Category Archives: acoustics

Christopher Bergevin, Chandan Narayan, Joy Williams, Natasha Mhatre, Jennifer KE Steeves, Joshua GW Bernstein, Brad Story : Overtone focusing in biphonic tuvan throat singing

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Overtone focusing in biphonic tuvan throat singing

  1. Christopher Bergevin  Is a corresponding author ,
  2. Chandan Narayan,
  3. Joy Williams,
  4. Natasha Mhatre,
  5. Jennifer KE Steeves,
  6. Joshua GW Bernstein,
  7. Brad Story  Is a corresponding author
  1. Physics and Astronomy, York University, Canada;
  2. Centre for Vision Research, York University, Canada;
  3. Fields Institute for Research in Mathematical Sciences, Canada;
  4. Kavli Institute of Theoretical Physics, University of California, United States;
  5. Languages, Literatures and Linguistics, York University, Canada;
  6. York MRI Facility, York University, Canada;
  7. Biology, Western University, Canada;
  8. Psychology, York University, Canada;
  9. National Military Audiology & Speech Pathology Center, Walter Reed National Military Medical Center, United States

Research Article Feb 12, 2020

Cite as: eLife 2020;9:e50476 doi: 10.7554/eLife.50476

Abstract

Khoomei is a unique singing style originating from the republic of Tuva in central Asia. Singers produce two pitches simultaneously: a booming low-frequency rumble alongside a hovering high-pitched whistle-like tone. The biomechanics of this biphonation are not well-understood. Here, we use sound analysis, dynamic magnetic resonance imaging, and vocal tract modeling to demonstrate how biphonation is achieved by modulating vocal tract morphology. Tuvan singers show remarkable control in shaping their vocal tract to narrowly focus the harmonics (or overtones) emanating from their vocal cords. The biphonic sound is a combination of the fundamental pitch and a focused filter state, which is at the higher pitch (1–2 kHz) and formed by merging two formants, thereby greatly enhancing sound-production in a very narrow frequency range. Most importantly, we demonstrate that this biphonation is a phenomenon arising from linear filtering rather than from a nonlinear source.eLife digest

The republic of Tuva, a remote territory in southern Russia located on the border with Mongolia, is perhaps best known for its vast mountainous geography and the unique cultural practice of “throat singing”. These singers simultaneously create two different pitches: a low-pitched drone, along with a hovering whistle above it. This practice has deep cultural roots and has now been shared more broadly via world music performances and the 1999 documentary Genghis Blues.

Despite many scientists being fascinated by throat singing, it was unclear precisely how throat singers could create two unique pitches. Singing and speaking in general involves making sounds by vibrating the vocal cords found deep in the throat, and then shaping those sounds with the tongue, teeth and lips as they move up the vocal tract and out of the body. Previous studies using static images taken with magnetic resonance imaging (MRI) suggested how Tuvan singers might produce the two pitches, but a mechanistic understanding of throat singing was far from complete.

Now, Bergevin et al. have better pinpointed how throat singers can produce their unique sound. The analysis involved high quality audio recordings of three Tuvan singers and dynamic MRI recordings of the movements of one of those singers. The images showed changes in the singer’s vocal tract as they sang inside an MRI scanner, providing key information needed to create a computer model of the process.

This approach revealed that Tuvan singers can create two pitches simultaneously by forming precise constrictions in their vocal tract. One key constriction occurs when tip of the tongue nearly touches a ridge on the roof of the mouth, and a second constriction is formed by the base of the tongue. The computer model helped explain that these two constrictions produce the distinctive sounds of throat singing by selectively amplifying a narrow set of high frequency notes that are made by the vocal cords. Together these discoveries show how very small, targeted movements of the tongue can produce distinctive sounds.Introduction

In the years preceding his death, Richard Feynman had been attempting to visit the small republic of Tuva located in geographic center of Asia (Leighton, 2000). A key catalyst came from Kip Thorne, who had gifted him a record called Melody tuvy, featuring a Tuvan singing in a style known as Khoomei, or Xöömij. Although he was never successful in visiting Tuva, Feynman was nonetheless captivated by Khoomei, which can be best described as a high-pitched tone, similar to a whistle carrying a melody, hovering above a constant booming low-frequency rumble. This is a form of biphonation, or in Feynman’s own words, “a man with two voices”. Khoomei, now a part of the UNESCO Intangible Cultural Heritage of Humanity, is characterized as “the simultaneous performance by one singer of a held pitch in the lower register and a melody … in the higher register” (Aksenov, 1973). How, indeed, does one singer produce two pitches at one time? Even today, the biophysical underpinnings of this biphonic human vocal style are not fully understood.

Normally, when a singer voices a song or speech, their vocal folds vibrate at a fundamental frequency (f0), generating oscillating airflow, forming the so-called source. This vibration is not, however, simply sinusoidal, as it also produces a series of harmonics tones (i.e., integer multiples of f0) (Figure 1). Harmonic frequencies in this sound above f0 are called overtones. Upon emanating from the vocal folds, they are then sculpted by the vocal tract, which acts as a spectral filter. The vocal-tract filter has multiple resonances that accentuate certain clusters of overtones, creating formants. When speaking, we change the shape of our vocal tract to shift formants in systematic ways characteristic of vowel and consonant sounds. Indeed, singing largely uses vowel-like sounds (Story, 2016). In most singing, the listener perceives only a single pitch associated with the f0 of the vocal production, with the formant resonances determining the timbre. Khoomei has two strongly emphasized pitches: a low-pitch drone associated with the f0

, plus a melody carried by variation in the higher frequency formant that can change independently (Kob, 2004). Two possible loci for this biphonic property are the source and/or the filter. Figure 1

Frequency spectra for three different singers transitioning from normal to biphonic singing.

Vertical white lines in the spectrograms (left column) indicate the time point for the associated spectrum in the right column. Transition points from normal to biphonic singing state are denoted by …

A source-based explanation could involve different mechanisms, such as two vibrating nonlinear sound sources in the syrinx of birds, which produce multiple notes that are harmonically unrelated (Fee et al., 1998; Zollinger et al., 2008). Humans however are generally considered to have only a single source, the vocal folds. But there are an alternative possibilities: for instance, the source could be nonlinear and produce harmonically-unrelated sounds. For example, aerodynamic instabilities are known to produce biphonation (Mahrt et al., 2016). Further, Khoomei often involves dramatic and sudden transitions from simple tonal singing to biophonation (see Figure 1 and the Appendix for associated audio samples). Such abrupt changes are often considered hallmarks of physiological nonlinearity (Goldberger et al., 2002), and vocal production can generally be nonlinear in nature (Herzel and Reuter, 1996; Mergell and Herzel, 1997; Fitch et al., 2002; Suthers et al., 2006). Therefore it remains possible that biphonation arises from nonlinear source considerations.

Vocal tract shaping, a filter-based framework, provides an alternative explanation for biphonation. In one seminal study of Tuvan throat singing, Levin and Edgerton examined a wide variety of song types and suggested that there were three components at play. The first two (‘tuning a harmonic’ relative to the filter and lengthening the closed phase of the vocal fold vibration) represented a coupling between source and filter. But it was the third, narrowing of the formant, that appeared crucial. Yet, the authors offered little empirical justification for how these effects are produced by the vocal tract shape in the presented radiographs. Thus it remains unclear how the high-pitched formant in Khoomei was formed (Grawunder, 2009). Another study (Adachi and Yamada, 1999) examined a throat singer using magnetic resonance imaging (MRI) and captured static images of the vocal tract shape during singing. These images were then used in a computational model to produce synthesized song. Adachi and Yamada argued that a “rear cavity” was formed in the vocal tract and its resonance was essential to biphonation. However, their MRI data reveal limited detail since they were static images of singers already in the biphonation state. Small variations in vocal tract geometry can have pronounced effects on produced song (Story et al., 1996) and data from static MRI would reveal little about how and which parts of the vocal tract change shape as the singers transition from simple tonal song to biphonation. To understand which features of vocal tract morphology are crucial to biophonation, a dynamic description of vocal tract morphology would be required.

Here we study the dynamic changes in the vocal tracts of multiple expert practitioners from Tuva as they produce Khoomei. We use MRI to acquire volumetric 3D shape of the vocal tract of a singer during biphonation. Then, we capture the dynamic changes in a midsagittal slice of the vocal tract as singers transition from tonal to biphonic singing while making simultaneous audio recordings of the song. We use these empirical data to guide our use of a computational model, which allows us to gain insight into which features of vocal tract morphology are responsible for the singing phonetics observed during biophonic Khoomei song (e.g., Story, 2016). We focus specifically on the Sygyt (or Sigit) style of Khoomei (Aksenov, 1973).Results

Audio recordings

We made measurements from three Tuvan singers performing Khoomei in the Sygyt style (designated as T1–T3) and one (T4) in a non-Sygyt style. Songs were analyzed using short-time Fourier transforms (STFT), which provide detailed information in both temporal and spectral domains. We recorded the singers transitioning from normal singing into biphonation, Figure 1 showing this transition for three singers. The f0 of their song is marked in the figure (approximately 140 Hz for subject T2, 164 Hz for both T1 and T3) and the overtone structure appears as horizontal bands. Varying degrees of vibrato can be observed, dependent upon the singer (Figure 1; see also longer spectrograms in Appendix 1—figure 6 and Appendix 1—figure 7). Most of the energy in their song is concentrated in the overtones and no subharmonics (i.e., peaks at half-integer multiples of f0

) are observed. In contrast to these three singers, singer T4 performing in a non-Sygyt style exhibited a fundamental frequency of approximately 130 Hz, although significant energy additionally appears around 50–55 Hz, well below an expected subharmonic (Appendix 1—figure 5).

If we take a slice, that is a time-point from the spectrogram and plot the spectrum, we can observe the peaks to infer the formant structure from this representation of the sound (red-dashed lines in Figure 1 and Appendix 1—figure 4). As the singers transition from normal singing to biphonation, we see that the formant structure changes significantly and the positions of formant peaks shift dramatically and rapidly. Note that considering time points before and after the transitions also provides an internal control for both normal and focused song types (Appendix 1—figure 4). Once in the biphonation mode, all three singers demonstrate overtones in a narrow spectral band around 1.5–2 kHz; we refer to this as the focused state. Specifically, Figure 1 shows that not only is just a single or small group of overtones accentuated, but also that nearby ones are greatly attenuated: ±1 overtones are as much 15–35 dB and ±2 overtones are 35–65 dB below the central overtone. Whereas the energy in the low-frequency region associated with the first formant (below 500 Hz) is roughly constant between the normal-singing and focused states, there is a dramatic change in the spectrum for the higher formants above 500 Hz. In normal singing (i.e., prior to the focused state), spectral energy is distributed across several formants between 500 and 4000 Hz. In the focused state after the transition, the energy above 500 Hz becomes narrowly focused in the 1.5–2 kHz region, generating a whistle-like pitch that carries the song melody.

To assess the degree of focus objectively and quantitatively, we computed an energy ratio eR(fL,fH) that characterizes the relative degree of energy brought into a narrow band against the energy spread over the full spectrum occupied by human speech (see Materials and methods). In normal speech and singing, for [fL,fH]=[1,2kHz], typically eR is small (i.e., energy is spread across the spectrum, not focused into that narrow region between 1 and 2 kHz). For the Tuvan singers, prior to a transition into a focused state, eR(1,2) is similarly small. However once the transition occurs (red triangle in Figure 1), those values are large (upwards of 0.5 and higher) and sustained across time (Appendix 1—figure 2 and Appendix 1—figure 3). For one of the singers (T2) the situation was more complex, as he created multiple focused formants (Figure 1 middle panels and Appendix 1—figure 6, Appendix 1—figure 8). The second focused state was not explicitly dependent upon the first: The first focused state clearly moves and transitions between approximately 1.5–2 kHz (by 30%) while the second focused state remains constant at approximately 3–3.5 kHz (changing less than 1%). Thus the focused states are not harmonically related. Unlike the other singers, T2 not only has a second focused state, but also had more energy in the higher overtones (Figure 1). As such, singer T2 also exhibited a different eR

time course, which took on values that could be relatively large even prior to the transition. This may be because he took multiple ways to approach the transition into a focused state (e.g., Appendix 1—figure 9).

Plotting spectra around the transition from normal to biphonation singing in a waterfall plot indicates that the sharp focused filter is achieved by merging two broader formants together (F2 and F3

in Figure 2Kob, 2004). This transition into the focused state is fast (∼40–60 ms), as are the shorter transitions within the focused state where the singer melodically changes the filter that forms the whistle-like component of their song (Figure 1, Appendix 1—figure 8). Figure 2

A waterfall plot representing the spectra at different time points as singer T2 transitions from normal singing into biphonation (T2_3short.wav).

The superimposed arrows are color-coded to help visualize how the formants change about the transition, chiefly with F3 shifting to merge with F2. This plot also indicates the second focused state …

Vocal tract MRI

While we can infer the shape of the formants in Khoomei by examining audio recordings, such analysis is not conclusive in explaining the mechanism used to achieve these formants. The working hypothesis was that vocal tract shape determines these formants. Therefore, it was crucial to examine the shape and dynamics of the vocal tract to determine whether the acoustic measurements are consistent with this hypothesis. To accomplish this, we obtained MRI data from one of the singers (T2) that are unique in two regards. First, there are two types of MRI data reported here: steady-state volumetric data Figure 3 and Appendix 1—figure 18) and dynamic midsagittal images at several frames per second that capture changes in vocal tract position (Figure 4A–B and Appendix 1—figure 20). Second is that the dynamic data allow us to examine vocal tract changes as song transitions into a focused state (e.g., Appendix 1—figure 20). Figure 3

3-D reconstruction of volumetric MRI data taken from singer T2 (Run3; see Appendix, including Appendix 1—figure 18).

(A) Example of MRI data sliced through three different planes, including a pseudo-3D plot. Airspaces were determined manually (green areas behind tongue tip, red for beyond). Basic labels are … Figure 4

Analysis of vocal tract configuration during singing.

