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<!DOCTYPE html>
<html lang="en" data-content_root="./" >
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Tutorial — librosa 1.0.0dev documentation</title>
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API documentation
</a>
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<a class="nav-link nav-internal" href="advanced/index.html">
Advanced topics
</a>
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<article class="bd-article">
<section id="tutorial">
<h1>Tutorial<a class="headerlink" href="#tutorial" title="Link to this heading">#</a></h1>
<p>This section covers the fundamentals of developing with <em>librosa</em>, including
a package overview, basic and advanced usage, and integration with the <em>scikit-learn</em>
package. We will assume basic familiarity with Python and NumPy/SciPy.</p>
<section id="overview">
<h2>Overview<a class="headerlink" href="#overview" title="Link to this heading">#</a></h2>
<p>The <em>librosa</em> package is structured as collection of submodules:</p>
<blockquote>
<div><ul class="simple">
<li><p>librosa</p>
<ul>
<li><dl class="simple">
<dt><a class="reference internal" href="beat.html#beat"><span class="std std-ref">librosa.beat</span></a></dt><dd><p>Functions for estimating tempo and detecting beat events.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="core.html#core"><span class="std std-ref">librosa.core</span></a></dt><dd><p>Core functionality includes functions to load audio from disk, compute various
spectrogram representations, and a variety of commonly used tools for
music analysis. For convenience, all functionality in this submodule is
directly accessible from the top-level <em class="xref py py-obj">librosa.*</em> namespace.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="decompose.html#decompose"><span class="std std-ref">librosa.decompose</span></a></dt><dd><p>Functions for harmonic-percussive source separation (HPSS) and generic
spectrogram decomposition using matrix decomposition methods implemented in
<em>scikit-learn</em>.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="display.html#display"><span class="std std-ref">librosa.display</span></a></dt><dd><p>Visualization and display routines using <a class="reference external" href="https://matplotlib.org/stable/index.html#module-matplotlib" title="(in Matplotlib v3.11.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">matplotlib</span></code></a>.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="effects.html#effects"><span class="std std-ref">librosa.effects</span></a></dt><dd><p>Time-domain audio processing, such as pitch shifting and time stretching.
This submodule also provides time-domain wrappers for the <em class="xref py py-obj">decompose</em>
submodule.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="feature.html#feature"><span class="std std-ref">librosa.feature</span></a></dt><dd><p>Feature extraction and manipulation. This includes low-level feature
extraction, such as chromagrams, Mel spectrogram, MFCC, and various other
spectral and rhythmic features. Also provided are feature manipulation
methods, such as delta features and memory embedding.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="filters.html#filters"><span class="std std-ref">librosa.filters</span></a></dt><dd><p>Filter-bank generation (chroma, pseudo-CQT, CQT, etc.). These are primarily
internal functions used by other parts of <em>librosa</em>.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="onset.html#onset"><span class="std std-ref">librosa.onset</span></a></dt><dd><p>Onset detection and onset strength computation.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="segment.html#segment"><span class="std std-ref">librosa.segment</span></a></dt><dd><p>Functions useful for structural segmentation, such as recurrence matrix
construction, time-lag representation, and sequentially constrained
clustering.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="sequence.html#sequence"><span class="std std-ref">librosa.sequence</span></a></dt><dd><p>Functions for sequential modeling. Various forms of Viterbi decoding,
and helper functions for constructing transition matrices.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><a class="reference internal" href="util.html#util"><span class="std std-ref">librosa.util</span></a></dt><dd><p>Helper utilities (normalization, padding, centering, etc.)</p>
</dd>
</dl>
</li>
</ul>
</li>
</ul>
</div></blockquote>
</section>
<section id="quickstart">
<span id="id1"></span><h2>Quickstart<a class="headerlink" href="#quickstart" title="Link to this heading">#</a></h2>
<p>Before diving into the details, we’ll walk through a brief example program</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="linenos"> 1</span><span class="c1"># Beat tracking example</span>
