A voice is a source filtered by the vocal tract. In a formant synthesizer every part of that
sentence is a number: the source's pitch and level, and the frequency and bandwidth of each
resonance (formant). so.klatt_synthesize follows Klatt (1980). Voicing is a set of harmonics
of F_0 with the spectrum of Klatt's glottal pulse, aspiration and frication are noise, and
formants are second-order resonators
with C = -e^{-2\pi B_k T}, B = 2e^{-\pi B_k T}\cos(2\pi F_k T) and A = 1 - B - C for a
formant at F_k Hz, B_k Hz wide, sampled every T seconds. Every parameter is a number or a
track of (times, values), so the sounds below are written down rather than recorded, and any
cue can be changed while the others stay put.
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.
All the sounds are at 16 kHz. Each one is drawn as a waveform and a wideband spectrogram (Hann 6 ms), which shows formants as dark bands, with the formant frequencies the synthesizer was given drawn over it.
import matplotlib.pyplot as plt
import numpy as np
import sonore as so
plt.rcParams.update({"font.size": 9, "axes.titlesize": 10, "figure.dpi": 100})
FS = 16000
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 onoff(dur, level=60, on=0.02, off=0.05):
"""An amplitude track: up over `on` seconds, down over the last `off` seconds."""
return ([0, on, dur - off, dur], [0, level, level, 0])
def show(snd, title, formants=()):
"""Waveform and wideband spectrogram, with formant tracks ((times, values) or numbers) drawn over it."""
fig = plt.figure(figsize=(10, 4.2), layout="constrained")
ax0, ax1 = fig.subplots(2, 1, sharex=True, height_ratios=[0.45, 1])
snd.plot(ax0, color="k", lw=0.4)
ax0.set(title=f"Waveform: {title}", xlabel="")
frame = so.GaborFrame(0.006, 0.001, n_fft=512) # zero-padded for smooth bands
so.STFT(snd, frame=frame).plot(ax1, db_range=60, colorbar=False, fmax=5000)
ax1.set_title("Spectrogram (Hann 6 ms), with the formant frequencies given to the synthesizer")
for f in formants:
t, v = ([0], [f]) if np.isscalar(f) else f # a track is held after its last point
ax1.plot([*t, snd.duration], np.array([*v, v[-1]]) / 1000, color="c", lw=1, ls="--") # in kHz
for ax in (ax0, ax1):
ax.set_xlim(0, snd.duration)
return fig, [ax0, ax1]The vowel of "hod", with Peterson and Barney's (1952) average male formants: 730, 1090 and
2440 Hz. The pitch falls from 130 to 100 Hz, as at the end of a statement. Here the pieces are
put together by hand with so.resonator, the same resonator so.klatt_synthesize uses.
DUR = 1.0
F0 = ([0, DUR], [130, 100])
HOD = [(730, 60), (1090, 90), (2440, 150), (3500, 200), (4500, 250)]
# Klatt's glottal source: harmonics with the spectrum of an impulse through a low-pass
# resonator at 0 Hz, 100 Hz wide (about -12 dB per octave above 50 Hz).
glottal = so.Sound(np.r_[1.0, np.zeros(2**14 - 1)], FS)
rgp = np.abs(np.fft.rfft(so.resonator(glottal, 0, 100).data[:, 0]))
freqs = np.fft.rfftfreq(2**14, 1 / FS)
source = so.harmonic_complex(DUR, FS, F0, amplitudes=lambda t, f: np.interp(f, freqs, rgp))
# Radiation from the lips: a first difference, +6 dB per octave.
source = so.Sound(np.diff(source.data[:, 0], prepend=0.0), FS)The source on its own: the glottal pulse train after radiation, a buzz with no vowel in it. Its harmonics fall smoothly with frequency, with no peaks.
fv1_the_source_alone.flac, 1.0 s, mono
sound = finish(source)
fig, playhead = show(sound, "the glottal source after radiation")Through the first formant only, at 730 Hz. The buzz becomes a dull, muffled vowel: all that is left is energy around F1.
