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librosa.feature.tonnetz(*, y=None, sr=22050, chroma=None, **kwargs)[source]

Computes the tonal centroid features (tonnetz)

This representation uses the method of [1] to project chroma features onto a 6-dimensional basis representing the perfect fifth, minor third, and major third each as two-dimensional coordinates.

ynp.ndarray [shape=(…, n,)] or None

Audio time series. Multi-channel is supported.

srnumber > 0 [scalar]

sampling rate of y

chromanp.ndarray [shape=(n_chroma, t)] or None

Normalized energy for each chroma bin at each frame. If None, a cqt chromagram is performed.

**kwargsAdditional keyword arguments to chroma_cqt,

if chroma is not pre-computed.

Cnp.ndarray [shape=(…, d, t)] [Optional]

a pre-computed constant-Q spectrogram

hop_lengthint > 0

number of samples between successive chroma frames

fminfloat > 0

minimum frequency to analyze in the CQT. Default: C1 ~= 32.7 Hz

normint > 0, +-np.inf, or None

Column-wise normalization of the chromagram.


Pre-normalization energy threshold. Values below the threshold are discarded, resulting in a sparse chromagram.


Deviation (in fractions of a CQT bin) from A440 tuning

n_chromaint > 0

Number of chroma bins to produce

n_octavesint > 0

Number of octaves to analyze above fmin

windowNone or np.ndarray

Optional window parameter to filters.cq_to_chroma

bins_per_octaveint > 0, optional

Number of bins per octave in the CQT. Must be an integer multiple of n_chroma. Default: 36 (3 bins per semitone) If None, it will match n_chroma.

cqt_mode[‘full’, ‘hybrid’]

Constant-Q transform mode

tonnetznp.ndarray [shape(…, 6, t)]

Tonal centroid features for each frame.

Tonnetz dimensions:
  • 0: Fifth x-axis

  • 1: Fifth y-axis

  • 2: Minor x-axis

  • 3: Minor y-axis

  • 4: Major x-axis

  • 5: Major y-axis

See also


Compute a chromagram from a constant-Q transform.


Compute a chromagram from an STFT spectrogram or waveform.


Compute tonnetz features from the harmonic component of a song

>>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=10, offset=10)
>>> y = librosa.effects.harmonic(y)
>>> tonnetz = librosa.feature.tonnetz(y=y, sr=sr)
>>> tonnetz
array([[ 0.007, -0.026, ...,  0.055,  0.056],
       [-0.01 , -0.009, ..., -0.012, -0.017],
       [ 0.006, -0.021, ..., -0.012, -0.01 ],
       [-0.009,  0.031, ..., -0.05 , -0.037]])

Compare the tonnetz features to chroma_cqt

>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True)
>>> img1 = librosa.display.specshow(tonnetz,
...                                 y_axis='tonnetz', x_axis='time', ax=ax[0])
>>> ax[0].set(title='Tonal Centroids (Tonnetz)')
>>> ax[0].label_outer()
>>> img2 = librosa.display.specshow(librosa.feature.chroma_cqt(y=y, sr=sr),
...                                 y_axis='chroma', x_axis='time', ax=ax[1])
>>> ax[1].set(title='Chroma')
>>> fig.colorbar(img1, ax=[ax[0]])
>>> fig.colorbar(img2, ax=[ax[1]])