<span class="linenos"> 2</span><span class="kn">import</span><span class="w"> </span><span class="nn">librosa</span>
<span class="linenos"> 3</span>
<span class="linenos"> 4</span><span class="c1"># 1. Get the file path to an included audio example</span>
<span class="linenos"> 5</span><span class="n">filename</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">example</span><span class="p">(</span><span class="s1">'nutcracker'</span><span class="p">)</span>
<span class="linenos"> 6</span>
<span class="linenos"> 7</span>
<span class="linenos"> 8</span><span class="c1"># 2. Load the audio as a waveform `y`</span>
<span class="linenos"> 9</span><span class="c1"># Store the sampling rate as `sr`</span>
<span class="linenos">10</span><span class="n">y</span><span class="p">,</span> <span class="n">sr</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">filename</span><span class="p">)</span>
<span class="linenos">11</span>
<span class="linenos">12</span><span class="c1"># 3. Run the default beat tracker</span>
<span class="linenos">13</span><span class="n">tempo</span><span class="p">,</span> <span class="n">beat_frames</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">beat</span><span class="o">.</span><span class="n">beat_track</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">)</span>
<span class="linenos">14</span>
<span class="linenos">15</span><span class="nb">print</span><span class="p">(</span><span class="s1">'Estimated tempo: </span><span class="si">{:.2f}</span><span class="s1"> beats per minute'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">tempo</span><span class="p">))</span>
<span class="linenos">16</span>
<span class="linenos">17</span><span class="c1"># 4. Convert the frame indices of beat events into timestamps</span>
<span class="linenos">18</span><span class="n">beat_times</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">frames_to_time</span><span class="p">(</span><span class="n">beat_frames</span><span class="p">,</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">)</span>
</pre></div>
</div>
<p>The first step of the program:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">filename</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">example</span><span class="p">(</span><span class="s1">'nutcracker'</span><span class="p">)</span>
</pre></div>
</div>
<p>gets the path to an audio example file included with <em>librosa</em>. After this step,
<code class="docutils literal notranslate"><span class="pre">filename</span></code> will be a string variable containing the path to the example audio file.</p>
<p>The second step:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">y</span><span class="p">,</span> <span class="n">sr</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">filename</span><span class="p">)</span>
</pre></div>
</div>
<p>loads and decodes the audio as a <a class="reference internal" href="glossary.html#term-time-series"><span class="xref std std-term">time series</span></a> <code class="docutils literal notranslate"><span class="pre">y</span></code>, represented as a one-dimensional
NumPy floating point array. The variable <em class="xref py py-obj">sr</em> contains the <a class="reference internal" href="glossary.html#term-sampling-rate"><span class="xref std std-term">sampling rate</span></a> of
<code class="docutils literal notranslate"><span class="pre">y</span></code>, that is, the number of samples per second of audio. By default, all audio is
mixed to mono and resampled to 22050 Hz at load time. This behavior can be overridden
by supplying additional arguments to <a class="reference internal" href="generated/librosa.load.html#librosa.load" title="librosa.load"><code class="xref py py-obj docutils literal notranslate"><span class="pre">librosa.load</span></code></a>.</p>
<p>Next, we run the beat tracker:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">tempo</span><span class="p">,</span> <span class="n">beat_frames</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">beat</span><span class="o">.</span><span class="n">beat_track</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">)</span>
</pre></div>
</div>
<p>The output of the beat tracker is an estimate of the tempo (in beats per minute),
and an array of frame numbers corresponding to detected beat events.</p>
<p><a class="reference internal" href="glossary.html#term-frame"><span class="xref std std-term">Frames</span></a> here correspond to short windows of the signal (<code class="docutils literal notranslate"><span class="pre">y</span></code>), each
separated by <code class="docutils literal notranslate"><span class="pre">hop_length</span> <span class="pre">=</span> <span class="pre">512</span></code> samples. <em>librosa</em> uses centered frames, so