fv2_the_first_formant.flac, 1.0 s, mono
one = so.resonator(source, *HOD[0])
sound = finish(one)
fig, playhead = show(sound, "the source through F1", [730])Through the first two formants. F1 and F2 are what tells most vowels apart, and with both, the sound is recognisably the vowel of "hod", if thin.
fv3_two_formants.flac, 1.0 s, mono
two = so.resonator(one, *HOD[1])
sound = finish(two)
fig, playhead = show(sound, "the source through F1 and F2", [730, 1090])All five formants in cascade (one after the other). F3 to F5 add the brightness of a real voice; their levels follow from their frequencies, as they do in a vocal tract.
fv4_five_formants.flac, 1.0 s, mono
vowel = source
for f, bw in HOD:
vowel = so.resonator(vowel, f, bw)
sound = finish(vowel)
fig, playhead = show(sound, "the source through F1 to F5", [f for f, _ in HOD])The same vowel from so.klatt_synthesize, with the voicing switched on and off over 20 and
50 ms. Apart from those ramps it is the sound above: the synthesizer does the same steps.
fv5_the_same_vowel_from_so.klatt_synthesize.flac, 1.0 s, mono
hod = dict(F1=730, F2=1090, F3=2440)
sound = finish(so.klatt_synthesize(DUR, FS, F0=F0, AV=onoff(DUR), **hod))
fig, playhead = show(sound, "so.klatt_synthesize", [730, 1090, 2440, 3500, 4500])Because the source and the formants are separate, the spectrum of the vowel is the product of their spectra: in dB, a sum. Here the pitch is held at 100 Hz, so the harmonics sit at multiples of 100 Hz; each one's level is the source's level at that frequency plus the formants' gain there.
vowel = so.klatt_synthesize(1.0, FS, F0=100, **hod)
spec = np.abs(np.fft.rfft(vowel.data[-FS // 2 :, 0])) # the last 0.5 s, 2 Hz per bin
k = np.arange(1, 50)
measured = 20 * np.log10(spec[k * 50]) # harmonic k at 100 k Hz is bin 50 k
f = np.linspace(50, 5000, 2000)
z = np.exp(-2j * np.pi * f / FS)
def gain(fk, bk, f):
c, b = -np.exp(-2 * np.pi * bk / FS), 2 * np.exp(-np.pi * bk / FS) * np.cos(2 * np.pi * fk / FS)
zf = np.exp(-2j * np.pi * f / FS)
return np.abs((1 - b - c) / (1 - b * zf - c * zf**2))
src_db = 20 * np.log10(gain(0, 100, f) * np.abs(1 - z))
filt_db = 20 * np.log10(np.prod([gain(fk, bk, f) for fk, bk in HOD], axis=0))
total = src_db + filt_db
harmonics = measured - measured[0] + np.interp(100, f, total) # the output's level is arbitrary
fig, ax = plt.subplots(figsize=(10, 3.4), layout="constrained")
ax.plot(f, src_db, color="0.6", label="source (glottal pulse and radiation)")
ax.plot(f, filt_db, color="c", label="formants (the filter)")
ax.plot(f, total, color="k", lw=0.8, label="source + formants")
ax.plot(k * 100, harmonics, "o", ms=3, color="C3", label="harmonics of the synthesized vowel")
ax.set(xlabel="Frequency (Hz)", ylabel="Level (dB)", xlim=(0, 5000))
ax.set_title("The vowel of 'hod' at 100 Hz: every harmonic lands on source + filter")
ax.legend(loc="upper right", fontsize=8)Peterson and Barney (1952) measured the formants of ten American English vowels, spoken in words of the form h-vowel-d by male and female adults and by children. Their male averages, for six of the vowels, synthesized with everything else the same: the pitch, the higher formants and the bandwidths.