(A) 2D measurement of tract shape. The inner and outer profiles were manually traced, whereas the centerline (white dots) was found with an iterative bisection technique. The distance from the inner …

The human vocal tract begins at the vocal folds and ends at the lips. Airflow produced by the vocal cords sets the air-column in the tract into vibration, and its acoustics determine the sound that emanates from the mouth. The vocal tract is effectively a tube-like cavity whose shape can be altered by several articulators: the jaw, lips, tongue, velum, epiglottis, larynx and trachea (Figure 4C). Producing speech or song requires that the shape of the vocal tract, and hence its acoustics, are precisely controlled (Story, 2016).

Several salient aspects of the vocal tract during the production of Khoomei can be observed in the volumetric MRI data. The most important feature however, is that there are two distinct and relevant constrictions when in the focused state, corresponding roughly to the uvula and alveolar ridge. Additionally, the vocal tract is expanded in the region just anterior to the alveolar ridge (Figure 4A). The retroflex position of the tongue tip and blade produces a constriction at 14 cm, and also results in the opening of this sublingual space. It is the degree of constriction at these two locations that is hypothesized to be the primary mechanism for creating and controlling the frequency at which the formant is focused.

Modeling

Having established that the shape of vocal tract during Khoomei does indeed have two constrictions, consistent with observations from other groups, the primary goals of our modeling efforts were to use the dynamic MRI data as morphological benchmarks and capture the merging of formants to create the focused states as well as the dynamic transitions into them. Our approach was to use a well-established linear “source/filter” model (e.g., Stevens, 2000) that includes known energy losses (Sondhi and Schroeter, 1987; Story et al., 2000; Story, 2013). Here, the vibrating vocals folds act as the broadband sound source (with the f0

and associated overtone cascade), while resonances of the vocal tract, considered as a series of 1-D concatenated tubes of variable uniform radius, act as a primary filter. We begin with a first order assumption that the system behaves linearly, which allows us for a simple multiplicative relationship between the source and filter in the spectral domain (e.g., Appendix 1—figure 10).

Acoustic characteristics of the vocal tract can be captured by transforming the three-dimensional configuration (Figure 3) into a tube with variation in its cross-sectional area from the glottis to the lips (Figure 4 and Figure 5). This representation of the vocal tract shape is called an area function, and allows for calculation of the corresponding frequency response function (from which the formant frequencies can be determined) with a one-dimensional wave propagation algorithm. Although the area function can be obtained directly from a 3D vocal tract reconstruction (e.g., Story et al., 1996), the 3D reconstructions of the Tuvan singer’s vocal tract were affected by a large shadow from a dental post (e.g., see Figure 4) and were not amenable to detailed measurements of cross-sectional area. Instead, a cross-sectional area function was measured from the midsagittal slice of the 3D image set (see Materials and methods and Appendix for details). Thus, the MRI data provided crucial bounds for model parameters: the locations of primary constrictions and thereby the associated area functions. Figure 5

Results of changing vocal tract morphology in the model by perturbing the baseline area function A0(x)
to demonstrate the merging of formants F2
and F3
, atop two separate overtones as apparent in the two columns of panels A and B.

(A) The frames from dynamic MRI with red and blue dashed circles highlighting the location of the key vocal tract constrictions. (B) Model-based vocal tract shapes stemming from the MRI data, … The frequency response functions derived from the above static volumetric MRI data (e.g., Figure 4D) indicate that two formants F2 and F3 cluster together, thus enhancing both their amplitudes. Clearly, if F2 and F3

could be driven closer together in frequency, they would merge and form a single formant with unusually high amplitude. We hypothesize that this mechanism could be useful for effectively amplifying a specific overtone, such that it becomes a prominent acoustic feature in the sound produced by a singer, specifically the high frequency component of Khoomei.

Next, we used the model in conjunction with time-resolved MRI data to investigate how the degree of constriction and expansion at different locations along the vocal tract axis could be a mechanism for controlling the transition from normal to overtone singing and the pitch while in the focused state. These results are summarized in Figure 5 (further details are in the Appendix). While the singers are in the normal song mode, there are no obvious strong constrictions in their vocal tracts (e.g., Appendix 1—figure 11). After they transition, in each MRI from the focused state, we observe a strong constriction near the alveolar ridge. We also observe a constriction near the uvula in the upper pharynx, but the degree of constriction here varies. If we examine the simultaneous audio recordings, we find that variations in this constriction are co-variant with the frequency of the focused formant. From this, we surmise that the mechanism for controlling the enhancement of voice harmonics is the degree of constriction near the alveolar ridge in the oral cavity (labeled CO in Figure 5), which affects the proximity of F2 and F3 to each other (Appendix 1—figure 12). Additionally, the degree of constriction near the uvula in the upper pharynx (CP) controls the actual frequency at which F2 and F3 converge (Appendix 1—figure 13). Other parts of the vocal tract, specifically the expansion anterior to CO

, may also contribute since they also show small co-variations with the focused formant frequency (Appendix 1—figure 14). Further, a dynamic implementation of the model, as shown in Appendix 1—figure 14, reasonably captures the rapid transition into/out of the focused state as shown in Figure 1. Taken together, the model confirms and explains how these articulatory changes give rise to the observed acoustic effects.

To summarize, an overtone singer could potentially ‘play’ (i.e., select) various harmonics of the voice source by first generating a tight constriction in the oral cavity near the alveolar ridge, and then modulating the degree of constriction in the uvular region of the upper pharynx to vary the position of the focused formant, thereby generating a basis for melodic structure.Discussion

This study has shown that Tuvan singers performing Sygyt-style Khoomei exercise precise control of the vocal tract to effectively merge multiple formants together. They morph their vocal tracts so to create a sustained focused state that effectively filters an underlying stable array of overtones. This focused filter greatly accentuates energy of a small subset of higher order overtones primarily in the octave-band spanning 1–2 kHz, as quantified by an energy ratio eR(1,2)

. Some singers are even capable of producing additional foci at higher frequencies. Below, we argue that a linear framework (i.e., source/filter model, Stevens, 2000) appears sufficient to capture this behavior including the sudden transitions into a focused state, demonstrating that nonlinearities are not a priori essential. That is, since the filter characteristics are highly sensitive to vocal tract geometry, precise biomechanical motor control of the singers is sufficient to achieve a focused state without invoking nonlinearities or a second source as found in other vocalization types (e.g., Herzel and Reuter, 1996; Fee et al., 1998). Lastly, we describe several considerations associated with how focused overtone song produces such a salient percept by virtue of a pitch decoherence.

Source or filter?

The notion of a focused state is mostly consistent with vocal tract filter-based explanations for biphonation in previous studies (e.g., Bloothooft et al., 1992; Edgerton et al., 1999; Adachi and Yamada, 1999; Grawunder, 2009), where terms such as an ‘interaction of closely spaced formants’, ‘reinforced harmonics’, and ‘formant melting’ were used. In addition, the merging of multiple formants is closely related to the ‘singer’s formant’, which is proposed to arise around 3 kHz due to formants F3–F5 combining (Story, 2016), though this is typically broader and less prominent than the focused states exhibited by the Tuvans. Our results explain how this occurs and are also broadly consistent with Adachi and Yamada (1999) in that a constricted ‘rear cavity’ is crucial. However, we find that this rear constriction determines the pitch of the focused formant, whereas it is the ‘front cavity’ constriction near the alveolar ridge that produces the focusing effect (i.e., merging of formants F2 and F3

).

Further, the present data appear in several ways inconsistent with conclusions from previous studies of Khoomei, especially those that center on effects that arise from changes in the source. Three salient examples are highlighted. First, we observed overtone structure to be highly stable, though some vibrato may be present. This contrasts the claim by Levin and Edgerton (1999) that “(t)o tune a harmonic, the vocalist adjusts the fundamental frequency of the buzzing sound produced by the vocal folds, so as to bring the harmonic into alignment with a formant’. That is, we see no evidence for the overtone ‘ladder’ being lowered or lifted as they suggested (note in Figure 1, f0

is held nearly constant). Further, this stability argues against a transition into a different mode of glottal pulse generation, which could allow for a ‘second source’ (Mergell and Herzel, 1997). Second, a single sharply defined harmonic alone is not sufficient to get the salient perception of a focused state, as had been suggested by Levin and Edgerton (1999). Consider Appendix 1—figure 9, especially at the 4 s mark, where the voicing is ‘pressed’. Pressed phonation, also referred to as ventricular voice, occurs when glottal flow is affected by virtue of tightening the laryngeal muscles such that the ventricular folds are brought into vibration. This has the perceptual effect of adding a degree of roughness to the voice sound (Lindestad et al., 2001; Edmondson and Esling, 2006). There, a harmonic at 1.51 kHz dominates (i.e., the two flanking overtones are approximately 40 dB down), yet the song has not yet perceptibly transitioned. It is not until the cluster of overtones at 3–3.5 kHz is brought into focus that the perceptual effect becomes salient, perhaps because prior to the 5.3 s mark the broadband nature of those frequencies effectively masks the first focused state. Third, we do not observe subharmonics, which contrasts a prior claim (Lindestad et al., 2001) that ”(t)his combined voice source produces a very dense spectrum of overtones suitable for overtone enhancement’. However, that study was focused on a different style of song called ‘Kargyraa’, which does not exhibit as clearly a focused state as in Sygyt.

Linear versus nonlinear mechanisms

An underlying biophysical question is whether focused overtone song arises from inherently linear or nonlinear processes. Given that Khoomei consists of the voicing of two or more pitches at once and exhibits dramatic and fast transitions from normal singing to biphonation, nonlinear phenomena may seem like an obvious candidate (Herzel and Reuter, 1996). It should be noted that Herzel and Reuter (1996) go so far to define biphonation explicitly through the lens of nonlinearity. We relax such a definition and argue for a perceptual basis for delineating the boundaries of biphonation. Certain frog species exhibit biphonation, and it has been suggested that their vocalizations can arise from complex nonlinear oscillatory regimes of separate elastically coupled masses (Suthers et al., 2006). Further, the appearance of abrupt changes in physiological systems (as seen in Figure 1) has been argued to be a flag for nonlinear mechanisms (Goldberger et al., 2002); for example, by virtue of progression through a bifurcation.

Our results present two lines of evidence that argue against Sygyt-style Khoomei arising primarily from a nonlinear process. First, the underlying harmonic structure of the vocal fold source appears highly stable through the transition into the focused state (Figure 1). There is little evidence of subharmonics. A source spectral structure that is comprised of an f0

and integral harmonics would suggest a primarily linear source mechanism. Second is that our modeling efforts, which are chiefly linear in nature, reasonably account for the sudden and salient transition. That is, the model is readily sufficient to capture the characteristic that small changes in the vocal tract can produce large changes in the filter. Thereby, precise and fast motor control of the articulators in a linear framework accounts for the transitions into and out of the focused state. Thus, in essence, Sygyt-style Khoomei could be considered a linear means to achieve biphonation. Connecting back to nonlinear phonation mechanisms in non-mammals, our results provide further context for how human song production and perception may be similar and/or different relative to that of non-humans (e.g., Doolittle et al., 2014; Kingsley et al., 2018).

Nevertheless, features that appear transiently in spectrograms do provide hints of source nonlinearity, such as the brief appearance of subharmonics in some instances (Appendix 1—figure 15B). This provides an opportunity to address the limitations of the current modeling efforts and to highlight future considerations. We suggest that further analysis (e.g., Theiler et al., 1992; Tokuda et al., 2002; Kantz and Schreiber, 2004) of Khoomei audio recordings may help to inform the model and might better capture focused filter sharpness and the origin of secondary focused states. Several potential areas for improvement are: nonlinear source–filter coupling (Titze et al., 2008); a detailed model of glottal dynamics (e.g., ratio of open/closed phases in glottal flow [Grawunder, 2009; Li and Hou, 2017], and periodic vibrations in f0

); inclusion of piriform sinuses as side-branch resonators (Dang and Honda, 1997; Titze and Story, 1997); inclusion of the 3-D geometry; and detailed study of the front cavity (e.g., lip movements) that may be used by the singer to maintain control of the focused state and to make subtle manipulations.

Perceptual consequences of overtone focusing

Although this study did not directly assess the percept associated with these vocal productions, the results raise pressing questions about how the spectro-temporal signatures of biphonic Khoomei described here create the classical perception of Sygyt-style Khoomei as two distinct sounds (Aksenov, 1973). The first, the low-pitched drone, which is present during both the normal singing and the focused-state biphonation intervals, reflects the pitch associated with f0, extracted from the harmonic representation of the stimulus. It is well established that the perceived pitch of a broadband sound comprised of harmonics reflects the f0 derived primarily from the perceptually resolved harmonics up to about 10f0 (Bernstein and Oxenham, 2003). The frequency resolution of the peripheral auditory system is such that these low-order harmonics are individually resolved by the cochlea, and it appears that such filtering is an important prerequisite for pitch extraction associated with that common f0. The second sound, the high-pitched melody, is present only during the focused-state intervals and probably reflects a pitch associated with the focused formant. An open question, however, is why this focused formant would be perceived incoherently as a separate pitch (Shamma et al., 2011), when it contains harmonics at multiples of f0

. The auditory system tends to group together concurrent harmonics into a single perceived object with a common pitch (Roberts et al., 2015), and the multiple formants of a sung or unsung voice are not generally perceived as separate sounds from the low harmonics.