that the <em>k</em>th frame is centered around sample <code class="docutils literal notranslate"><span class="pre">k</span> <span class="pre">*</span> <span class="pre">hop_length</span></code>.</p>
<p>The next operation converts the frame numbers <code class="docutils literal notranslate"><span class="pre">beat_frames</span></code> into timings:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">beat_times</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">frames_to_time</span><span class="p">(</span><span class="n">beat_frames</span><span class="p">,</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">)</span>
</pre></div>
</div>
<p>Now, <code class="docutils literal notranslate"><span class="pre">beat_times</span></code> will be an array of timestamps (in seconds) corresponding to
detected beat events.</p>
<p>The contents of <code class="docutils literal notranslate"><span class="pre">beat_times</span></code> should look something like this:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">7.43</span>
<span class="mf">8.29</span>
<span class="mf">9.218</span>
<span class="mf">10.124</span>
<span class="o">...</span>
</pre></div>
</div>
</section>
<section id="advanced-usage">
<h2>Advanced usage<a class="headerlink" href="#advanced-usage" title="Link to this heading">#</a></h2>
<p>Here we’ll cover a more advanced example, integrating harmonic-percussive separation,
multiple spectral features, and beat-synchronous feature aggregation.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="linenos"> 1</span><span class="c1"># Feature extraction example</span>
<span class="linenos"> 2</span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="linenos"> 3</span><span class="kn">import</span><span class="w"> </span><span class="nn">librosa</span>
<span class="linenos"> 4</span>
<span class="linenos"> 5</span><span class="c1"># Load the example clip</span>
<span class="linenos"> 6</span><span class="n">y</span><span class="p">,</span> <span class="n">sr</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">librosa</span><span class="o">.</span><span class="n">ex</span><span class="p">(</span><span class="s1">'nutcracker'</span><span class="p">))</span>
<span class="linenos"> 7</span>
<span class="linenos"> 8</span><span class="c1"># Set the hop length; at 22050 Hz, 512 samples ~= 23ms</span>
<span class="linenos"> 9</span><span class="n">hop_length</span> <span class="o">=</span> <span class="mi">512</span>
<span class="linenos">10</span>
<span class="linenos">11</span><span class="c1"># Separate harmonics and percussives into two waveforms</span>
<span class="linenos">12</span><span class="n">y_harmonic</span><span class="p">,</span> <span class="n">y_percussive</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">effects</span><span class="o">.</span><span class="n">hpss</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="linenos">13</span>
<span class="linenos">14</span><span class="c1"># Beat track on the percussive signal</span>
<span class="linenos">15</span><span class="n">tempo</span><span class="p">,</span> <span class="n">beat_frames</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">beat</span><span class="o">.</span><span class="n">beat_track</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="n">y_percussive</span><span class="p">,</span>
<span class="linenos">16</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">)</span>
<span class="linenos">17</span>
<span class="linenos">18</span><span class="c1"># Compute MFCC features from the raw signal</span>
<span class="linenos">19</span><span class="n">mfcc</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">feature</span><span class="o">.</span><span class="n">mfcc</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">,</span> <span class="n">hop_length</span><span class="o">=</span><span class="n">hop_length</span><span class="p">,</span> <span class="n">n_mfcc</span><span class="o">=</span><span class="mi">13</span><span class="p">)</span>
<span class="linenos">20</span>
<span class="linenos">21</span><span class="c1"># And the first-order differences (delta features)</span>
<span class="linenos">22</span><span class="n">mfcc_delta</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">feature</span><span class="o">.</span><span class="n">delta</span><span class="p">(</span><span class="n">mfcc</span><span class="p">)</span>
<span class="linenos">23</span>
<span class="linenos">24</span><span class="c1"># Stack and synchronize between beat events</span>
<span class="linenos">25</span><span class="c1"># This time, we'll use the mean value (default) instead of median</span>
<span class="linenos">26</span><span class="n">beat_mfcc_delta</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">util</span><span class="o">.</span><span class="n">sync</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">mfcc</span><span class="p">,</span> <span class="n">mfcc_delta</span><span class="p">]),</span>
