A ripple is a sinusoidal pattern drawn on the time-frequency plane: its level rises and falls along frequency, and the whole pattern drifts over time. Ripples are to hearing what gratings are to vision. They were used to map the spectrotemporal receptive fields of auditory neurons (Kowalski et al., 1996) and to measure how sensitive listeners are to modulation (Chi et al., 1999).
Press play and a line follows the sound across every time axis in its plots. Click any time axis to play from that point. Start with your volume low.
so.Ripple(rate, density, depth) is the envelope
where x is frequency in octaves above the lowest, \omega the rate in Hz, \Omega the density
in cycles per octave and m the depth. A positive rate drifts down in frequency, a negative one
up. Ripples add: so.Ripple(...) + so.Ripple(...) is a sum of patterns. so.ripple_sound
imposes the envelope on a carrier spanning 250 Hz to 8 kHz, by default 20 log-spaced tones per
octave with random phases.
Each figure shows the pattern as specified, the envelopes measured back from the sound in 24 bands per octave (a cochleagram), the waveform, and the modulation spectrum measured from the sound: the two-dimensional Fourier transform of the cochleagram, with rate across and density up (Singh & Theunissen, 2003). A single ripple puts a single peak in it.
import matplotlib.pyplot as plt
import sonore as so
plt.rcParams.update({"font.size": 9, "axes.titlesize": 10, "figure.dpi": 100})
FS = 44100
def finish(snd):
"""How every sound in the gallery is played: 5 ms ramps, RMS 0.1, peak at most 0.95."""
snd = snd.ramp(5e-3).normalize(rms=0.1)
return snd.normalize(peak=0.95) if snd.peak > 0.95 else snd
def show(snd, pattern, dmr=False):
"""The pattern as specified, then the sound's cochleagram, waveform and modulation spectrum.
Returns the figure and the panels the playhead follows."""
fig, axes = plt.subplots(2, 2, figsize=(10, 6.2), layout="constrained")
pattern.plot(duration=snd.duration, f_lo=250, f_hi=8000, ax=axes[0, 0], colorbar=False)
axes[0, 0].set_title("Pattern as specified (envelope, dB)")
bank = so.cosine_filterbank(f_lo=250, f_hi=8000, spacing=1 / 24, scale="octave")
bank.analyze(snd).envelopes(lowpass=200, fs=1000).plot(axes[0, 1], db_range=30, colorbar=False)
axes[0, 1].set_title("Measured envelopes of the sound (cochleagram)")
snd.plot(axes[1, 0], lw=0.4)
axes[1, 0].set_title("Waveform (the pattern barely shows here)")
ms = so.ModulationSpectrum.octave(snd, f_lo=250, f_hi=8000, scale="db" if dmr else "linear")
ms.plot(axes[1, 1], db_range=30, wt_max=50 if dmr else 20, wf_max=4, colorbar=False)
axes[1, 1].set_title("Measured modulation spectrum")
return fig, [axes[0, 0], axes[0, 1], axes[1, 0]]Rate 4 Hz, density 1 cycle/octave, on log-spaced tones. Listen for a continuous downward sweep, four times a second. The diagonal bands in the cochleagram are what you are hearing; the waveform alone shows almost none of it.
01_downward_ripple.flac, 3.0 s, mono
down = so.Ripple(4, 1)
sound = finish(so.ripple_sound(down, 3, FS, rng=0))
fig, playhead = show(sound, down)The same ripple at −4 Hz, so the sweep rises. Its modulation-spectrum peak moves to negative rate.
02_upward_ripple.flac, 3.0 s, mono
up = so.Ripple(-4, 1)
sound = finish(so.ripple_sound(up, 3, FS, rng=0))
fig, playhead = show(sound, up)4 Hz at 1 cycle/octave plus −12 Hz at 2.5 cycles/octave: two motions in opposite directions, superimposed. The modulation spectrum separates them into two clean peaks.
03_two_ripples_at_once.flac, 3.0 s, mono
both = so.Ripple(4, 1, depth=0.45) + so.Ripple(-12, 2.5, depth=0.45)
sound = finish(so.ripple_sound(both, 3, FS, rng=0))
fig, playhead = show(sound, both)The pattern is an envelope; what carries it changes how it sounds, not where it sits in the modulation spectrum.
The first ripple on harmonics of 60 Hz. The motion is the same, now over a low pitch; resolved low harmonics show as horizontal lines in the cochleagram.
04_same_ripple_harmonic_carrier.flac, 3.0 s, mono
sound = finish(so.ripple_sound(down, 3, FS, carrier="harmonic", f0=60, rng=0))
fig, playhead = show(sound, down)The same pattern on narrowband noise, which brings its own random fluctuations, so the sweep sounds rougher.
05_same_ripple_noise_carrier.flac, 3.0 s, mono
sound = finish(so.ripple_sound(down, 3, FS, carrier="noise", rng=0))
fig, playhead = show(sound, down)Escabí & Schreiner (2002) let a ripple's rate and density wander slowly and at random, so that one long sound covers many combinations of the two: a stimulus for mapping receptive fields without choosing the ripples in advance.
Rate and density wander randomly (rates within ±40 Hz at the lowest frequency). Where the density passes through zero, every band pulses together, and only there does the waveform show the modulation.
06_dynamic_moving_ripple.flac, 4.0 s, mono
dmr = so.DynamicRipple(rate_range=(-40, 40), seed=3)
sound = finish(so.ripple_sound(dmr, 4, FS, rng=0))
fig, playhead = show(sound, dmr, dmr=True)Iterated rippled noise has a rippled spectrum too, but a different kind. Its ripple does not move, so all of it sits at zero rate; and it is periodic on a linear frequency axis, one peak every 1/d hertz, rather than on the logarithmic axis used here. An 8 ms delay gives a density of 8 cycles/kHz, which is where its modulation spectrum peaks. Equally spaced peaks along linear frequency are harmonics, which is why rippled noise has a pitch and these ripples, sinusoidal along log frequency, do not.
ripples.Ripple modulation.ModulationSpectrumripples.DynamicRippleripples.Ripplemodulation.ModulationSpectrum