The fact that the focused formant is so narrow apparently leads the auditory system to interpret this sound as if it were a separate tone, independent of the low harmonics associated with the drone percept, thereby effectively leading to a pitch decoherence. This perceptual separation could be attributable to a combination of both bottom-up (i.e., cochlear) and top-down (i.e., perceptual) factors. From the bottom-up standpoint, even if the focused formant is broad enough to encompass several harmonic components, the fact that it consists of harmonics at or above 10 f0 (i.e., the 1500 Hz formant frequency represents the 10th harmonic of a 150 Hz f0) means that these harmonics will not be spectrally resolved by cochlear filtering (Bernstein and Oxenham, 2003). Instead, the formant will be represented as a single spectral peak, similar to the representation of a single pure tone at the formant frequency. Although the interaction of harmonic components at this cochlear location will generate amplitude modulation at a rate equal to the f0 (Plack and Oxenham, 2005), it has been argued that a common f0 is a weak cue for binding low- and high-frequency formants (Culling and Darwin, 1993). Rather, other top-down mechanisms of auditory-object formation may play a more important role in generating a perception of two separate objects in Khoomei. For example, the rapid onsets of the focused formant may enhance its perceptual separation from the constant drone (Darwin, 1984). Further, the fact that the focused formant has a variable frequency (i.e., frequency modulation, or FM) while the drone maintains a constant f0

is another difference that could facilitate their perceptual separation. Although it has been argued that FM differences between harmonic sounds generally have little influence on their perceived separation (Darwin, 2005), others have reported enhanced separation in the special case in which one complex was static and the other had applied FM (Summerfield and Culling, 1992) – similar to the first and second formants during the Tuvan focused state.

The perceptual separation of the two sounds in the Tuvan song might be further affected by a priori expectations about the spectral qualities of vocal formants (Billig et al., 2013). Because a narrow formant occurs so rarely in natural singing and speech, the auditory system might be pre-disposed against perceiving it as a phonetic element, limiting its perceptual integration with the other existing formants. Research into ‘sine-wave speech’ provides some insights into this phenomenon. When three or four individual frequency-modulated sinusoids are presented at formant frequencies in lieu of natural formants, listeners can, with sufficient training, perceive the combination as speech (Remez et al., 1981). Nevertheless, listeners largely perceive these unnatural individual pure tones as separate auditory objects (Remez et al., 2001), much like the focused formant in Khoomei. Further research exploring these considerations would help close the production–perception circle underlying the unique percept arising from Tuvan throat song.Materials and methods

Acoustical recordings

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Recordings were made at York University (Toronto, ON, Canada) in a double-walled acoustic isolation booth (IAC) using a Zoom H5 24-bit digital recorder and an Audio-Technica P48 condenser microphone. A sample rate of 96 kHz was used. Spectral analysis was done using custom-coded software in Matlab. Spectrograms were typically computed using 4096 point window segments with 95% fractional overlap and a Hamming window. Harmonics (black circles in Figure 1) were estimated using a custom-coded peak-picking algorithm. Estimated formant trends (red dashed lines in Figure 1) were determined using a lowpass interpolating filter built into Matlab’s digital signal processing toolbox with a scaling factor of 10. From this trend, the peak-picking was reapplied to determine ‘formant’ frequencies (red ‘x’s in Figure 1). This process could be repeated across the spectrogram to track overtone and formant frequency/strength effectively, as shown in Appendix 1—figure 1.

To quantify the focused states, we developed a dimension-less measure eR(fL,fH) to represent the energy ratio of that spanning a frequency range fHfL relative to the entire spectral output. This can be readily computed from the spectrogram data as follows. First take a ‘slice’ from the spectrogram and convert spectral magnitude to linear ordinate and square it (as intensity is proportional to pressure squared). Then integrate across frequency, first for a limited range spanning [fL,fH] (e.g., 1–2 kHz) and then for a broader range of [0,fmax] (e.g., 0–8 kHz; 8 kHz is a suitable maximum as there is little acoustic energy in vocal output above this frequency). The ratio of these two is then defined as eR

, and takes on values between 0 and 1. This can be expressed more explicitly as: (1) eR(fL,fH)=(∫fHfLP(f)dffmax0P(f)df)2

where P is the magnitude of the scaled sound pressure, f is frequency, and fL and fH are filter limits for considering the focused state. The choice of [fL,fH]=[1,2] kHz has the virtue of spanning an octave, which also closely approximates the ‘seventh octave’ from about C6 to C7. eR did not depend significantly upon the length of the fast Fourier transform (FFT) window. Values of eR

for the waveforms used in Figure 1 are shown in Appendix 1—figures 2 and 3.

MRI acquisition and volumetric analysis

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MRI images were acquired at the York MRI Facility on a 3.0 Tesla MRI scanner (Siemens Magnetom TIM Trio, Erlangen, Germany), using a 12-channel head coil and a neck array. Data were collected with the approval of the York University Institutional Review Board. The participant was fitted with an MRI compatible noise-cancelling microphone (Optoacoustics, Mazor, Israel) mounted directly above the lips. The latency of the microphone and noise-cancelling algorithm was 24 ms. Auditory recordings were made in QuickTime on an iMac during the scans to verify performance.

Images were acquired using one of two paradigms, static or dynamic. Static images were acquired using a T1-weighted 3D gradient echo sequence in the sagittal orientation with 44 slices centered on the vocal tract, TR = 2.35 ms, TE = 0.97 ms, flip angle = 8 degrees, FoV = 300 mm, and a voxel dimension of 1.2 × 1.2×1.2 mm. Total acquisition time was 11 s. The participant was instructed to begin singing a tone, and to hold it in a steady state for the duration of the scan. The scan was started immediately after the participant began to sing and had reached a steady state. Audio recordings verified a consistent tone for the duration of the scan. Dynamic images were acquired using a 2D gradient echo sequence. A single 10.0 mm thick slice was positioned in a sagittal orientation along the midline of the vocal tract, TR = 4.6 ms, TE = 2.04 ms, flip angle = 8 degrees, FoV = 250 mm, and a voxel dimension of 2.0 × 2.0×10.0 mm. One hundred measurements were taken for a scan duration of 27.75 s. The effective frame rate of the dynamic images was 3.6 Hz. Audio recordings were started just prior to scanning. Only subject T2 participated in the MRI recordings. The participant was instructed to sing a melody for the duration of the scan, and took breaths as needed.

For segmentation (Figure 3), 3D MRI images (Run1; see Appendix) were loaded into Slicer (version 4.6.2 r25516). The air-space in the oral cavity was manually segmented using the segmentation module, identified and painted in slice by slice. Careful attention was paid to the parts of the oral cavity that were affected by the artifact from the dental implant. The air cavity was manually repainted to be approximately symmetric in this region using the coronal and axial view (Figure 3A). Once completely segmented, the sections were converted into a 3D model and exported as a STL file. This mesh file was imported into MeshLab (v1.3.4Beta) for cleaning and repairing the mesh. The surface of the STL was converted to be continuous by removing non-manifold faces and then smoothed using depth and Laplacian filters. The mesh was then imported into Meshmixer where further artifacts were removed. This surface-smoothed STL file was finally reimported into Slicer, generating the display in Figure 3B.

Computational modeling

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Measurement of the cross-distance function is illustrated in Figure 4. The inner and outer profiles of the vocal tract were first determined by manual tracing of the midsagittal image. A 2D iterative bisection algorithm (Story, 2007) was then used to find the centerline within the profiles extending from the glottis to the lips, as shown by the white dots in Figure 4A. Perpendicular to each point on the centerline, the distance from the inner to outer profiles was measured to generate the cross-distance function shown in Figure 4B; the corresponding locations of the anatomic landmarks shown in the midsagittal image are also indicated on the cross-distance function.

The cross-distance function, D(x), can be transformed to an approximate area function, A(x), with the relation A(x)=kDα(x), where k and α are a scaling factor and exponent, respectively. If the elements of D(x) are considered to be diameters of a circular cross-section, k=(π/4) and α=2. Although other values of k and α have been proposed to account for the complex shape of the vocal tract cross-section (Heinz and Stevens, 1964; Lindblom and Sundberg, 1971; Mermelstein, 1973), there is no agreement on a fixed set of numbers for each parameter. Hence, the circular approximation was used in this study to generate an estimate of the area function. In Figure 4C, the area function is plotted as its tubular equivalent, where the radii D(x)/2

were rotated about an axis to generate circular sections from the glottis to the lips.

The associated frequency response of that area function is shown in Figure 4D and was calculated with a transmission line approach (Sondhi and Schroeter, 1987; Story et al., 2000), which included energy losses due to yielding walls, viscosity, heat conduction, and acoustic radiation at the lips. Side branches such the piriform sinuses were not considered in detail in this study. The first five formant frequencies (resonances), F1,…,F5

, were determined by finding the peaks in the frequency response functions with a peak-picking algorithm (Titze et al., 1987) and are located at 400, 1065, 1314, 3286, and 4029 Hz, respectively.

To examine changes in pitch, a particular vocal tract configuration was manually ‘designed (Appendix 1—figure 6) such that it included constrictive and expansive regions at locations similar to those measured from the singer (i.e., Figure 4), but to a less extreme degree. We henceforth denote this area function as A0(x), and it generates a frequency response with widely spaced formant frequencies (F1…5=[529,1544,2438,3094,4236]Hz), essentially a neutral vowel. In many of the audio signals recorded from the singer, the fundamental frequency, fo (i.e., the vibratory frequency of the vocal folds), was typically about 150 Hz. The singer then appeared to enhance one of the harmonics in the approximate range of 8fo…12fo. Taking the 12th harmonic (12×150=1800 Hz) as an example target frequency (dashed line in the frequency response shown in Figure 5c), the area function A0(x) was iteratively perturbed by the acoustic-sensitivity algorithm described in Story (2006) until F2 and F3

converged on 1800 Hz and became a single formant peak in the frequency response. Additional details on the perturbation process leading into Figure 5 are detailed in the Appendix.Appendix 1

This appendix contains supporting information for the document Overtone focusing in biphonic Tuvan throat singing by Bergevin et al. Citations here refer to the bibliography of the main document. First (Methodological considerations), we include several methodological components associated with the quantitative analysis of the waveforms, helping illustrate different approaches towards characterizing the acoustic data and rationale underlying control measures. Second (Additional waveform analyses), we include additional plots to support results and discussion in the main text. For example, different spectrograms are presented, as are analyses for additional waveforms. This section also helps to provide additional context for a second independent focused state. The third section (Additional modeling analysis figures) details theoretical components leading into the results of the computational model and how the MRI data constrain the key parameters, justifying arguments surrounding the notion of formant merging. Fourth (Instability in focused state), some speculative discussion and basic modeling aspects are presented with regard to the notion of instabilities present in the motor control of the focused state. In the fifth section (Additional MRI analysis figures), images stemming from the MRI data are presented. Last, the final three sections detail accessing the acoustic waveforms, MRI data files, and waveform analysis (Matlab-based) software via an online repository.

Methodological considerations

Overtone and formant tracking

To facilitate quantification of the waveforms, we custom-coded a peak-picking/tracking algorithm to analyze the time-frequency representations produced by the spectrogram. Appendix 1—figure 1 shows an example of the tracking of the overtones (red dots) and formants (grayscale dots; intensity coded by relative magnitude as indicated by the colorbar). This representation provides an alternative view (compared to Figure 1) to help demonstrate that, by and large, the overtone structure is highly consistent throughout, while the formant structure varies significantly across the transition.  Appendix 1—figure 1

Same as Figure 1 (middle left panel; subject T2, same sound file as shown in the middle panel of Figure 1), except with overtones and estimated formant structure tracked across time.

Quantifying focused states

Appendix 1—figures 2 and 3 show calculation of the energy ratio eR used as a means to quantify the degree of focus. For Appendix 1—figure 2, the waveforms are the same as those shown in Figure 1 (those with slightly different axis limits). In general, we found that eR(1,2) provided a clear means to distinguish the focused state, as values were close to zero prior to the transition and larger/sustained beyond the transition. Singer T2 was an exception. Appendix 1—figure 3 is for singer T2, using the same file (i.e., the transition point into the focused state at between 6 and 7 s in this figure is the same as that shown in the middle panel of Figure 1), but with an expanded timescale to illustrate the larger eR values prior to the transition. This is due to the relatively large amount of energy present between 2.5–4 kHz. We also explored eR(1,2) values in a wide range of phonetic signals, such as child and adult vocalizations, other singing styles (e.g., opera), non-Tuvan singers (e.g., Westerners) performing ‘overtone singing’, and older recordings of Tuvan singers. In general, it was observed that eR(1,2)

was relatively large and sustained across time for focused overtone song, whereas the value was close to zero and/or highly transient for other vocalizations. Appendix 1—figure 2

Same data/layout as in Figure 1 but now showing eR(1,2)
as defined in the ‘Materials and methods’.

These plots show the energy ratio focused between 1–2 kHz. Vertical red dashed lines indicate approximate time of transition into the focused state. An expanded timescale is also shown for singer T2 … Appendix 1—figure 3

Similar to Figure 2 for singer T2 (middle panel), except an expanded time scale is shown to demonstrate the earlier dynamics as this singer approaches the focused state (see T2_5longer.wav).

Control measurements

The waveforms from the Tuvan singers provide an intrinsic degree of control (i.e., voicing not in the focused state). Similar to Figure 1, Appendix 1—figure 4 shows the spectra prior to the transition into the focused state. Although relatively narrow harmonics can be observed, they tend to occur below 1 kHz. Such is consistent with our calculations of eR(1,2)

: prior to a transition into a focused state, this value is close to zero. The exception is singer T2, who instead shows a relatively large amount of energy about 1.8–3 kHz that may have some sort of masking effect (see ‘Discussion’ in the main text,and the ‘Pressed transition’ section below). In addition, Tuvan singer T4, who used a non-Sygyt style (Appendix 1—figure 5) , can also effectively be considered a ‘control’. Appendix 1—figure 4

Stemming directly from Figure 1, the right-hand column now shows a spectrum from a time point prior to transition into the focused state (as denoted by the vertical black lines in the left column). The shape of the spectra from Figure 1 is also included for reference.

Appendix 1—figure 5

Spectrogram for singer T4 singing in non-Sygyt style (first song segment of T2_4shortA.wav sound file). For the spectrogram, 4096 point windows were used for the fast Fourier transform (FFT) with 95% fractional overlap and a Hamming window.

Additional waveform analyses

Other spectrograms

Appendix 1—figure 5 shows spectrogram from singer T4 (T4_shortA.wav) singing in non-Sygyt style. While producing a distinctive sound, note the relative lack of energy above approximately 1 kHz. Appendix 1—figure 6 shows a spectrogram from singer T2 (T2_5.wav) over a longer timescale than that shown in Figure 1. Similarly for Appendix 1—figure 7, but for singer T1. Both of these plots provide a spectral-temporal view of how the singer maintains and modulates the song over the course of a single exhalation. Note both the sudden transitions into different maintained pitches and the briefer transient excursions. Appendix 1—figure 6

Spectrogram of the entire T2_5.wav sound file. The sample rate was 96 kHz. The analysis parameters used were the same as those used for Figure 5.

