soundgen (version 1.5.0)

schwa: Schwa-related formant conversion

Description

This function performs several conceptually related types of conversion of formant frequencies in relation to the neutral schwa sound based on the one-tube model of the vocal tract. Case 1: if we know vocal tract length (VTL) but not formant frequencies, schwa() estimates formants corresponding to a neutral schwa sound in this vocal tract, assuming that it is perfectly cylindrical. Case 2: if we know the frequencies of a few lower formants, schwa() estimates the deviation of observed formant frequencies from the neutral values expected in a perfectly cylindrical vocal tract (based on the VTL as specified or as estimated from formant dispersion). Case 3: if we want to geneate a sound with particular relative formant frequencies (e.g. high F1 and low F2 relative to the schwa for this vocal tract), schwa() calculates the corresponding formant frequencies in Hz. See examples below for an illustration of these three suggested uses.

Usage

schwa(formants = NULL, vocalTract = NULL, formants_relative = NULL,
  nForm = 8, speedSound = 35400)

Arguments

formants

a numeric vector of observed (measured) formant frequencies, Hz

vocalTract

the length of vocal tract, cm

formants_relative

a numeric vector of target relative formant frequencies, % deviation from schwa (see examples)

nForm

the number of formants to estimate (integer)

speedSound

speed of sound in warm air, cm/s. Stevens (2000) "Acoustic phonetics", p. 138

Value

Returns a list with the following components:

vtl_measured

VTL as provided by the user, cm

vocalTract_apparent

VTL estimated based on formants frequencies provided by the user, cm

formantDispersion

average distance between formants, Hz

ff_measured

formant frequencies as provided by the user, Hz

ff_schwa

formant frequencies corresponding to a neutral schwa sound in this vocal tract, Hz

ff_theoretical

formant frequencies corresponding to the user-provided relative formant frequencies, Hz

ff_relative

deviation of formant frequencies from those expected for a schwa, % (e.g. if the first ff_relative is -25, it means that F1 is 25% lower than expected for a schwa in this vocal tract)

ff_relative_semitones

deviation of formant frequencies from those expected for a schwa, semitones

Details

Algorithm: the expected formant dispersion is given by \(speedSound / (2 * vocalTract)\), and F1 is expected at half the value of formant dispersion. See e.g. Stevens (2000) "Acoustic phonetics", p. 139. Basically, we estimate vocal tract length and see if each formant is higher or lower than expected for this vocal tract. For this to work, we have to know either the frequencies of enough formants (not just the first two) or the true length of the vocal tract. See also estimateVTL on the algorithm for estimating formant dispersion if VTL is not known (note that schwa calls estimateVTL with the option method = 'regression'.

Examples

# NOT RUN {
## CASE 1: known VTL
# If vocal tract length is known, we calculate expected formant frequencies
schwa(vocalTract = 17.5)
schwa(vocalTract = 13, nForm = 5)

## CASE 2: known (observed) formant frequencies
# Let's take formant frequencies in three vocalizations
#       (/a/, /i/, /roar/) by the same male speaker:
formants_a = c(860, 1430, 2900, 4200, 5200)
s_a = schwa(formants = formants_a)
s_a
# We get an estimate of VTL (s_a$vtl_apparent = 15.2 cm),
#   same as with estimateVTL(formants_a)
# We also get theoretical schwa formants: s_a$ff_schwa
# And we get the difference (% and semitones) in observed vs expected
#   formant frequencies: s_a[c('ff_relative', 'ff_relative_semitones')]
# [a]: F1 much higher than expected, F2 slightly lower

formants_i = c(300, 2700, 3400, 4400, 5300, 6400)
s_i = schwa(formants = formants_i)
s_i
# The apparent VTL is slightly smaller (14.5 cm)
# [i]: very low F1, very high F2

formants_roar = c(550, 1000, 1460, 2280, 3350,
                  4300, 4900, 5800, 6900, 7900)
s_roar = schwa(formants = formants_roar)
s_roar
# Note the enormous apparent VTL (22.5 cm!)
# (lowered larynx and rounded lips exaggerate the apparent size)
# s_roar$ff_relative: high F1 and low F2-F4

schwa(formants = formants_roar[1:4])
# based on F1-F4, apparent VTL is almost 28 cm!
# Since the lowest formants are the most salient,
# the apparent size is exaggerated even further

# If you know VTL, a few lower formants are enough to get
#   a good estimate of the relative formant values:
schwa(formants = formants_roar[1:4], vocalTract = 19)
# NB: in this case theoretical and relative formants are calculated
#  based on user-provided VTL (vtl_measured) rather than vtl_apparent

## CASE 3: from relative to absolute formant frequencies
# Say we want to generate a vowel sound with F1 20% below schwa
#    and F2 40% above schwa, with VTL = 15 cm
s = schwa(formants_relative = c(-20, 40), vocalTract = 15)
# s$ff_schwa gives formant frequencies for a schwa, while
#   s$ff_theoretical gives formant frequencies for a sound with
#   target relative formant values (low F1, high F2)
schwa(formants = s$ff_theoretical)
# }