VOWELS = {
"heed": (270, 2290, 3010),
"head": (530, 1840, 2480),
"had": (660, 1720, 2410),
"hod": (730, 1090, 2440),
"hawed": (570, 840, 2410),
"who'd": (300, 870, 2240),
}
VOWEL_DUR = 0.42
gap = so.silence(0.15, FS)
parts, starts = [], []
t = 0.0
for f1, f2, f3 in VOWELS.values():
v = so.klatt_synthesize(
VOWEL_DUR, FS, F0=([0, VOWEL_DUR], [125, 105]), AV=onoff(VOWEL_DUR), F1=f1, F2=f2, F3=f3
)
parts += [v, gap]
starts.append(t)
t += VOWEL_DUR + gap.durationThe six vowels in turn, from "heed" to "who'd". The dashed lines are each vowel's F1, F2 and F3.
fw1_six_vowels.flac, 3.4 s, mono
sound = finish(so.concat(parts))
tracks = [
(np.repeat(starts, 2) + np.tile([0, VOWEL_DUR], 6), np.repeat([v[i] for v in VOWELS.values()], 2))
for i in range(3)
]
fig, playhead = show(sound, "heed, head, had, hod, hawed, who'd")
for tt, ff in tracks:
for j in range(6):
playhead[1].plot(tt[2 * j : 2 * j + 2], ff[2 * j : 2 * j + 2] / 1000, color="c", lw=1, ls="--")
fig, ax = plt.subplots(figsize=(5, 4), layout="constrained")
for word, (f1, f2, _) in VOWELS.items():
ax.plot(f2, f1, "o", color="C0")
ax.annotate(word, (f2, f1), textcoords="offset points", xytext=(6, 4))
ax.set(xlabel="F2 (Hz)", ylabel="F1 (Hz)", xlim=(2500, 600), ylim=(800, 200))
ax.set_title("F1 against F2, axes reversed as is usual:\nthe tongue's height and backness")A continuum from "heed" to "hod" in seven equal steps of F1, F2 and F3, made with
so.klatt_continuum. Somewhere in the middle the vowel stops being one and becomes the
other; experiments on vowel categories use continua like this one.
fw3_from_heed_to_hod_in_seven_steps.flac, 3.6 s, mono
steps = so.klatt_continuum(dict(F1=270, F2=2290, F3=3010), dict(F1=730, F2=1090, F3=2440), 7)
STEP_DUR = 0.36
parts = []
for p in steps:
parts += [so.klatt_synthesize(STEP_DUR, FS, p, F0=110, AV=onoff(STEP_DUR)), so.silence(0.15, FS)]
sound = finish(so.concat(parts))
fig, playhead = show(sound, "seven steps from heed to hod")
for i, p in enumerate(steps):
for name in ("F1", "F2", "F3"):
step_start = (STEP_DUR + 0.15) * i
playhead[1].plot([step_start, step_start + STEP_DUR], [p[name] / 1000] * 2, color="c", lw=1, ls="--")Peterson and Barney's female averages, for the same six vowels. Every formant is higher than the male ones, since female vocal tracts are on average shorter, but not by one common factor: the printout gives the ratios, from 1.04 to 1.30. The pitch is higher too, falling from 230 to 200 Hz, and F4 and F5 are raised to 4100 and 4900 Hz to stay above the female F3.