Appendix 1—figure 7

Spectrogram of the first song segment of the T1_3.wav sound file. The analysis parameters used were the same as those for Figure 5.

Second independent focused state

Appendix 1—figure 8 shows another example of a transition in Sygyt-style song for singer T2, clearly showing a second focused state about 3–3.5 kHz. Two aspects merit highlighting. First, the spectral peaks are not harmonically related: at t=4.5

s, the first focused state is at 1.36 kHz and the other at 3.17 kHz (far from to 2.72 kHz as expected). Second, during the singer-induced pitch change at 3.85 s, the two peaks do not move in unison. Although not ruling out correlations between the two focused states, these observations suggest that they are not simply nor strongly related to one another. Appendix 1—figure 8

Singer T2’s transition into a focused state. Note that while the first focused state transitions from approximately 1.36 to 1.78 kHz, the second state remains nearly constant, decreasing only slightly from 3.32 to 3.17 kHz (T2_1shortB.wav).

Pressed transition

Appendix 1—figure 9 shows a spectrogram and several spectral slices for the sound file in which the voicing was ‘pressed’ (Adachi and Yamada, 1999; Edmondson and Esling, 2006) prior to the transition into the focused state. That is, prior to the 1.8 s mark, voicing is relatively normal. But after that point (prior to the transition into the focused state around 5.4 s, substantial energy appears between 2–4 kHz along with a degree of vibrato. Note, however, that there is no change to the overall overtone structure (e.g., no emergence of subharmonics). The spectrum at t=4.0s

, prior to the transition, provides a useful comparison back to Levin and Süzükei (2006). Specifically, one particular overtone is singled out and highly focused, yet the broadband cluster of overtones about 2.5–4 kHz effectively mask it. It is not until about the 5.4 s mark, when those higher overtones are also brought into focus, that a salient perception of the Sygyt-style emerges. Appendix 1—figure 9

Spectrogram of singer T2 exhibiting pressed voicing heading into transition to focused state (T2_2short.wav).

Additional modeling analysis figures

The measurement of the cross-distance function (as described in the ‘Materials and methods’), along with calculation of the frequency response from an estimate of the area function, suggested that constrictions of the vocal tract in the region of the uvula and alveolar ridge may play a significant role in controlling the spectral focus generated by the convergence of F2 and F3. Assuming that an overtone singer configures the vocal tract to merge these two formants deliberately such that, together, they enhance the amplitude of a selected harmonic of the voice source, the aim was to investigate how the vocal tract can be systematically shaped with precisely placed constrictions and expansions to both merge F2 and F3

into a focused cluster and move the cluster along the frequency axis to allow for selection of a range of voice harmonics.

Appendix 1—figure 11b shows the same area function as that in Appendix 1—figure 11a (see ‘Materials and methods’) but plotted by extending the equivalent radius of each cross-sectional area, outward and inward, along a line perpendicular to the centerline measured from the singer (see Figure 4A), resulting in an inner and outer outline of the vocal tract shape as indicated by the thick black lines. The measured centerline is also shown in the figure, along with anatomic landmarks. As this does not represent a true midsagittal plane, it will be referred to here as a pseudo-midsagittal plot (Story et al., 2001). Appendix 1—figure 10

Overview of source/filter theory, as advanced by Stevens (2000). The left column shows normal phonation, whereas the right indicates one example of a focused state.

Appendix 1—figure 11

Setup of the baseline vocal tract configuration used in the modeling study.

(a) The area function (A0(x)

) is in the lower panel and its frequency response is in the upper panel. (b) The area function from (a) is shown as a pseudo-midsagittal plot (see text).

Appendix 1—figure 12a shows the new area function and frequency response generated by the perturbation process, whereas the pseudo-midsagittal plot is shown in Appendix 1—figure 12b. Relative to the shape of A0(x) (shown as the thin gray line), the primary modification is a severe constriction imposed between 12.5–13.5 cm from the glottis, essentially at the alveolar ridge. Although the line thickness might suggest that the vocal tract is occluded in this region, the minimum cross-sectional area is 0.09 cm2. There is also a more moderate constriction at about 5 cm from the glottis, and a slight expansion between 7–10.5 cm from the glottis. The frequency response in upper panel of Appendix 1—figure 12a demonstrates that the new area function was successful in driving F2 and F3 together to form a single formant peak centered at 1800 Hz, which is at least 15 dB higher in amplitude than any of the other formants. Exactly the same process was used to generate area functions for which F2 and F3 converge on the target harmonic frequencies: 8fo,9fo,10fo,11fo=1200,1350,1500,1650 Hz, respectively. The results, along with those from the previous figure for 12fo, are shown in Appendix 1—figure 13. The collection of frequency responses in the upper panel of Appendix 1—figure 13b shows that F2 and F3 successfully converged to become one formant peak in each of the cases, and their locations on the frequency axis are centered around the specified target frequencies. The corresponding area functions in the lower panel suggests that the constriction between 12.5–13.5 cm from the glottis (alveolar ridge region) is present in roughly the same form for all five cases. By contrast, an increasingly severe constriction must be imposed in the region between 6–8.5 cm from the glottis (uvular region) in order to shift the target frequency (i.e., the frequency at which F2 and F3 converge) downward through progression of specified harmonics. Coincident with this constriction is a progressively larger expansion between 14–15.5 cm from the glottis, which probably assists in positioning the focal regions of F2 and F3 downward. It can also be noted that the area function that generates a focus at 8fo

(1200 Hz; thinnest line) is most similar to the one generated from the cross-distance measurements (i.e., Figure 4c). In both, there are constrictions located at about 7.5 cm and 13 cm from the glottis; the expansions in the lower pharynx and oral cavity are also quite similar. The main difference is the greater expansion of the region between 8–13 cm from the glottis in the acoustically derived area function.

On the basis of the results, a mechanism for controlling the enhancement of voice harmonics can be proposed: the degree of constriction near the alveolar ridge in the oral cavity (labeled Co in Figure 5 of the main text) controls the proximity of F2 and F3 to each other, whereas the degree of constriction near the uvula in the upper pharynx, Cp, controls the frequency at which F2 and F3 converge (the expansion anterior to Co may also contribute). Thus, an overtone singer could potentially ‘play’ (i.e., select) various harmonics of the voice source by first generating a tight constriction in the oral cavity near the alveolar ridge to generate the focus of F2 and F3

, and then modulating the degree of constriction in the uvular region of the upper pharynx to position the focus on a selected harmonic.

This proposed mechanism of controlling the spectral focus is supported by observation of vocal tract changes based on dynamic MRI data sets. Using this approach, midsagittal movies of the Tuvan singer were acquired in which each image represented approximately 275 ms. Shown in Figure 5 is a comparison of vocal tract configurations derived with the acoustic-sensitivity algorithm (middle panels) to image frames from an MRI-based movie (upper panels) associated with the points in time indicated by the vertical lines superimposed across the waveform and spectrogram in the lower part of the figure. The image frames were chosen such that they appeared to be representative of the singer placing the spectral focus at 8fo (left) and 12fo (right), respectively, based on the evidence available in the spectrogram. The model-based vocal tract shape in the upper left panel, derived for a spectral focus of 8fo (1200 Hz), exhibits a fairly severe constriction in the uvular region, similar to the constrictive effect that can be seen in the corresponding image frame (middle left). Likewise, the vocal tract shape derived for a spectral focus of 12fo

(1800 Hz) (upper right) and the image frame just below it both demonstrate an absence of a uvular constriction. Thus, the model-based approach generated vocal tract shapes that appear to possess characteristics similar to those produced by the singer, and provides support for the proposed mechanism of spectral focus control. Appendix 1—figure 12

Results of perturbing the baseline area function A0(x)
so that F2
and F3
converge on 1800 Hz.

(a) Perturbed area function (thick black line) and the corresponding frequency response; for comparison, the baseline area function is also shown (thin gray line). The frequency response shows the … Appendix 1—figure 13

Results of perturbing the baseline area function A0(x)
so that F2
and F3
converge on 1200, 1350, 1500, 1650, and 1800 Hz.

(A) Perturbed area functions and corresponding frequency responses; line thicknesses and gray scale are matched in the upper and lower panels. (B) Pseudo-midsagittal plot of the perturbed area …

Second focused state

Given that singer T2 was the subject for the MRI scans and uniquely exhibited a second focused state (e.g., Appendix 1—figure 8), the model was also utilized to explore how multiple states could be achieved. Two possibilities appear to be the sharpening of formant F4 alone, or the merging of F4 and F5 (Appendix 1—figure 14). However, it is unclear how reasonable those vocal tract configurations may be and further study is required. Appendix 1—figure 14

Similar to Figure 5, but additional manipulations were considered to create a second focused state by merging F4 and F5, as exhibited by singer T2 (see middle row in Figure 1). In addition, the spectrogram shown here is from the model (not the singer’s audio). See also Appendix 1—figure 20 for connections back to dynamic MRI data.

Animations and synthesized song

Animations and audio clips demonstrating various quantitative aspects of the model are included in the data files posted to datadryad.org. Specifically they are:

o Animation (no sound) of vocal tract changes during transition into focused state and subsequent pitch changes – Medley 0 to5 1 cluster.mp4Audioclipof simulatedsong

o Audio clip of simulated song – Medley 0 to5 1 cluster s im.wav

Instability in focused state

Appendix 1—figure 15 and Appendix 1—figure 16 show that brief transient instabilities in the focused state can and do regularly occur. Specifically, it can be observed that there are brief transient lapses while the singer is maintaining the focused overtone condition, thereby providing insight into how focus is actively maintained. One possible explanation is control by virtue of biomechanical feedback, where the focused state can effectively be considered to be an unstable equilibrium point, akin to balancing a ruler vertically on the palm of your hand. An alternative consideration might be that singers learn to create additional quasi-stable equilibrium points (e.g., Appendix 1—figure 17). The sudden transitions observed (Figure 1) could then be likened to two-person cheerleading moves such as a ‘cupie’, where one person standing on the ground suddenly throws another up vertically and has them balancing atop their shoulders or upward-stretched hands. A simple proposed model for the transition into the focused state is shown in Appendix 1—figure 17. There, a stable configuration of the vocal tract would be the low point (pink ball). Learning to achieve a focused state would give rise to additional stable equilibria (red ball), which may be more difficult to maintain. Considerations along these lines, combined with a model for biomechanical control (e.g., Sanguineti et al., 1998), can lead to testable predictions specific to when a highly experienced singer is maintaining balance about the transition point into/out of a focused state (e.g., T2_4.wav audio file). Appendix 1—figure 15

Brief instability in the focused state.

(A) Spectrogram of singer T3 during period during which the focused state briefly falters (T3_2shortB.wav, extracted from around the 33 s mark of T3_2.wav). (B) Spectral slices taken at two … Appendix 1—figure 16

Spectrogram of singer T2 (T2_1shortA.wav) about a transition into a focused state. Note that there is a slight instability around 4.5 s.

Appendix 1—figure 17

Schematic illustrating a simple possible mechanical analogy (ball confined to a potential well) for the transition into a focused state.

Additional MRI analysis figures

Volumetric data

An example of the volumetric data (arranged as tiled midsagittal slices) is shown in Appendix 1—figure 18. Note that the NMR artifact resulting from the presence of a dental post is apparently lateralized to one side.

Appendix 1—figure 19 shows a spectrogram of audio segment (extracted from Run3Vsound.wav) associated with the volumetric scan shown in Appendix 1—figure 18. Segments both with and without the scanner noise are shown.

Vocal tract shape and associated spectrograms

Examples of the vocal tract taken during the dynamic MRI runs (i.e., midsagittal only) are shown for very different representative time points in Appendix 1—figure 20. Appendix 1—figure 18

Mosaic of single slices from the volumetric MRI scan (Run3) of subject T2 during focused overtone state. Spectrogram of corresponding audio shown in Appendix 1—figure 19.

Appendix 1—figure 19

Spectrogram of steady-state overtone voicing assocaited with the volumetric scan shown in Appendix 1—figure 18.

Two different one-second segments are shown: the top segment shows images there were made during the scan (and thus includes acoustic noise from the scanner during image acquisition), while the botto… Appendix 1—figure 20

Representative movie frames and their corresponding spectra for singer T2, as input into modeling parameters (e.g., Figure 5).

The corresponding Appendix data files are DynamicRun2S.mov (MRI images) and DynamicRun2sound.wav (spectra; see also DynamicRun2SGrid.pdf). The top row shows a ‘low pitch’ (first) focused state at …

Data

All data relevant to the study have been placed in the online repository – https://datadryad.org/stash (Bergevin, 2020). Below is a list of the data placed there, along with a brief description (see ‘Materials and methods’ section for additional details).

Acoustic data

All waveforms were obtained at a sample rate of 96 kHz and a bit-depth of 24 bits.

  • T1_1.wav
  • T1_2.wav
  • T1_3.wav
  • T1_3short.wav
  • T2_1.wav
  • T2_1shortA.wav
  • T2_1shortB.wav
  • T2_1shortC.wav
  • T2_2.wav
  • T2_2short.wav
  • T2_3.wav
  • T2_4.wav
  • T2_5.wav
  • T2_5longer.wav
  • T2_5short.wav
  • T3_2.wav
  • T3_2shortA.wav
  • T3_2shortB.wav
  • T4_1.wav
  • T4_1shortA.wav

MRI data

* Images Images were only obtained from singer T2. Note that all image data are saved as DICOM files (i.e., .dcm) :

  • Volumetric Run1
  • Volumetric Run2
  • Volumetric Run3
  • Dynamic midsagittal Run1
  • Dynamic midsagittal Run2
  • Dynamic midsagittal Run3

* Audio recordings acquired during MRI acquisition (see ‘Materials and methods’).