<span class="linenos">27</span> <span class="n">beat_frames</span><span class="p">)</span>
<span class="linenos">28</span>
<span class="linenos">29</span><span class="c1"># Compute chroma features from the harmonic signal</span>
<span class="linenos">30</span><span class="n">chromagram</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">feature</span><span class="o">.</span><span class="n">chroma_cqt</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="n">y_harmonic</span><span class="p">,</span>
<span class="linenos">31</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">)</span>
<span class="linenos">32</span>
<span class="linenos">33</span><span class="c1"># Aggregate chroma features between beat events</span>
<span class="linenos">34</span><span class="c1"># We'll use the median value of each feature between beat frames</span>
<span class="linenos">35</span><span class="n">beat_chroma</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">util</span><span class="o">.</span><span class="n">sync</span><span class="p">(</span><span class="n">chromagram</span><span class="p">,</span>
<span class="linenos">36</span> <span class="n">beat_frames</span><span class="p">,</span>
<span class="linenos">37</span> <span class="n">aggregate</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">)</span>
<span class="linenos">38</span>
<span class="linenos">39</span><span class="c1"># Finally, stack all beat-synchronous features together</span>
<span class="linenos">40</span><span class="n">beat_features</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">beat_chroma</span><span class="p">,</span> <span class="n">beat_mfcc_delta</span><span class="p">])</span>
</pre></div>
</div>
<p>This example builds on tools we’ve already covered in the <a class="reference internal" href="#quickstart"><span class="std std-ref">quickstart example</span></a>, so here we’ll focus just on the new parts.</p>
<p>The first difference is the use of the <a class="reference internal" href="effects.html#effects"><span class="std std-ref">effects module</span></a> for time-series
harmonic-percussive separation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">y_harmonic</span><span class="p">,</span> <span class="n">y_percussive</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">effects</span><span class="o">.</span><span class="n">hpss</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
</pre></div>
</div>
<p>The result of this line is that the time series <code class="docutils literal notranslate"><span class="pre">y</span></code> has been separated into two time
series, containing the harmonic (tonal) and percussive (transient) portions of the
signal. Each of <code class="docutils literal notranslate"><span class="pre">y_harmonic</span></code> and <code class="docutils literal notranslate"><span class="pre">y_percussive</span></code> have the same shape and duration
as <code class="docutils literal notranslate"><span class="pre">y</span></code>.</p>
<p>The motivation for this kind of operation is two-fold: first, percussive elements
tend to be stronger indicators of rhythmic content, and can help provide more stable
beat tracking results; second, percussive elements can pollute tonal feature
representations (such as chroma) by contributing energy across all frequency bands, so
we’d be better off without them.</p>
<p>Next, we introduce the <a class="reference internal" href="feature.html#feature"><span class="std std-ref">feature module</span></a> and extract the Mel-frequency
cepstral coefficients from the raw signal <code class="docutils literal notranslate"><span class="pre">y</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">mfcc</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">feature</span><span class="o">.</span><span class="n">mfcc</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">,</span> <span class="n">hop_length</span><span class="o">=</span><span class="n">hop_length</span><span class="p">,</span> <span class="n">n_mfcc</span><span class="o">=</span><span class="mi">13</span><span class="p">)</span>
</pre></div>
</div>
<p>The output of this function is the matrix <code class="docutils literal notranslate"><span class="pre">mfcc</span></code>, which is a <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.5)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.ndarray</span></code></a> of
shape <code class="docutils literal notranslate"><span class="pre">(n_mfcc,</span> <span class="pre">T)</span></code> (where <code class="docutils literal notranslate"><span class="pre">T</span></code> denotes the track duration in <a class="reference internal" href="glossary.html#term-frame"><span class="xref std std-term">frames</span></a>).