VOWELS_FEMALE = {
"heed": (310, 2790, 3310),
"head": (610, 2330, 2990),
"had": (860, 2050, 2850),
"hod": (850, 1220, 2810),
"hawed": (590, 920, 2710),
"who'd": (370, 950, 2670),
}
parts_female = []
for f1, f2, f3 in VOWELS_FEMALE.values():
v = so.klatt_synthesize(
VOWEL_DUR,
FS,
F0=([0, VOWEL_DUR], [230, 200]),
AV=onoff(VOWEL_DUR),
F1=f1,
F2=f2,
F3=f3,
F4=4100,
F5=4900,
)
parts_female += [v, gap]
for word, (f1, f2, f3) in VOWELS_FEMALE.items():
male = VOWELS[word]
ratios = ", ".join(f"{f / m:.2f}" for f, m in zip((f1, f2, f3), male, strict=True))
print(f"{word:6} female / male, F1 F2 F3: {ratios}")heed female / male, F1 F2 F3: 1.15, 1.22, 1.10 head female / male, F1 F2 F3: 1.15, 1.27, 1.21 had female / male, F1 F2 F3: 1.30, 1.19, 1.18 hod female / male, F1 F2 F3: 1.16, 1.12, 1.15 hawed female / male, F1 F2 F3: 1.04, 1.10, 1.12 who'd female / male, F1 F2 F3: 1.23, 1.09, 1.19
The six vowels with female formants. The harmonics are now about 215 Hz apart, so each formant peak is drawn by fewer of them than in the male vowels above.
fw4_six_vowels_with_female_formants.flac, 3.4 s, mono
sound = finish(so.concat(parts_female))
tracks = [
(np.repeat(starts, 2) + np.tile([0, VOWEL_DUR], 6), np.repeat([v[i] for v in VOWELS_FEMALE.values()], 2))
for i in range(3)
]
fig, playhead = show(sound, "heed, head, had, hod, hawed, who'd, female formants")
for tt, ff in tracks:
for j in range(6):
playhead[1].plot(tt[2 * j : 2 * j + 2], ff[2 * j : 2 * j + 2] / 1000, color="c", lw=1, ls="--")Both sets of vowels by their first two formants, joined vowel by vowel. The female vowel space is shifted up and outward, most of all in F2 for the front vowels.
fig, ax = plt.subplots(figsize=(5, 4), layout="constrained")
for word in VOWELS:
(f1_male, f2_male, _), (f1_female, f2_female, _) = VOWELS[word], VOWELS_FEMALE[word]
ax.plot([f2_male, f2_female], [f1_male, f1_female], color="0.7", lw=0.8)
ax.annotate(word, (f2_female, f1_female), textcoords="offset points", xytext=(6, 4))
ax.plot([v[1] for v in VOWELS.values()], [v[0] for v in VOWELS.values()], "o", color="C0", label="male")
ax.plot(
[v[1] for v in VOWELS_FEMALE.values()],
[v[0] for v in VOWELS_FEMALE.values()],
"o",
color="C1",
label="female",
)
ax.set(xlabel="F2 (Hz)", ylabel="F1 (Hz)", xlim=(3000, 600), ylim=(950, 200))
ax.legend(loc="lower left", fontsize=8)
ax.set_title("Peterson and Barney's averages, male and female")A stop consonant before a vowel is mostly heard in the first few tens of milliseconds of the vowel: the formants move from where the closure left them to the vowel's values. Here F1 rises from 250 Hz in each, and only the starting points of F2 and F3 differ. A short burst of frication marks the release: flat for /b/, high for /d/, near F2 for /g/.
DUR_CV = 0.4
ONSETS = {"ba": (900, 2100), "da": (1700, 2700), "ga": (1500, 2000)}
BURSTS = {"ba": dict(AB=55), "da": dict(A4=55, A5=52), "ga": dict(A2=58)}
def syllable(name):
f2, f3 = ONSETS[name]
tracks = dict(F1=([0, 0.04], [250, 700]), F2=([0, 0.04], [f2, 1220]), F3=([0, 0.04], [f3, 2500]))
snd = so.klatt_synthesize(
DUR_CV,
FS,
F0=([0, DUR_CV], [125, 100]),
AV=onoff(DUR_CV, on=0.005),
AF=([0, 0.001, 0.008, 0.01], [0, 66, 60, 0]),
rng=0,
**tracks,
**BURSTS[name],
)
return finish(snd), [tracks["F1"], tracks["F2"], tracks["F3"]]/ba/: F2 and F3 rise into the vowel, from low starting points (the lips close the front of the tract).