  • Vol. Run1 audio
  • Vol. Run2 audio
  • Vol. Run3 audio
  • Dyn. Run1 audio
  • Dyn. Run2 audio
  • Dyn. Run3 audio

* MRI Midsagittal movies with sound were also created by animating the frames in Matlab and syncing the recorded audio via Wondershare Filmora. They are saved as .mov files (Apple QuickTime Movie files):

  • Dyn. Run1 video
  • Dyn. Run2 video
  • Dyn. Run3 video

To facilitate connecting movie frames back to the associated sound produced by singer T2 at that moment, the movies include frame numbers. Those have been labeled on the corresponding time location in the spectrograms (see red labels at top):

  • Dyn. Run1 spectrogram
  • Dyn. Run2 spectrogram
  • Dyn. Run3 spectrogram

* Segmented volumetric data files (like those shown in Figure 3), data saved as STL files (i.e., .stl):

  • Segmented data (T2)

Software and synthesized song

Simulations and waveform analysis were implemented in Matlab. The TubeTalker software is provided ‘as is’:

  • Code to analyze general aspects of the waveforms (e.g., Figure 1 spectrograms)
  • Code to quantify eR

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Decision letter

  1. Timothy D Griffiths Reviewing Editor; University of Newcastle, United Kingdom
  2. Barbara G Shinn-Cunningham Senior Editor; Carnegie Mellon University, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

Tuvan throat singing, in which people are able to simultaneously produce and independently control two different distinct pitches using the human vocal apparatus, has fascinated hearing and speech researchers for decades. This careful study examines the acoustics of the produced sound and offers new insights into why the produced sound results in two distinct, separately controllable pitches.

Decision letter after peer review:

Thank you for submitting your article “Overtone focusing in biphonic Tuvan throat singing” for consideration by eLife. Your article has been reviewed by two peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Barbara Shinn-Cunningham as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another, and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary

We enjoyed this work addressing mechanisms by which throat singers produce dual pitches that assesses the mechanism for this in terms of the ways in which the vocal tract is precisely controlled based on MRI videos. The work mentions other biological examples of dual fundamentals in songbirds for the broad eLife audience. One of the issues that came up in discussion was the control for normal vocalisations without biphonation, but I think the authors make a reasonable case that the singers act as their own controls. Basically, the work shows that the dual pitch mechanism is associated with changes in the vocal tract morphology based on two constrictions that merge second and third formants and is associated with what they call a ‘focussed state’ in which the harmonics at 1.5kHz to 2kHz are accentuated. The idea as I understand it is that this accentuates a single harmonic of the fundamental glottal pulse rate so that a new high frequency component of Khoomei emerges that is in effect perceptually ‘released’ from the harmonic series to allow the emergence of the high pitched whistling part of the song.

Major comments

1) From first principles, dual pitch singing could be achieved by a different type of glottal pulse generation in the larynx so that two vibration modes were present (as in avian syrinx). This is not the mechanism suggested here, and it is hard to see how the anatomy and physiology of the human larynx might allow this, but this has not been directly examined in the MRI work. The authors carried out a careful acoustic analysis which shows only one harmonic series before and after transitions to throat singling (without shifting), which I think is adequate. But they might comment on the other possible mechanism for biological readers, if only to dismiss it.

2) Both reviewers thought the discussion of the basis for the perceived dual pitch was not clear. The authors discuss differences in cochlear mechanisms between low frequency regions and high frequency regions. More effort could be made to explain how the dual pitch, which is attributed to a type of spectral emphasis, can be reconciled with current models of pitch perception. The fundamental for the singers assessed was ~150Hz so that the >1.5 kHz region will be unresolved (H10 and above). The greatest contribution to the salience of the low pitch will be the resolved harmonics at frequencies below the focus region, which are well represented. The high-frequency harmonics will usually contribute (weakly) to the low pitch based on the temporal firing patterns due to merged harmonics in frequency bands. The authors appear to be arguing that a different spectral pitch emerges in the high frequency focussed region, distinct from that associated with the lower harmonics.

3) The argument about decreased phase locking at high frequency was not convincing: this occurs in a much higher frequency region that the focussed region. The argument that the high pitch was not easily explained by a non-linear distortion was convincing.

4) In conclusion, we thought the work nicely shows the changes in vocal tract morphology and associated spectrum as an explanation for the dual pitch, but more teasing out of mechanism for the dual pitch perception is required in a way that might be accessible to readers.

[Editors’ note: further revisions were suggested prior to acceptance, as described below.]

Thank you for submitting your article “Overtone focusing in biphonic Tuvan throat singing” for consideration by eLife. Your article has been reviewed by a member of our Board of Reviewing Editors and Barbara Shinn-Cunningham as the Senior Editor.

We are afraid we are still not satisfied with the discussion of the basis for the dual pitch at the end of the Discussion. The authors have demonstrated a region of spectral focus as a proposed mechanism for the new pitch. But we still do not understand why the focussed overtones produce a different pitch. They are still harmonics of the same fundamental and interactions between them in this unresolved region would be expected to produce beating at the same frequency as the fundamental, in the absence of non-linear mechanisms. We also do not understand what the additional relevance of a decrease in phase locking in this region would be that the authors highlight. Are the authors claiming that the focused region produces spectral excitation in a region without the usual coding of beating between harmonics (because of decreased phase locking) and that this is the cause of the new pitch? If so an explicit suggestion along those lines might help readers who are familiar with conventional pitch models.

eLife does not usually encourage multiple rounds of revision but this is a critical point in the interpretation of an interesting study, and I would encourage a revision with a much shorter final section of Discussion that explains a clear hypothesis related to the cause of the new pitch.https://doi.org/10.7554/eLife.50476.sa1Author response

Major comments

1) From first principles, dual pitch singing could be achieved by a different type of glottal pulse generation in the larynx so that two vibration modes were present (as in avian syrinx). This is not the mechanism suggested here, and it is hard to see how the anatomy and physiology of the human larynx might allow this, but this has not been directly examined in the MRI work. The authors carried out a careful acoustic analysis which shows only one harmonic series before and after transitions to throat singling (without shifting), which I think is adequate. But they might comment on the other possible mechanism for biological readers, if only to dismiss it.

We attempted to further clarify the point (that we saw no evidence for a nonlinear source mechanism) and added an additional line of text as per the suggestion.

2) Both reviewers thought the discussion of the basis for the perceived dual pitch was not clear. The authors discuss differences in cochlear mechanisms between low frequency regions and high frequency regions. More effort could be made to explain how the dual pitch, which is attributed to a type of spectral emphasis, can be reconciled with current models of pitch perception. The fundamental for the singers assessed was ~150Hz so that the >1.5 kHz region will be unresolved (H10 and above). The greatest contribution to the salience of the low pitch will be the resolved harmonics at frequencies below the focus region, which are well represented. The high-frequency harmonics will usually contribute (weakly) to the low pitch based on the temporal firing patterns due to merged harmonics in frequency bands. The authors appear to be arguing that a different spectral pitch emerges in the high frequency focussed region, distinct from that associated with the lower harmonics.

This criticism was given particularly serious thought and consideration. As a result, we totally rewrote this section to make the proposed ideas clearer, as well as accessible to a broad readership. We tried to find a better balance between issues/questions related to pitch coding and those to cochlear mechanics.

3) The argument about decreased phase locking at high frequency was not convincing: this occurs in a much higher frequency region that the focussed region. The argument that the high pitch was not easily explained by a non-linear distortion was convincing.

As alluded to in the comments above, we clarified the nature of the argument (re phase locking) by expanding upon the discussion of pitch coding. While a reasonable degree of phase locking would still be expected around the 1.5-2 kHz region, this is also where temporal coding starts to fall off dramatically (e.g., Verschooten et al., 2018, PLoS Biol.). That facet, that in the 1-2 kHz region of the human cochlea the fidelity of timing information changes, is what is relevant to the narrative thread here.

4) In conclusion, we thought the work nicely shows the changes in vocal tract morphology and associated spectrum as an explanation for the dual pitch, but more teasing out of mechanism for the dual pitch perception is required in a way that might be accessible to readers.

See comments above.

[Editors’ note: further revisions were suggested prior to acceptance, as described below.]

[…]

eLife does not usually encourage multiple rounds of revision but this is a critical point in the interpretation of an interesting study, and I would encourage a revision with a much shorter final section of Discussion that explains a clear hypothesis related to the cause of the new pitch.

As we would like to see this work published with eLife, we have drastically truncated the highlighted section to create “a much shorter final section” as suggested. Given our lack of expertise in pitch perception, coupled with our appreciation for the comments raised, we instead (succinctly) reframed through the lens of looking ahead at future work. Specifically, we include only what we think are some quite interesting and provocative parallels we have observed between Sygyt song and cochlear mechanics. We believe that providing this as a summary to the narrative will help stimulate crosstalk between emerging viewpoints in cochlear mechanics and central processing (e.g., pitch perception).

As such, hopefully we have a more streamlined “story” that will be sufficient for

publication. We believe the rest of the work paints a clear picture as to how the

morphology leads to biphonation and that can stand on its own without over speculation on other facets.https://doi.org/10.7554/eLife.50476.sa2Article and author information

Author details

  1. Christopher Bergevin
    1. Physics and Astronomy, York University, Toronto, Canada
    2. Centre for Vision Research, York University, Toronto, Canada
    3. Fields Institute for Research in Mathematical Sciences, Toronto, Canada
    4. Kavli Institute of Theoretical Physics, University of California, Santa Barbara, United States
    Contribution Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology For correspondence cberge@yorku.ca Competing interests No competing interests declared

0000-0002-4529-399X

Chandan Narayan

Languages, Literatures and Linguistics, York University, Toronto, Canada

Contribution

Conceptualization, Investigation

Competing interests

No competing interests declared

Joy Williams

York MRI Facility, York University, Toronto, Canada

Contribution

Investigation, Methodology

Competing interests

No competing interests declared

Natasha Mhatre

Biology, Western University, London, Canada

Contribution

Investigation, Visualization, Methodology

Competing interests

No competing interests declared 0000-0002-3618-306X

Jennifer KE Steeves

  1. Centre for Vision Research, York University, Toronto, Canada
  2. Psychology, York University, Toronto, Canada
Contribution

Investigation, Methodology

Competing interests

No competing interests declared 0000-0002-7487-4646

Joshua GW Bernstein

National Military Audiology & Speech Pathology Center, Walter Reed National Military Medical Center, Bethesda, United States

Contribution

Investigation, Writing – original draft

Competing interests

No competing interests declared

Brad Story

Speech, Language, and Hearing Sciences, University of Arizona, Tucson, United States

Contribution

Software, Formal analysis, Investigation, Visualization, Methodology

For correspondence

bstory@email.arizona.edu

Competing interests

No competing interests declared

  1. 0000-0002-6530-8781

Funding

Natural Sciences and Engineering Research Council of Canada (RGPIN-430761-2013)

  • Christopher Bergevin

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

A heartfelt thank you to Huun Huur Tu, without whom this study would not have been possible. Input/suggestions from Ralf Schlueter, Greg Huber, Dorothea Kolossa, Chris Rozell, Tuomas Virtanen, and the reviewers are gratefully acknowledged. Support from York University, the Fields Institute for Research in Mathematical Sciences, and the Kavli Institute of Theoretical Physics is also gratefully acknowledged. CB was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant RGPIN-430761–2013. The identification of specific products or scientific instrumentation does not constitute endorsement or implied endorsement on the part of the author, Department of Defense, or any component agency. The views expressed in this article are those of the authors and do not reflect the official policy of the Department of Army/Navy/Air Force, the Department of Defense, or the U.S. Government.

Ethics

Human subjects: Data were collected with approval of the York University Institutional Review Board (IRB protocol to Prof Jennifer Steeves) This study was approved by the Human Participants Review Board of the Office of Research Ethics at York University (certificate #2017-132) and adhered to the tenets of the Declaration of Helsinki. All participants gave informed written consent and consent to publish prior to their inclusion in the study.

Senior Editor

  1. Barbara G Shinn-Cunningham, Carnegie Mellon University, United States

Reviewing Editor

  1. Timothy D Griffiths, University of Newcastle, United Kingdom

Publication history

  1. Received: July 24, 2019
  2. Accepted: January 31, 2020
  3. Accepted Manuscript published: February 12, 2020 (version 1)
  4. Accepted Manuscript updated: February 17, 2020 (version 2)
  5. Version of Record published: March 10, 2020 (version 3)

Copyright

© 2020, Bergevin et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.Metrics

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  1. Further reading

Further reading

  1. Listen to Chandan Narayan discuss throat singing Podcast A new study reveals how throat singing is produced.
    1. Physics of Living Systems
    Decoding the physical principles of two-component biomolecular phase separation Yaojun Zhang et al. Research Article Mar 11, 2021 Cells possess a multiplicity of non-membrane-bound compartments, which form via liquid-liquid phase separation. These condensates assemble and dissolve as needed to enable central cellular functions. One important class of condensates is those composed of two associating polymer species that form one-to-one specific bonds. What are the physical principles that underlie phase separation in such systems? To address this question, we employed coarse-grained molecular dynamics simulations to examine how the phase boundaries depend on polymer valence, stoichiometry, and binding strength. We discovered a striking phenomenon – for sufficiently strong binding, phase separation is suppressed at rational polymer stoichiometries, which we termed the magic-ratio effect. We further developed an analytical dimer-gel theory that confirmed the magic-ratio effect and disentangled the individual roles of polymer properties in shaping the phase diagram. Our work provides new insights into the factors controlling the phase diagrams of biomolecular condensates, with implications for natural and synthetic systems.