Note that we use the same <code class="docutils literal notranslate"><span class="pre">hop_length</span></code> here as in the beat tracker, so the detected <code class="docutils literal notranslate"><span class="pre">beat_frames</span></code>
values correspond to columns of <code class="docutils literal notranslate"><span class="pre">mfcc</span></code>.</p>
<p>The first type of feature manipulation we introduce is <code class="docutils literal notranslate"><span class="pre">delta</span></code>, which computes
(smoothed) first-order differences among columns of its input:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">mfcc_delta</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">feature</span><span class="o">.</span><span class="n">delta</span><span class="p">(</span><span class="n">mfcc</span><span class="p">)</span>
</pre></div>
</div>
<p>The resulting matrix <code class="docutils literal notranslate"><span class="pre">mfcc_delta</span></code> has the same shape as the input <code class="docutils literal notranslate"><span class="pre">mfcc</span></code>.</p>
<p>The second type of feature manipulation is <code class="docutils literal notranslate"><span class="pre">sync</span></code>, which aggregates columns of its
input between sample indices (e.g., beat frames):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">beat_mfcc_delta</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">util</span><span class="o">.</span><span class="n">sync</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">mfcc</span><span class="p">,</span> <span class="n">mfcc_delta</span><span class="p">]),</span>
<span class="n">beat_frames</span><span class="p">)</span>
</pre></div>
</div>
<p>Here, we’ve vertically stacked the <code class="docutils literal notranslate"><span class="pre">mfcc</span></code> and <code class="docutils literal notranslate"><span class="pre">mfcc_delta</span></code> matrices together. The
result of this operation is a matrix <code class="docutils literal notranslate"><span class="pre">beat_mfcc_delta</span></code> with the same number of rows
as its input, but the number of columns depends on <code class="docutils literal notranslate"><span class="pre">beat_frames</span></code>. Each column
<code class="docutils literal notranslate"><span class="pre">beat_mfcc_delta[:,</span> <span class="pre">k]</span></code> will be the <em>average</em> of input columns between
<code class="docutils literal notranslate"><span class="pre">beat_frames[k]</span></code> and <code class="docutils literal notranslate"><span class="pre">beat_frames[k+1]</span></code>. (<code class="docutils literal notranslate"><span class="pre">beat_frames</span></code> will be expanded to
span the full range <code class="docutils literal notranslate"><span class="pre">[0,</span> <span class="pre">T]</span></code> so that all data is accounted for.)</p>
<p>Next, we compute a chromagram using just the harmonic component:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">chromagram</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">feature</span><span class="o">.</span><span class="n">chroma_cqt</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="n">y_harmonic</span><span class="p">,</span>
<span class="n">sr</span><span class="o">=</span><span class="n">sr</span><span class="p">)</span>
</pre></div>
</div>
<p>After this line, <code class="docutils literal notranslate"><span class="pre">chromagram</span></code> will be a <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.5)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.ndarray</span></code></a> of shape <code class="docutils literal notranslate"><span class="pre">(12,</span> <span class="pre">T)</span></code>, and
each row corresponds to a pitch class (e.g., <em>C</em>, <em>C#</em>, etc.). Each column of
<code class="docutils literal notranslate"><span class="pre">chromagram</span></code> is normalized by its peak value, though this behavior can be overridden
by setting the <code class="docutils literal notranslate"><span class="pre">norm</span></code> parameter.</p>
<p>Once we have the chromagram and list of beat frames, we again synchronize the chroma
between beat events:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">beat_chroma</span> <span class="o">=</span> <span class="n">librosa</span><span class="o">.</span><span class="n">util</span><span class="o">.</span><span class="n">sync</span><span class="p">(</span><span class="n">chromagram</span><span class="p">,</span>
<span class="n">beat_frames</span><span class="p">,</span>
<span class="n">aggregate</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">)</span>
</pre></div>
</div>
<p>This time, we’ve replaced the default aggregate operation (<em>average</em>, as used above
for MFCCs) with the <em>median</em>. In general, any statistical summarization function can
be supplied here, including <code class="docutils literal notranslate"><span class="pre">np.max()</span></code>, <code class="docutils literal notranslate"><span class="pre">np.min()</span></code>, <code class="docutils literal notranslate"><span class="pre">np.std()</span></code>, etc.</p>
<p>Finally, the all features are vertically stacked again:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">beat_features</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">beat_chroma</span><span class="p">,</span> <span class="n">beat_mfcc_delta</span><span class="p">])</span>
</pre></div>
</div>
<p>resulting in a feature matrix <code class="docutils literal notranslate"><span class="pre">beat_features</span></code> of shape
<code class="docutils literal notranslate"><span class="pre">(12</span> <span class="pre">+</span> <span class="pre">13</span> <span class="pre">+</span> <span class="pre">13,</span> <span class="pre">#</span> <span class="pre">beat</span> <span class="pre">intervals)</span></code>.</p>
</section>
<section id="more-examples">
<h2>More examples<a class="headerlink" href="#more-examples" title="Link to this heading">#</a></h2>
<p>More example scripts are provided in the <a class="reference internal" href="advanced.html#advanced"><span class="std std-ref">advanced examples</span></a> section.</p>
</section>
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