fc1_the_syllable_ba.flac, 0.4 s, mono
sound, tracks = syllable("ba")
fig, playhead = show(sound, "/ba/", tracks)/da/: F2 and F3 fall into the vowel from high starting points.
fc2_the_syllable_da.flac, 0.4 s, mono
sound, tracks = syllable("da")
fig, playhead = show(sound, "/da/", tracks)/ga/: F2 and F3 start close together and part, F2 falling and F3 rising.
fc3_the_syllable_ga.flac, 0.4 s, mono
sound, tracks = syllable("ga")
fig, playhead = show(sound, "/ga/", tracks)Klatt's synthesizer has two noise sources. Aspiration goes through the same formants as voicing (the cascade), as the breath noise of /h/ does. Frication goes through a separate, parallel set of formants, each with its own level, because a fricative's noise is made in a constriction near the front of the mouth and excites mainly the resonances in front of it. While voicing is on, both noises are modulated at F_0, 50% deep, as breath through vibrating vocal folds is.
/sa/: frication through the parallel formants 5 and 6 (4500 and 5500 Hz), then the vowel. As in speech, there is no silence between them: the voicing starts while the frication is still fading, and the first two formants glide from where the tongue left them (F1 low, F2 near 1700 Hz) to the vowel's values over the first 60 ms of voicing.
fn1_the_syllable_sa.flac, 0.5 s, mono
dur = 0.515
tracks = dict(F1=([0.08, 0.14], [300, 730]), F2=([0.08, 0.14], [1700, 1090]))
sound = finish(
so.klatt_synthesize(
dur,
FS,
F0=([0, dur], [125, 100]),
AV=([0, 0.08, 0.085, 0.105, dur - 0.05, dur], [0, 0, 48, 60, 60, 0]),
AF=([0, 0.015, 0.085, 0.1, 0.115], [0, 74, 74, 64, 0]),
A5=60,
A6=62,
F6=5500,
B6=500,
F3=2440,
rng=0,
**tracks,
)
)
fig, playhead = show(sound, "/sa/: frication, then voicing", [tracks["F1"], tracks["F2"], 4500, 5500])/ha/: aspiration alone through the vowel's formants, then voicing. The formants of the vowel are already there in the breath, and the breath carries on into the first 50 ms or so of the voicing, fading as it goes, so the vowel starts breathy.
fn2_the_syllable_ha.flac, 0.5 s, mono
sound = finish(
so.klatt_synthesize(
dur,
FS,
F0=([0, dur], [125, 100]),
AV=([0, 0.08, 0.085, 0.105, dur - 0.05, dur], [0, 0, 48, 60, 60, 0]),
AH=([0, 0.015, 0.095, 0.125, 0.165], [0, 62, 62, 56, 0]),
rng=0,
**hod,
)
)
fig, playhead = show(sound, "/ha/: aspiration, then voicing", [730, 1090, 2440])A breathy "hod": voicing with aspiration 6 dB below it throughout, and a wider first formant. The noise fills in between the harmonics, most at high frequencies where the harmonics are weak.
fn3_a_breathy_vowel.flac, 1.0 s, mono
sound = finish(
so.klatt_synthesize(DUR, FS, F0=F0, AV=onoff(DUR), AH=onoff(DUR, level=54), B1=120, rng=0, **hod)
)
fig, playhead = show(sound, "breathy: aspiration 6 dB below voicing", [730, 1090, 2440])In the cascade, formants run one after another and their levels follow from their frequencies. In the parallel branch each formant gets the source separately and is added at a level of its own. Added with the same sign, neighbouring formants partly cancel between their peaks, because their phases differ by about half a cycle there. Klatt adds them with alternating signs, and then the sum follows the cascade closely, given the right levels.