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https://elifesciences.org/articles/50476

Tisato G., Ricci Maccarini A., Tran Quang Hai (2001), “Caratteristiche fisiologiche e acustiche del canto difonico”

Standard

TQH TISATO 2004

Trân Quang Hai & Graziano Tisato in Venice, 2004

dav

Graziano Tisato & Trân Quang Hai in Padova, 13 october 2017

 

4-Andrea-Ricci-Maccarini-2

Dr. Andrea Ricci Maccarini

Click on this link below to read the integral article illustrated with spectral & acoustical analyses :

Tisato G., Ricci Maccarini A., Tran Quang Hai (2001), “Caratteristiche fisiologiche e acustiche del canto difonico”

II Convegno Internazionale di Foniatria – Ravenna 19 ottobre 2001

Caratteristiche fisiologiche e acustiche del Canto Difonico

Graziano G. Tisato, Andrea Ricci Maccarini, Tran Quang Hai

Introduzione
Il Canto Difonico (Overtone Singing o Canto delle Armoniche) è una tecnica di canto
affascinante dal punto di vista musicale, ma particolarmente interessante anche dal punto di vista scientifico. In effetti con questa tecnica si ottiene lo sdoppiamento del suono vocale in due suoni distinti: il più basso corrisponde alla voce normale, nel consueto registro del cantante, mentre il più alto è un suono flautato, corrispondente ad una delle parziali armoniche, in un registro acuto (o molto acuto). A seconda dell’altezza della fondamentale, dello stile e della bravura, l’armonica percepita può andare dalla seconda alla 18° (e anche oltre).
Per quanto riguarda la letteratura scientifica, il Canto Difonico compare per la prima
volta in una memoria presentata da Manuel Garcia di fronte all’Accademia delle Scienze a Parigi il 16 novembre 1840, relativa alla difonia ascoltata da cantanti Bashiri negli Urali (Garcia, 1847).
In un trattato di acustica pubblicato qualche decennio più tardi (Radau, 1880), la realtà di questo tipo di canto è messa in discussione: “…Si deve classificare fra i miracoli ciò che Garcia racconta dei contadini russi da cui avrebbe sentito cantare contemporaneamente una melodia con voce di petto e un’altra con voce di testa”.
Deve trascorrere quasi un secolo dal 1840 prima che si ottenga un riscontro obbiettivo
della verità del rapporto di Garcia, con le registrazioni fatte nel 1934, fra i Tuva, da etnologi russi. Di fronte all’evidenza della analisi compiuta nel 1964 da Aksenov su quelle registrazioni, i ricercatori cominciarono a prendere in considerazione il problema del Canto Difonico (Aksenov, 1964, 1967, 1973). Aksenov è il primo ad attribuire la spiegazione del fenomeno al filtraggio selettivo dell’inviluppo formantico del tratto vocale sul suono glottico, e a paragonarlo allo scacciapensieri (con la differenza che la lamina di questo strumento può ovviamente produrre solo una fondamentale fissa). In quel periodo compare anche un articolo sul Journal of Acoustical Society of America (JASA) sulla difonia nel canto di alcune sette buddiste tibetane, in cui gli autori interpretano correttamente l’azione delle formanti sulla sorgente glottica, senza
tuttavia riuscire a spiegare come i monaci possano produrre fondamentali così basse (Smith et al., 1967).
A partire dal 1969, Leipp con il Gruppo di Acustica Musicale (GAM) dell’Università
Paris VI s’interessa al fenomeno dal punto di vista acustico (Leipp, 1971). Tran Quang Hai, del Musée de l’Homme di Parigi, intraprende in quel periodo una serie di ricerche sistematiche, che portano alla scoperta della presenza del Canto Difonico in un numero insospettato di tradizioni culturali diverse (Tran Quang,1975, 1980, 1989, 1991a, 1991b, 1995, 1998, 1999, 2000, e il sito Web http://www.baotram.ovh.org). L’aspetto distintivo della ricerca di Tran Quang Hai è la sperimentazione e verifica sulla propria voce delle diverse tecniche e stili di canto, che gli ha permesso la messa a punto di metodi facili di apprendimento (Tran Quang, 1989). Nel 1989 Tisato analizza e sintetizza il Canto Difonico con un modello LPC, dimostrando per questa via che la percezione degli armonici dipende esclusivamente dalle risonanze del tratto vocale (Tisato, 1989a, 1991). Nello stesso anno anche il rilevamento endoscopico delle corde vocali di Tran Quang Hai confermava la normalità della vibrazione laringea (Sauvage, 1989, Pailler, 1989). Nel 1992 compare uno studio più approfondito dal punto di vista fonetico e percettivo,
che mette in risalto la funzione della nasalizzazione nella percezione della difonia, la presenza di una adduzione molto forte delle corde vocali e una loro chiusura prolungata (Bloothooft et al., 1992). Gli autori contestano l’ipotesi fatta da Dmitriev che il Canto Difonico sia una diplofonia, con due sorgenti sonore prodotte dalle vere e dalle false corde vocali (Dmitriev et al., 1983). Nel 1999 Levin pubblica sul sito Web di Scientific American un articolo particolarmente interessante per gli esempi musicali che si possono ascoltare, le radiografie filmate della posizione degli articolatori e della lingua, e la spiegazione delle tecniche di produzione dei vari stili del Canto Difonico (Levin et al., 1999, http://www.sciam.com/1999/0999issue/0999levin.html).
Il lavoro che presentiamo qui è il risultato di una recente sessione di lavoro con Tran
Quang Hai (ottobre 2001), in cui abbiamo esaminato i meccanismi di produzione del canto difonico con fibroendoscopia. La strumentazione utilizzata era costituita da un fibroendoscopio flessibile collegato ad una fonte di luce stroboscopica, per valutare quello che succedeva a livello della faringe e della laringe, e un’ottica rigida 0°, collegata ad una fonte di luce alogena, per esaminare il cavo orale.

Gerrit Bloothooft, Eldrid Bringmann, Marieke van Cappellen, Jolanda B. van Luipen, and Koen P. Thomassen : A phonetic study of overtone singing

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Abstract

We describe the phenomenon of overtone singing in terms of the classical theory of speech production. The overtone sound stems from the second formant or a combination of both the second and third formants, as the result of careful, rounded articulation from //, via schwa // to /y/ and /i/. Strong nasalisation provides, at least for the lower overtones, an acoustic separation between the second and first formants, and can also reduce the amplitude of the first formant. The bandwidth of the overtone peak is remarkably small and suggests a firm and relatively long closure of the glottis during overtone phonation. Perception experiments showed that listeners categorize the overtone sounds differently from normally sung vowels.

A phonetic study of overtone singing

 

Gerrit Bloothooft, Eldrid Bringmann, Marieke van Cappellen, Jolanda B. van Luipen, and Koen P. Thomassen

 

 

Research Institute for Language and Speech, University of Utrecht
Trans 10, 3512 JK Utrecht, The Netherlands

 


1. Introduction

Overtone singing is a special type of voice production resulting in a very pronounced, high and separate tone which can be heard over a more or less constant base sound. The technique is rarely used in Western music but in Asia (especially Mongolia and Tibet) it is more common and overtone singing can be heard during secular and religious festivities. The high tone follows a characteristic musical scale [for instance, for pitch C3 (130.8 Hz) (- and + indicate a deviation from the exact tone): C3, C4, G4, C5, E5-, G5, A5+, C6, D6, E6-, F6+, G6, G#6+, A6+, B6-, C7,… ], from which it can be concluded that one really hears an overtone of the fundamental.

The literature contains only a few reports on overtone singing [1,5,7,8], which indicate both the importance of formants and register type. In this paper we present both an acoustic analysis of overtone singing and a study to evaluate the perception of the overtone sounds, in relation to normally sung vowels.


2. Material

We have recorded series of sung overtones from a singer with many years of experience in overtone singing, both as a performer and as a teacher. In this paper we describe the results for an Fo value of 138 Hz (C#3). In addition, 12 Dutch vowels /a/, /a/, //, /o/, /e/, //, //, /i/, /oe/, //, /u/, and /y/, sung in a normal way at the same Fo, were recorded.


3. Acoustic analysis

The recordings were digitized at a rate of 10 kHz and stored in a computer. From the middle, stable, part of each recording 300 ms was segmented. Average power spectra were obtained from FFT analyses (1024 points, shift 6.4 ms) over this segment. Formant frequencies were computed on the basis of appropriate LPC or ARMA analysis.


3.1. FFT-Spectra

Figure 1 shows the average FFT spectra of all overtone recordings. Despite the averaging procedure, the width of each individual harmonic is limited, indica-ting the stability of Fo over the interval (standard deviation of Fo was less than 0.1 semitone in all cases). It can be seen from the shifting peak in the spectra that overtone singing seems interpretable as a special use of a formant. Obviously, the singer tries to match a formant with the intended overtone frequency and succeeds very well.

Frequency (kHz)

FIG. 1. Average FFT spectra for overtone sounds, sung at Fo = 138 Hz (C#3). The overtone sounds are numbered according to the main partial involved.

3.2. Formant frequency analysis

In Fig. 2 we present formant frequency results for both the overtone sounds and the sung vowels in the F1 – F2 plane. The figure shows two modes in the production: firstly, the overtone sounds 4-6 around /u/, and secondly, the track from // to /i/.

In the first mode, it can be seen from the FFT-spectra that there is energy absorbtion around 400 Hz, indicating a strong nasalisation. The characteristic overtone sound resides in the second formant, as others [1,8] had already suggested. The bandwidth of the second formant is very narrow and, especially for the lower overtones, seldom exceeds 40 Hz. This indicates little acoustic damping in production: firm glottal closure and small losses in the vocal tract. All these characteristics indicate a low, rounded, nasalised, back vowel /u/ or // (low F1 and F2, a nasal pole/zero pair, and suppressed F3 [3]).

The second mode in the production of an overtone sound, applies for overtone frequencies higher than 800 Hz. The main peak of the spectrum still rises in tune with the intended overtone frequency and is interpreted as a combination of F2 and F3. It may be of interest that the singer explains this series of overtones with the articulatory variation during the word ‘worry’. It is known, already from the Peterson and Barney data, that in a retroflex /r/ the F3 frequency can be remarkably low and can approach the F2 frequency. This has also been mentioned by Stevens (1989), especially in combination with liprounding, while Sundberg (1987) mentioned the effect as the acoustic result of a larger cavity directly behind the front teeth.

For the higher overtone sounds, the articulation comes near /y/ and /i/, where continued lip rounding makes it possible to bring F2 and F3 together [4], although for the highest overtones a subtle lip spread may be needed to reduce the front cavity to a minimum.

 

FIG. 2. F1 – F2 plane for stimuli sung at Fo = 138 Hz, with positions of the vowels (IPA symbols) and overtone sounds (represented by the number of the corresponding partial).


3.3. The glottal factor

The very narrow bandwidth of the “overtone formant” suggests a good and long glottal closure. We believe that the singer used modal register, with a relatively long glottal closure, originating from a firm glottal adduction. This hypothesis does not exclude that performers may use the vocal fry register as well [7]. In all cases, the long glottal closure requires a strong adduction of the vocal folds, which could easily result in general muscular hypertension in the pharyngeal region. This may relate to the prominent role of the buccal cavity, suggested by Hai (1991).


3.4. Intensity analysis

Up to an overtone frequency of 1.5 kHz, the overtone harmonic has a stable relative intensity of -10 dB relative to overall SPL, and dominates the spectrum. For higher frequencies, the relative level of the overtone harmonic sharply drops with a slope of about -18 dB/octave.


4. The perception of overtone singing

4.1. Material, listening experiment, and analysis

As stimuli we used the combined set of 14 overtone sounds and 12 Dutch vowels. From these stimuli we used the same segment (300 ms) as had been used for the acoustical analyses, but we shaped the first and final 25 ms sinusoidally to avoid the perception of clicks. In a computer-controlled experiment, these stimuli were judged by fifteen listeners on ten 7-point bipolar semantic scales. Further details of semantic scales will be presented in a forthcoming paper. The judgements were analyzed by means of multidimensional preference analysis MDPREF [2]. In the technique of MDPREF a stimulus space is constructed in which distance corresponds to perceptual (dis)similarity.


4.2. The perceptual stimulus space

The plane of the first two dimensions of the stimulus space is shown in Fig. 3. 41 % of the total variation in the judgements was explained in this plane, while higher dimensions each explained less than 6.3 %.

 

FIG. 3. The perceptual stimulus space. The overtone sounds are given by the number of their corresponding partial, the vowels by their IPA symbol.

The overtone sounds and normally sung vowels are perceptually separated clusters. The vowels are situated roughly in a triangle, with the cardinal vowels /i/, /u/, and /a/ at the angles. The overtone sounds are roughly ordered according to their harmonic number, although the stimuli numbered from 4 to 10 can be described as a cluster. This probably relates to the constant relative energy of the overtone harmonic for this set. The direction of the overtone sounds is, from the lower to the higher numbers, about the same as from /u/ to /i/, as may be expected from the relation between harmonic numbers and F2 frequency values.


4.3. A physical description of the perceptual stimulus space

We attempted to match the perceptual stimulus space with multidimensional physical descriptions of the stimuli [formant frequency space (see Fig. 2), 1/3-octave bandfilter energy space both by means of the Plomp metric and the Klatt metric [2,6]]. These attempts were not successful (low correlations between coordinate values along dimensions) because of the division into two clusters of the stimulus space, for which these metrics do not present an explanation. Some additional perceptual sensitivity to the very small bandwidth of the “overtone formant”, which clearly physically separates overtone sounds and normally sung vowels, seems necessary to explain the results.


