat estimates derived from dynamic tempo, align well to the audio recording. On the contrary, `beats_static` suffers from alignment problems. Indeed, it has too many detections towards the beginning of the recording—where the static tempo estimate is too fast—and too few detections towards the end of the recording—where the static tempo estimate is too slow. .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.919 seconds) .. _sphx_glr_download_auto_examples_plot_dynamic_beat.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_dynamic_beat.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_dynamic_beat.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_