music.note_with_fm

music.note_with_fm(freq=220, duration=2, fm=100, max_fm_deviation=2, waveform_table=array([-1., -0.99975586, -0.99951172, ..., -0.99926758, -0.99951172, -0.99975586], shape=(16384,)), fm_waveform_table=array([0., 0.0003835, 0.00076699, ..., -0.00115049, -0.00076699, -0.0003835], shape=(16384,)), number_of_samples=None, sample_rate=None)

Synthesize a musical note with FM synthesis.

Set fm=0 or max_fm_deviation=0 (or use synth_note()) for a note without FM. A FM is a linear oscillatory pattern of frequency [1].

Parameters:

freqscalar

The frequency of the note in Hertz.

durationscalar

The duration of the note in seconds.

fmscalar

The frequency of the modulator in Hertz.

max_fm_deviationscalar

The maximum deviation of frequency in the modulator in Hertz.

waveform_tablearray_like

The table with the waveform for the carrier.

fm_waveform_tablearray_like

The table with the waveform for the modulator.

number_of_samplesinteger or None

The number of samples in the sound. If given, duration is ignored, and zero is no samples.

sample_rateinteger or None

The sample rate. None, the default, is the rate music.get_sample_rate() returns.

Returns:

resultndarray

A numpy array where each value is a PCM sample of the note.

Parameters:

• freq (float)

• duration (float)

• fm (float)

• max_fm_deviation (float)

• waveform_table (ArrayLike)

• fm_waveform_table (ArrayLike)

• number_of_samples (int | None)

• sample_rate (int | None)

Return type:

NDArray[float64]

See also

note

A basic musical note without vibrato.

note_with_vibrato

A musical note with an oscillation of pitch.

tremolo

A tremolo, an oscillation of loudness.

am

A linear oscillation of amplitude (not linear loudness).

Notes

The modulator is read from its table as a vibrato’s pattern is, and it moves the carrier’s frequency by up to \(\mu\) Hertz either way, as the article writes FM [1]:

\[ \begin{align}\begin{aligned}t'_i = \tilde{m}_{\gamma'_i \bmod \tilde{\Lambda}_M}, \qquad \gamma'_i = \left\lfloor i f' \frac{\tilde{\Lambda}_M}{f_s} \right\rfloor,\\f_i = f + \mu \, t'_i, \qquad t_i = \tilde{l}_{\gamma_i \bmod \tilde{\Lambda}}, \qquad \gamma_i = \left\lfloor \sum_{j=0}^{i} f_j \frac{\tilde{\Lambda}}{f_s} \right\rfloor,\end{aligned}\end{align} \]

where \(\tilde{m}\) is fm_waveform_table, \(f'\) is fm, \(\mu\) is max_fm_deviation and \(f\) is freq. The deviation is in Hertz, where a vibrato’s is in semitones: this is the linear modulation whose spectrum the article expands into sidebands at \(f \pm k f'\), weighted by Bessel functions of the index \(\mu / f'\) (eq:fmEsp).

Cite the following article whenever you use this function.

References

[1]

Fabbri, Renato, et al. “Musical elements in the discrete-time representation of sound.” arXiv preprint arXiv:abs/1412.6853 (2017)

Examples

>>> write_wav_mono(note_with_fm())  # writes a WAV file of a note
>>> sonic_vector = horizontal_stack(
...     *[note_with_fm(i, j) for i, j in zip([200, 500, 100],
... [2, 1, 2])])
>>> s2 = note_with_fm(440, 1.5, 600, 10)