5. REFERENCES

[1] Barnett, B.M. (1977), “Aspects of vocal multiphonics”, Interface 6, 117-149.
[2] Bloothooft, G. and Plomp, R. (1988), “The timbre of sung vowels”, JASA 84, 847-860.
[3] Fant, G. (1960), ” Acoustic theory of speech production” The Hague: Mouton.
[4] Fujimora, O., and Lindquist, J. (1970), “Sweep-tone measurements of vocal tract characteristics”, JASA 49, 541-558.
[5] Hai, T.Q. (1991), “New experiments about the Overtone Singing Style”, Proc. Conference ‘New ways of the voice’, Becançon, 61.
[6] Klatt, D.H. (1982), “Prediction of perceived phonetic distance from critical-band spectra: a first step”, Proc. ICASSP, Paris, 1278-1281.
[7] Large, J. and Murry, T. (1981), “Observations on the nature of Tibetan chant”, J. of Exp. Research in Singing 5, 22-28.
[8] Smith, H., Stevens, K.N., and Tomlinson, R.S. (1967), “On an unusual mode of chanting by certain tibetan lamas”, JASA 41, 1262-1264.
[9] Stevens, K.N. (1989), “On the quantal nature of speech”, J. of Phonetics 17, 3-45.
[10] Sundberg, J. (1987), “The science of the singing voice“, Dekalb: Northern Illinois University

 http://www.let.uu.nl/~Gerrit.Bloothooft/personal/Publications/ICPhS1991overtones.htm

Werner A. Deutsch & Franz Födermayr: Visualization of Multi – Part Music

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 Frequency analysis of musical sounds came up to practical applications with the development of the Sound Spectrograph (Koenig, Dunn and Lacey, 1946). From the beginning much care has been taken to choice the frequency resolution and the time window properly in order to highlite important acoustical features as well as perceptual ones. It has been demonstrated by several studies (i.e. Potter, Kopp and Green, 1947) that the aural presentation of speech (and music) and its simultaneous graphic representation produces significantly deeper insight into the generation of acoustical signals and the ongoing perception as listening alone can provide.

Visualization of Multi – Part Music
(Acoustics and Perception)

Werner A. Deutsch (Austrian Academy of Sciences, Acoustics Research Laboratory) and
Franz Födermayr (Institute of Musicology, University of Vienna)

Introduction

Frequency analysis of musical sounds came up to practical applications with the development of the Sound Spectrograph (Koenig, Dunn and Lacey, 1946). From the beginning much care has been taken to choice the frequency resolution and the time window properly in order to highlite important acoustical features as well as perceptual ones. It has been demonstrated by several studies (i.e. Potter, Kopp and Green, 1947) that the aural presentation of speech (and music) and its simultaneous graphic representation produces significantly deeper insight into the generation of acoustical signals and the ongoing perception as listening alone can provide.

Graf (1963) recognized the enormous potential of spectrographic analysis for applications in ethnomusicology. His theoretical concept assumes the acoustical signal to be the primary stimulus which is processed by the human psychophysiological system very much in the same way, even in different ethnic populations. What makes the various differences in interpretation, reception and perception under very similar acoustical stimulus representations prominent, is due to the influence of the so called social-cultural context in which music plays an important role.

Production Models

The pertinent acoustic analysis of musical signals with acoustic laboratory methods (which today can be performed by using a specially equipped laptop computer.) produces basically a complete set of acoustical parameters which can be displayed as graphical images of the spectral content, i.e. the physics of the musical signal in real time or of those performances which have been recorded in advance. The analysis data can be used as input to comprehensive production models of voice( see: Fant, G. (1970) Acoustic theory of speech production. Mouton, The Hague; 2nd edition), musical instruments and musical ensembles. Sound source characteristics, tuning, musical scales, timbre, agogics, free field and room acoustics etc. can be observed on the analysis parameters extracted directly from the musical signal. Musical scales, vibrato, pulsato, beats are measured and detected on the basis of the fundamental frequency analysis data and their related spectral components, timbre is very much determined by the spectral envelope of the signals, duration and rhythms are mainly derived from the energy contour etc.

Perception Models

Whereas production models of the singing voice and musical instruments describe the acoustics of musical sound sources only, perception models deal with the signal processing of the listeners auditory periphery, its associated central pathways and cortical functions. It has to be admitted that psychoacoustics first started from an acoustical engineering approach in order to collect all technical basic data of the human auditory system, as selectivity measured in terms of absolute thresholds, difference limens in frequency, sound pressure level, signal duration and many other psychophysical functions. Most of the early psychoacoustical research was launched by telephone technical laboratories ( Fletcher, H. 1929, 1953), by the need to avoid noise and distortions on the telephone lines or for compensation of the hearing loss of listeners. Engineers, physiologists and neurologists have described the mechanics of the outer and middle ear, the hydromechanics of the inner ear ( Bekesy, G.v. 1960), the hair cell system and the resulting neural response up to the brainstem ganglions as well as acoustical evoked responses on the cortex. For technical and methodological limitations this early research has been done in most cases applying musically less relevant sinusoids, which could be controlled in experimental procedures with sufficient accuracy. This has been critisized frequently by musicologists for dealing rather with musicological non relevant aspects of sound and arbitrary functions of the auditory system instead of referring to the cognitive concepts of music.

Nevertheless, as the work in psychoacoustics progressed, the basic data obtained from the human auditory system contributed to a comprehensive theory of hearing, which today is capable to include highly relevant aspects of auditory localization, speech and music perception. Today psychoacoustical models explain complex perceptual functions, as musical pitch of complex tones, melody contours, consonance-dissonance, simultaneous masking, forward and backward masking, figure-background discrimination as well as Gestalt of musical rhythms etc.

Visualization of polyphony

FFTs and Spectrograms

Applying the psychoacoustic knowledge to spectrographic analysis of polyphony, the visualization of musical signals represents both, the graphical output of psychoacoustic perception models and the physics of sound. The spectral analysis of any arbitrary acoustical signal at a given instant is obtained by its Fourier Transform which produces a pair of real-valued functions of frequency, called the amplitude (or magnitude) spectrum and the phase spectrum. The amplitude spectrum stays moreover as a first approximation for the (neuro-) physiological representation of the signal in the human auditory system, the phase spectrum can be neglected for spectrographical purposes:

As the time variant signal goes on, many closely time windowed overlapping Fourier Transforms have to be computed at short successive intervals (< 30 ms) in order to produce a pseudo-3dimensional continuous graphic display of the sound, the spectrogram. In general narrow band frequency components with slow variations in frequency are detectable as horizontal frequency lines, whereas very fast changes or signal envelopes of a transient nature appear as vertical broad band bars in the spectrogram. Many musical instrument sounds (plucked strings, striked bars etc.) have a very short broad band attack and a narrow band slowly decreasing decay. Thus the onset of a note is easily identified, not so the end of the decay especially in reverberant environments).

Beats: From left to right: simple tone 220 Hz, simple tone 227 Hz, two tone complex 220 Hz + 227 Hz with beating, two tone complex 220 Hz + 240 Hz (light roughness), two tone complex 220 + 260 Hz (roughness), two tone complex (musical fifth).

Interference, Beats and Roughness

Usually directly incident or reflected waves from many sources, sounding simultaneously (musical instruments, singing voices etc.), are superposed at the listeners ear position, producing interference when components of equal frequency appear. Constructive interference takes place when the crests of two waves coincide, resulting the amplitude will be twice that of either wave. Destructive interference occurs when the crests of one wave fall on the troughs of the second and cancellation will be obtained. In case of interference of components slightly different in frequency beats can be perceived. The beat frequency is given by difference between the frequencies sounding together; beats can be detected on the spectrogram as periodic rise and fall in amplitude on a single (horizontal) frequency line. Whenever the frequency difference exceeds a certain value of 20 Hz no beating can be heard anymore and the perception of roughness is raised which has its maximum between 40 and 70 Hz. Increasing the frequency difference further on (see: critical bandwidth) produces two tone perception.

Masking

One of the most difficult phases in the investigation of spectrograms is the decision wether or not a spectral component of a signal which physically exists can be perceived by the auditory system and to what extent. The phenomenon that spectral components of a complex tone are not audible, despite their considerable amplitude measured, is described by the human auditory masking function. Masking is (1) the process by which the threshold of audibility for one sound is raised by the presence of another (masking) sound and (2) the amount by which the threshold of audibility of a sound is raised by the presence of another (masking) sound. The unit customarily used is the decibel (ANSI S3.20-1973). Masking may be seen as a general loss of information or as an undesired decrease of sensitivity of the auditory system but in contrary it is one of the most important auditory functions in order to perform the frequency analysis of the ear. Masking helps to process the sound into perceptual relevant components either belonging to the same or different sounds; it determines which components are resolved by the ear as audible harmonics with spectral pitch as well as it fuses higher harmonics according to the auditory critical bandwidth.

Critical Bands

The critical band in hearing can roughly be described as that frequency band of sound, in between that two spectral components influence one another. This influence can be expressed in terms of masking, loudness summation, roughness, consonance, dissonance etc. The bandwidth of the critical bands remains constant with 100 Hz up to a frequency of 500 Hz and increases up to 17\% of the midfrequency value beyond 500 Hz. Consequently the distribution of the spectral components of any acoustical signal along the basilar membrane of the inner ear is best approximated by the Bark\footnote{according to the acoustician Barkhausen (1926). scale which corresponds to the frequency spacing of the critical bands. A formal expression for the computation of the Bark scale has been given by Zwicker and Terhardt (1980). The unit of frequency (f) is assumed to be in kHz, arctan in radiants:

  •  z_c /Bark = 13 arctan (0.76 f/kHz) + 3.5 arctan (f /7.5 kHz)2

As a result of the Bark transformation a much better frequency resolution in the linear low frequency range up to 500 Hz is obtained. The resolution is progressively reduced at higher frequencies. Spectrograms using the Bark scale represent the psychoacoustical frequency spacing of the inner ear and can be interpreted in terms of perceptual relevant spectral frequency distribution.

Relevance-Spectrography

The transformation of the frequency axis into Bark scale and the extraction of irrelevant spectral components from the signal creates a so-called Relevance-Spectrogram which contains those frequency components only which evoke neurophysiological activity (SPL-Ecxess). It represents the signal associated to the neural excitation pattern in the auditory nerve, containing the relevant information parameters for the processing at higher neural levels. Thus the musical interpretation of spectrograms is highly facilitated as irrelevant signal parts can not show up. Moreover by applying an categorized intensity detection procedure (a concept of overmasking) the most prominent spectral peaks of the signal are extracted and figure-background discrimination can be obtained ( Deutsch \& Noll, 1993). This enables the listener to follow the leading voice without interference of the background signal in many cases.

Pitch

The perception of pitch of complex tones has been a topic discussed extensively in psychoacoustics since the well known controversy beween Hermann von Helholtz and Georg Simon Ohm on one side and August Seebeck on the other. The problem, which is still an important question in hearing theories, started from Seebecks observation that the pitch of a complex tone with a missing fundamental still remains at the pitch level of the fundamental frequency. Ohms acoustic law followed Fouriers theorem and stated in contrary, pitches of frequencies which existe objectively (as components of a complex tone) can be heard only. Ohms acoustical law strongly supported Helmholtzs hearing theory according to which the partials of a complex tone are distributed along the basilar membrane (place theory) and resonance is responsible {Note: Helmholtzs experimental setup consisted mainly in resonators, he invented). His acoustical sources have been tuning folks. Seebeck used an acoustic siren, blowing air against the holes of a turning disk. By proper spacing of the holes a complex tone is produced without its fundamental frequency. for the mechanical stimulation of the hair cells. He explained Seebecks missing fundamental phenomenon by arguing nonlinearities in the inner ear would evoke the low frequency pitch, creating an objective product of nonlinearity (difference tone or combination tone between the higher harmonics) at the place of the fundamental frequency.

Modern pitch theory is based on the results of Georg von Bekesys and J. F. Schoutens work. Both have stimulated the research on pitch perception for about 50 years. Bekesys travelling wave theory is strongly supported by physiological experiments (Bekesy, 1960) and Schoutens (1940) observations on the residue pitch made evident, that the ear works in both domains simultaneously: in the frequency domain by means of hydromechanics with a far then perfect result of a Fourier Transform and in the time domain where any onset or even a slight change in the regular vibration of the basilar membrane is detected.

Fianlly pitch has been defined as that attribute of an auditory sensation in terms of which sounds may be ordered on a scale extending from low to high. The unit of pitch was assigned the mel (ANSI S3.20-1973). Thus pitch depends primarily upon the frequency of the sound stimulus, but it also depends upon the sound pressure and the waveform on the stimulus. The pitch of a sound may be described by the frequency or frequency level of that pure tone having a specified sound pressure level that is judged by subjects to have the same pitch.

The discussion on pitch perception came to an premature end when Terhardt (1974) published a model of pitch perception which includes both, the virtual pitch and the spectral pitch. He applied the concept of Gestalt perception, which in musicology frequently is understood to describe sequential melody contours only, on simultaneous sounding partials of a single complex tone. This enables the listener to still perceive the complex tone as a whole even when prominent components are missing (e.g. the fundamental frequency) or when their amplitude is as low that they can not contribute to pitch perception. Thus two general modes of pitch perception have to be encountered: the holistic mode integrating the partials of any complex tone to a good Gestalt, evoking virtual pitches and the analytic mode, focussing more on the spectral components of the sound and isolating individual partials of the complex tone as it is described by the concept of spectral pitch.

The following conclusions for the today work in pitch perception and music transcription have to be drawn:

  • the pitch of a complex tone very likely may be ambiguous,
  • pitch matches have therefore to be done with sinusoids only,
  • spectral pitch and virtual pitch may exist in between the same individuum, responding to the same sound, dependent upon subjective experiences,
  • musical theories of melody and counterpart introduce interpretative framework which not necessarily must correspond with perception.

Example 1: Highland Bagpipe

In the case of drone polyphony at least two psychoacoustical phenomena are generally relevant: masking and interference; the special characteristic of the drone sound is given by its relative stationarity in pitch and timbre throughout the total duration of the musical piece or a part of it, enabling melody tones to interfer with related spectral components of the drone. The following example is taken from a pibroch played on a Piob Mhor (highland bagpipe, Vienna Phonogramm Archive, Tape 17979, J. Brune, 1973). The key of the pipe chanter is usually spoken as A. The two tenor drones are tuned to the octave below the A of the chanter and the bass drone sounds an octave lower still ( Mac Neill, S. & Richardson, 1987). In our example the frequency value of /A/ is 116 Hz. The drone pipes produce a harmonic amplitude spectrum up to 7 kHz. Some partials show slow beats appearantly according to the slight mistuning of both tenor pipes. The ornamental sections of the sound probe are of equal overall duration (820 ms), whereas the sustained melody tones vary in duration from 1920 to 2830 ms. Interference is given mainly between the 4th, 5th, 6th and 8th harmonic of the drone and 1st harmonic of the sustained melody tones (/a3/, /c4 sharp/, /e4/, /a5/) depending upon their amplitude relation.