f = np.linspace(50, 5000, 4000)
z = np.exp(-2j * np.pi * f / FS)
def response(fk, bk):
c, b = -np.exp(-2 * np.pi * bk / FS), 2 * np.exp(-np.pi * bk / FS) * np.cos(2 * np.pi * fk / FS)
return (1 - b - c) / (1 - b * z - c * z**2)
hs = [response(fk, bk) for fk, bk in HOD]
cascade = np.prod(hs, axis=0)
peaks = [np.argmin(np.abs(f - fk)) for fk, _ in HOD]
levels = [np.abs(cascade[i]) / np.abs(h[i]) for h, i in zip(hs, peaks, strict=True)]
same = sum(g * h for g, h in zip(levels, hs, strict=True))
alternating = sum((-1) ** k * g * h for k, (g, h) in enumerate(zip(levels, hs, strict=True)))
fig, ax = plt.subplots(figsize=(10, 3.4), layout="constrained")
db = lambda h: 20 * np.log10(np.abs(h)) # noqa: E731
ax.plot(f, db(cascade), color="k", lw=2.5, alpha=0.35, label="cascade")
ax.plot(f, db(same), color="C3", lw=1, label="parallel, same signs")
ax.plot(f, db(alternating), color="C0", lw=1, ls="--", label="parallel, alternating signs")
ax.set(xlabel="Frequency (Hz)", ylabel="Gain (dB)", xlim=(0, 5000), ylim=(-40, 50))
ax.set_title("The vowel of 'hod': parallel formants, each set to the cascade's level at its peak")
ax.legend(loc="upper right", fontsize=8)inside = (f > 100) & (f < 4000)
print("Largest difference from the cascade, 100-4000 Hz:")
print(f" same signs {np.abs(db(same) - db(cascade))[inside].max():5.1f} dB")
print(f" alternating signs {np.abs(db(alternating) - db(cascade))[inside].max():5.1f} dB")Largest difference from the cascade, 100-4000 Hz: same signs 13.7 dB alternating signs 0.1 dB
Everything above used Klatt's 1980 source, whose spectrum is fixed. The glottal pulse itself changes with how the vocal folds are held: pressed together they close abruptly, which makes strong high harmonics; held loosely they close gradually, leaving little but the fundamental. The Liljencrants-Fant (LF) model (Fant, Liljencrants & Lin, 1985) describes one period of the glottal flow's derivative E(t): an exponentially growing sinusoid while the glottis opens,
down to its sharp negative peak -E_e at closure t_e, then an exponential return to zero. Fant (1995) set the whole shape with one number,
the peak flow U_0 against the strength of the closure, in a period T_0: about 0.3 for a
tense, pressed voice to 2.7 for a lax, breathy one, and close to 0.7 for typical male
voices. so.glottal_source makes LF pulses from their harmonics, which have an exact
formula, so nothing aliases, and so.klatt_synthesize uses them with SS=3 (the source
switch of Klatt & Klatt's KLSYN88) and RD.
The same peak excitation E_e in all three. The tense pulse opens for a shorter part of the period and passes less air; the lax one stays open longer, and its closure is a gentle slope rather than a sharp corner. The sharp corner is what makes high harmonics.
x = np.linspace(0, 1, 1000)
RDS = {0.5: "tense, Rd 0.5", 1.0: "modal, Rd 1", 2.5: "lax, Rd 2.5"}
fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(10, 3.2), layout="constrained")
for (rd, label), color in zip(RDS.items(), ["C3", "k", "C0"], strict=True):
ax0.plot(x, so.lf_pulse(x, rd, flow=True), color=color, label=label)
ax1.plot(x, so.lf_pulse(x, rd), color=color, label=label)
ax0.set(xlabel="Time (fraction of a period)", ylabel="Flow (units of $E_e T_0$)")
ax0.set_title("Glottal flow")
ax1.set(xlabel="Time (fraction of a period)", ylabel="$E(t)$ (units of $E_e$)")
ax1.set_title("Its derivative: the excitation, with radiation from the lips")
ax0.legend(fontsize=8)The harmonics' levels depend on the harmonic number only, not on F_0. The difference between the first two harmonics, H1-H2, is the usual measure of this in recordings; Fant's (1995) fit to it, -7.6 + 11.1\,R_d dB, agrees with these spectra to within 0.4 dB up to R_d 1.4. Klatt's 1980 source has the H1-H2 of a modal voice, but around 3 kHz its harmonics are stronger than even the tense pulse's.