Spectrogram: Piob Mhor (highland bagpipe, Vienna Phonogramm Archive, Tape B17979, J. Brune, 1973). Spectrogram unprocessed.
Piob Mhor: according to the irrelevance-threshold signal processed, all spectral components below the masked threshold have been extracted. Approximately 67% of the weaker FFT-amplitudes have been set to zero.

Piob Mhor: difference signal, 67\% of the weaker amplitudes represent the signal below the masked threshold (irrelevance threshold). After being extracted from the original signal these components can be made audible again. The superposition of this spectrogram and the 2nd exactly produces the first spectrogram as well as the difference signal + irrelevance corrected signal = original..
Generally the sustained longer chanter (melody) pipe tones interfere (11s to 16s) with higher harmonics of drone tones, alternating with notes having no interference with the drone (see 8s to 11s) and short melody tones constituing the melismes (at 2s to 8s, 14s). The occurence of beats at each 2nd harmonic of the drone spectrum indicates beating between the two tenor drone pipes with a frequency difference of 0.85 Hz. The beating between the 2nd and the 4th harmonic of the drone with a rate of approximately 1.7 Hz is not of most perceptual importance. This beating does not effect the overall drone sound dominantely. Perceptually more relevant is the beating between the partials of the drone and sustained melody tones seen at 2.6s to 6s, 11s to 13s etc.

The interference of spectral components of both, the drone and the melody tones can be observed already on the spectrogram (fig. 1). Its perceptual relevance as indicated above can be seen in the relevance-spectrogram (fig. 2) from which the masked components of the signal have been removed. What happens to the signal when the masked threshold has been computed is demonstrated in the difference signal (fig. 3). From the lower harmonics of the drone sound, a2 and a3 are not affected by masking, as well as the 6th harmonic (e5). This results in a continous prominence of the fundamental and the fifth of the drone, the first corresponding to the basic tone of the melody, the second corresponding to the dominant tone of the melody. This fact has been mentioned already by Collinson (1970:167); Brune (1981:48) and MacNeill & Richardson (1987:32) but they all explained it by focussing on a strong 3rd harmonic of the bass drone. In contrary the example currently under investigation shows a very week 3rd harmonic of the bass drone and a strong, almost unmasked 3rd harmonic of the tenor pipes.

Several harmonics of the chanter pipes are stroger than the drone and consequently mask their neighbouring partials of the drone. The first partial of a4 of the chanter masks e4 and c-sharp5 of the drone sound and the first partial of e5 of the chanter masks c-sharp and g of the drone sound; whereas the sustained melody tones c-sharp5 and f-sharp5 themselves are partially masked by the harmonics of the drone sound. Taken together, the results of these observations provide psychoacoustical evidence (1) for the characteristic hierarchical structure given by the fifth a-e of the melody, which is strongly supported by the masking phenomenon. (2) The continuous sounding drone enlarges the overall frequency range downward, anchoring the melody into the tonal space.

Example 2: Bulgarian Multi-Part Song

The next example (fig.4 to 6) shows the role of roughness and frequency fluctuations (tremolo) as characteristics of a diaphonic type of Bulgarian multi-part singing (Messner, 1980:passim; Brandl, 1992; Födermayr & Deutsch, 1992:381-384). Masking has no effect in the region of the fundamental frequencies, even at the strongest partials (2 and 4) weak masking can be observed only. It does not influence the constituting elements of the sounds. Thus the partials of the individual voices interact with their full objective existent amplitudes. Throughout the whole piece a characteristic interval between two voices is produced, fairly constant with a width of three quarters of a whole tone. The resulting frequency differences between the fundamental frequencies are in the range of 30 Hz, evoking the sensation of roughness. Even when strong tremolo appears in Tressene figures, the average frequency difference remains close to 150 cents. Generally start and target points of exclamations fall on frequency values of the characteristic interval. The rate of the tremolo ranges between approximately 4 and 8 fluctuations /s which is known close to the ears maximum of sensitivity to frequency modulation.

Long term spectrogram of Bulgarian multi-part song: Balkanton BHA 2067, II 6. The duration of the piece is 39s. The spectrogram shows the segmentation of the song in  3 x 3 parts of equal duration.

Segment No. 3 (8s – 13s) of Bulgarian multi-part song: Balkanton BHA 2067, II 6. The spectrogram shows the characterstic interval of 150 Cents, several exclamations and two tremolo of 8 and 4 Hz fluctuation rate

Example 3: Epic Chant, Gujarat

The sound of the drone instrument ( Tharisar, Födermayr, 1968) is characterized by a single pitched (233 Hz) harmonic spectrum with decreasing amplitudes. The recitation as well as the sung parts follow the fundamental frequency of the drone sound with distinct variations. Short quasi-stationary tones of the recitation have an ambitus up to several whole tones using the fundamental frequency of the drone as midfrequency value, those of the sung parts are asymmetric and clother to the drone frequency with intervals downwards to a semi tone and upwards to a third. The drone implements a tonal function as finalis of the song. Roughness is produced during the sung parts only due to the interference of the drone and sustained voiced tones.

Long term spectrogram: Epic Chant of the Kunkana, Gujarat (PhA B 12125). The first 3s of the sound example show the drone isolated, followed by drone and recitation (3s – 15.5s) and sung part segments (15.5s – 30s). This example demonstrates the special kind of voicing during the parlando up to the first half duration of the sound segment displayed (up to 15s) and the song section with melodic lines closely related to the drone tones. The drone is given by a friction idiophone (Tharisar).

Epic Chant of the Kunkana, sung part segment, duration 3.5 s. The asymetry of the sung part in relation to the drone frequency can easily be detected from the first and 2nd harmonic.

Example 4: Lullaby in Yodel-technic, Bangombe Pygmies

The interdependence of pitch and timbre has been pointed out already in the section on pitch perception. The Yodel-technique of the Bangombe Pygmies elicitates both different modes of pitch perception: virtual pitch and spectral pitch. Two female voices exhibit the following variations:

  • tone to tone change of voice register: chest – falsetto
  • no isoparametric tone sequences with register change
  • unisono with different register: upper voice chest, lower voice falsetto
  • tone to tone vowel quality change (first and second vowel formant effect), upper voice: vowel /a/ chest, lower voice vowel /i/ falsetto, vowels /a/, /ae/ chest voice

The interaction between pitch, vowel quality and register change causes selective amplification of partials in the area of the vowel formant peak frequency, in the range of the first or 2ndnd partial of the female voices (633 Hz). The harmonics are sufficiently spaced apart to be resolved by the ear, producing virtual as well as spectral pitches. Whenever the fundamental frequency is significantly weaker as the 2ndnd harmonic, spectral pitch can be perceived by the analytic type of listeners. At will the perception can be focussed on the fundamental again and a holistic type of listening occurs.

Lullaby of Bangombe pygmy women (PhA B10840 G. Kubik, 1965): the peak amplitude contour of the solo part shows the A-B-A pattern of fundamental /e5-flat/ – 2nd harmonic /b4-flat/ – fundamental /e5-flat/ and so on. Falsetto tones are marked in diamonds. The inherent pattern of the upper voice is indicated, starting at 114 s.

The perceptual pitch ambiguity can best be described on the basis of the spectrogram: the peak amplitude of the beginning solo part shows the A-B-A pattern of fundamental /e-flat/ – 2ndnd harmonic /b-flat/ – fundamental /e-flat/ etc. According to the virtual pitch perception /e5-flat/ /b4-flat/ /e5-flat/ has to be perceived whereas subjects following the sepctral pitch hear /e5-flat/ /b5-flat/ /e5-flat/. The spectrogramm clearly shows the fundamental frequency contour. The phenomenon described has been addressed by a number of investigators and in detail by Albrecht (1972). By further analysing the spectrogram a melo-rhythmic pattern in the upper voice (120s to 134s) can be identified; it is aready seen as inherent pattern in the beginning of the solo part starting from the third phrase. The perception of the inherent pattern can be explained by the similarity of timbre of neighbouring tones, the falsetto /f/ and /e-flat/ of phase 3 and the chest voice /c/ /b-flat/ as well as /b-flat/ /g/ of phrase 4. Approximately at location 115s (marked with an asterix) /b4-flat/ is perceived instead of /b5-flat/ which exists objectively. This octave error helps to obtain the continuity of the melody in order to support the good Gestalt. Finally even in parts both voices are in unisono the distinction between the individual voices can easily maintained due to the predominant difference ebtween the chest and falsetto register.

In conclusion and for further studies on that line the spectrogram has been proved as an indespensible basis for the evaluation of complex tonal patterns as represented by the example described.

Lullaby of Bangombe pygmy women: duet. The arrows pointing downward indicate spectral components associated witjh the upper voice. Arrows pointing upward indicate those belonging to lower voice.


continuation of previous spectrogram.

Example 5: Overtone Singing: Tran Quang Hai

Overtone singing of the nature given by mongolian and turk people (as well as by Tran Quang Hai’s reproductive performances) is characterized by (1) a sustained fundamental frequency contour and (2) a melody which is composed from harmonic overtones of that fundamental frequency. The overtone phenomenon has been recognized to be an acoustical factor of the special setting of resonances of the human vocal tract. It has been sufficiently explained by the acoustic theory of voice production (Fant, 1960). Moreover this example shows the coincidence of a production model and the corresponding perception model.

Tran Quang Hai: overtone singing, spectrogram.

The acoustic model of the speech production assumes the glottal spectrum as the primary source for voiced sounds and the vocal tract acting as a filter attached on it: the glottal spectrum consists of a series of harmonics produced by glottal air pulses described in a model according to the myoelastic theory of {Berg (1957)} which has been accepted widely. The slope of the {\em source spectrum} depends on the shape of the individual closing and opening of the vocal folds during one fundamental period; a glottal waveform with more sudden closures produces stronger high frequency harmonics and a sharper timbre or voice quality. The fundamental frequency of the voice is determined by the repetition rate of the glottal pulses which is controlled (1) by the laryngeal musculature affecting the tension and the mass distribution of the vocal chords and (2) by changes of subglottal pressure. Decreased subglottal pressure, reduced mass of the vocal chords and increased tension raise the fundamental frequency.

The tube of the human vocal tract with a length of approximately 17,5 cm is attached on top of the laryngeal section. Its cross section can be changed to wider and narrower constrictions by the walls of the pharynx, the tongue, the jaw opening and the lips. The formant frequencies of vowels are related to the length of the tube and its shape. They represent the resonance frequencies of the vocal tract in non nasalized sounds. When the nasal tract is coupled on, by lowering the soft palate, the amplitude of the vowel formants decreases and a more complex resonace/antiresonace behavior of the vocal tract can be observed. The special setting of overtone singing suppresses the formant frequencies of the normal voice and emphasizes a very small frequency range, as narrow that one partial is amplified only. The result is shown in the spectrograms (fig. 12,13); the fundamental frequency is continuously sounding on one sustained low pitch and the melody is controlled by proper changing of the main resonace frequency. Thus overtone melodies can be played by picking out individual harmonics from the complex tone of the glottal pulse.

Tran Quang Hai: overtone singing. The output of the model of voice production (Linear Prediction Coding, 24 coefficients) extracts the first overtone of the fundamental frequency and the harmonics with the peak amplitude. The overtone melody is produced by setting the vocal tract main resonances accordingly.

The point to be emphasized is that in this case a coincidence of a (voice) production model and the associated perception model can be stablished. Nevertheless it has to be examined from case to case which aspects of the production model can be considered as significant for the perception.

Conclusion

Although these examples are of demonstrative nature only they are consistent with the general concept of introducing acoustics, physiology and psychoacoustics into the process of musical analysis. We have excluded for reasons not outranging the size of this contribution only the very challenging approach of {\em Analysis by Synthesis} as it has been applied in speech research since the beginning of vocoder techniques. Resynthesis of musical sounds can be extremly forceful when appropriate sound analysis data are available. As long as the physical parameters of musical sounds have not been evaluated upon their psychoacoustical effects, the perceptual relevance of individual components of complex sounds can be determined by trial and error only. The introduction of perceptual concepts in the analysis of music yields to results typically much better than would be obtained from acoustics alone.

Aknowledgments

Our special thanks to Prof. Dr. Kreysig for reading the english version of this paper and improving its style.

References

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http://www.kfs.oeaw.ac.at/research/psychoacoustics/musicology/vis_multipart_music/poly1.htm

 

Johan Sundberg – The voice as a musical instrument

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Johan Sundberg – The voice as a musical instrument

Ajoutée le 29 avr. 2014

CIRMMT Distinguished Lectures in the Science and Technology of Music
Johan Sundberg, Royal Institute of Technology, Sweden
22 January 2009 – Clara Lichtenstein Recital Hall
http://www.cirmmt.org/activities/dist…

JOHAN SUNDBERG, biography

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Johan Sundberg

Johan Sundberg (born in 1936, Ph.D. in musicology Uppsala University 1966, doctor honoris causae 1996 University of York, UK) had a personal chair in Music Acoustics at the department from 1979 to his retirement 2001. Since 2002 he is Visiting Professor at the University of London, UK.

He early became interested in the acoustical aspects of music, starting with a doctoral dissertation work on organ pipes. After the dissertation, singing voice and music performance have been his main research topics. He was the head of the music acoustics research group from 1970 to 2001. He has supervised or co-supervised 17 doctoral dissertations, 7 in medical faculties.

In Musikens Ljudlära Sundberg presents music acoustics in popularized form to the interested layman. The book Röstlära, 3rd edition 2001, presents an overview of research on the singing voice. As the President of the Music Acoustics Committee of the Royal Swedish Academy of Music, Sundberg was editor or co-editor of twelve volumes in a series of proceedings of public seminars on music acoustic themes arranged in Stockholm since 1975.

Sundberg has also had extensive experience of performing music. For 24 years he was a member of the Stockholm Bach Choir, 9 years as its president. He has studied singing for Dagmar Gustafson and made his public debute with a Lieder recital on his 50th birthday. He is a member of the Royal Swedish Academy of Music, of the Swedish Acoustical Society (President 1976-81) and a fellow of the Acoustical Society of America.