k = np.arange(1, 41)
klatt_1980 = gain(0, 100, k * 100) * np.abs(1 - np.exp(-2j * np.pi * k * 100 / FS))
fig, ax = plt.subplots(figsize=(10, 3.4), layout="constrained")
ax.plot(
k * 100,
20 * np.log10(klatt_1980 / klatt_1980[0]),
"s-",
ms=3,
lw=0.8,
color="0.6",
label="Klatt's 1980 source",
)
for (rd, label), color in zip(RDS.items(), ["C3", "k", "C0"], strict=True):
levels = 20 * np.log10(np.abs(so.lf_harmonics(k, rd)))
levels -= levels[0]
ax.plot(k * 100, levels, "o-", ms=3, lw=0.8, color=color, label=f"{label}: H1-H2 {-levels[1]:.1f} dB")
ax.set(xlabel="Frequency at F0 = 100 Hz (Hz)", ylabel="Level re first harmonic (dB)", xlim=(0, 4100))
ax.set_title("Harmonics of the excitation (the flow derivative), relative to the first")
ax.legend(fontsize=8)The vowel of "hod" three times, with everything the same except the pulse: tense (Rd 0.5), modal (Rd 1) and lax (Rd 2.5). The vowel stays the same; the voice goes from pressed and bright to soft and muffled.
fq3_one_vowel_three_voices.flac, 3.4 s, mono
parts = []
for rd in RDS:
snd = so.klatt_synthesize(DUR, FS, F0=F0, AV=onoff(DUR), SS=3, RD=rd, **hod)
parts += [snd, so.silence(0.2, FS)]
sound = finish(so.concat(parts[:-1]))
fig, playhead = show(sound, "Rd 0.5, Rd 1, Rd 2.5", [730, 1090, 2440])Klatt's 1980 source, then an LF pulse at the default Rd of 0.7, close to typical male voices. The LF voice is darker: at 3 kHz its harmonics are about 12 dB weaker, relative to the first.
fq4_the_1980_source_then_lf_at_rd_0.7.flac, 2.2 s, mono
parts = [
so.klatt_synthesize(DUR, FS, F0=F0, AV=onoff(DUR), **hod),
so.silence(0.2, FS),
so.klatt_synthesize(DUR, FS, F0=F0, AV=onoff(DUR), SS=3, **hod),
]
sound = finish(so.concat(parts))
fig, playhead = show(sound, "SS=1 (the default), then SS=3 with RD=0.7", [730, 1090, 2440])A voice relaxing at the end of a phrase: Rd rises from 0.6 to 2.4 while the pitch falls. The
LF model is the periodic pulse only, and a lax pulse alone sounds soft rather than breathy;
Klatt & Klatt (1990) found aspiration noise the most important cue to breathiness, so the
aspiration (AH) rises with Rd.
fq5_relaxing_into_breathy_voice.flac, 1.6 s, mono
dur = 1.6
sound = finish(
so.klatt_synthesize(
dur,
FS,
F0=([0, dur], [130, 90]),
AV=onoff(dur),
SS=3,
RD=([0.3, 1.3], [0.6, 2.4]),
AH=([0.3, 1.3, dur - 0.05, dur], [0, 52, 52, 0]),
rng=0,
**hod,
)
)
fig, playhead = show(sound, "Rd from 0.6 to 2.4, with aspiration rising", [730, 1090, 2440])klatt.klatt_synthesize processing.resonatorwaveforms.glottal_sourcewaveforms.lf_harmonicsSS source switch.