1aNS4 – Musical mind control: Human speech takes on characteristics of background music – Ryan Podlubny

1aNS4 – Musical mind control: Human speech takes on characteristics of background music – Ryan Podlubny

Musical mind control: Human speech takes on characteristics of background music

Ryan Podlubny

 – ryan.podlubny@pg.canterbury.ac.nz

Department of Linguistics, University of Canterbury
20 Kirkwood Avenue, Upper Riccarton
Christchurch, NZ, 8041

Popular version of paper 1aNS4, “Musical mind control: Acoustic convergence to background music in speech production.”
Presented Monday morning, November 28, 2016
172nd ASA Meeting, Honolulu

 

People often adjust their speech to resemble that of their conversation partners – a phenomenon known as speech convergence. Broadly defined, convergence describes automatic synchronization to some external source, much like running to the beat of music playing at the gym without intentionally choosing to do so. Through a variety of studies a general trend has emerged where we find people automatically synchronizing to various aspects of their environment 1,2,3. With specific regard to language use, convergence effects have also been observed in many linguistic domains such as sentence-formation4, word-formation 5, and vowel production6 (where differences in vowel production are well associated with perceived accentedness 7,8). This prevalence in linguistics raises many interesting questions about the extent to which speakers converge. This research uses a speech-in-noise paradigm to explore whether or not speakers also converge to non-linguistic signals in the environment: Specifically, will a speaker’s rhythm, pitch, or intensity (which is closely related to loudness) be influenced by fluctuations in background music such that the speech echoes specific characteristics of that background music (for example, if the tempo of background music slows down, will that influence those listening to unconsciously decrease their speech rate)?

In this experiment participants read passages aloud while hearing music through headphones. Background music was composed by the experimenter to be relatively stable with regard to pitch, tempo/rhythm, and intensity, so we could manipulate and test only one of these dimensions at a time, within each test-condition. We imposed these manipulations gradually and consistently toward a target, which can be seen in Figure 1, and would similarly return to the level at which they started after reaching that target. We played the participants music with no experimental changes in between all manipulated sessions. (Examples of what participants heard in headphones are available as sound-files 1 and 2]

podlubny_fig1

Fig. 1
Using software designed for digital signal processing (analyzing and altering sound), manipulations were applied in a linear fashion (in a straight line) toward a target – this can be seen above as the blue line, which first rises and then falls. NOTE: After manipulations reach their target (the target is seen above as a dashed, vertical red line), the degree of manipulation would then return to the level at which it started in a similar linear fashion. Graphic captured while using Praat 9 to increase and then decrease the perceived loudness of the background music.     

 

Data from 15 native speakers of New Zealand English were analyzed using statistical tests that allow effects to vary somewhat for each participant where we observed significant convergence in both the pitch and intensity conditions. Analysis of the Tempo condition, however, has not yet been conducted. Interestingly, these effects appear to differ systematically based on a person’s previous musical training. While non-musicians demonstrate the predicted effect and follow the manipulations, musicians appear to invert the effect and reliably alter aspects of their pitch and intensity in the opposite direction of the manipulation (see Figure 2). Sociolinguistic research indicates that under certain conditions speakers will emphasize characteristics of their speech to distinguish themselves socially from conversation partners or groups, as opposed to converging with them6. It seems plausible then that, given a relatively heightened ability to recognize low-level variations of sound, musicians may on some cognitive level be more aware of the variation in their sound environment, and as a result similarly resist the more typical effect. However, more work is required to better understand this phenomenon.

podlubny_fig2

Fig. 2
The above plots measure pitch on the y-axis (up and down on the left edge), and indicate the portions of background music that have been manipulated on the x- axis (across the bottom). The blue lines show that speakers generally lower their pitch as an un-manipulated condition progresses. However the red lines show that when global pitch is lowered during a test-condition, such lowering is relatively more dramatic for non-musicians (left plot) and that the effect is reversed by those with musical training (right plot). NOTE: A follow-up model further accounts for the relatedness of Pitch and Intensity and shows much the same effect.

This work indicates that speakers are not only influenced by human speech partners in production, but also, to some degree, by noise within the immediate speech environment, which suggests that environmental noise may constantly be influencing certain aspects of our speech production in very specific and predictable ways. Human listeners are rather talented when it comes to recognizing subtle cues in speech 10, especially compared to computers and algorithms that can’t  yet match this ability. Some language scientists argue these changes in speech occur to make understanding easier for those listening 11. That is why work like this is likely to resonate in both academia and the private sector, as a better understanding of how speech will change in different environments contributes to the development of more effective aids for the hearing impaired, as well as improvements to many devices used in global communications.

 

Sound-file 1.
An example of what participants heard as a control condition (no experimental manipulation) in between test-conditions.

 

Sound-file 2.
An example of what participants heard as a test condition (Pitch manipulation, which drops 200 cents/one full step).

 

 

References

1.  Hill, A. R., Adams, J. M., Parker, B. E., & Rochester, D. F. (1988). Short-term entrainment of ventilation to the walking cycle in humans. Journal of Applied Physiology65(2), 570-578.
2. Will, U., & Berg, E. (2007). Brain wave synchronization and entrainment to periodic acoustic stimuli. Neuroscience letters424(1), 55-60.
3.  McClintock, M. K. (1971). Menstrual synchrony and suppression. Nature, Vol 229, 244-245.
4.  Branigan, H. P., Pickering, M. J., McLean, J. F., & Cleland, A. A. (2007). Syntactic alignment and participant role in dialogue. Cognition, 104(2), 163-197.
5.  Beckner, C., Rácz, P., Hay, J., Brandstetter, J., & Bartneck, C. (2015). Participants Conform to Humans but Not to Humanoid
Robots in an English Past Tense Formation Task. Journal of Language and Social Psychology, 0261927X15584682.
Retreived from: http://jls.sagepub.com.ezproxy.canterbury.ac.nz/content/early/2015/05/06/0261927X15584682.
6.  Babel, M. (2012). Evidence for phonetic and social selectivity in spontaneous phonetic imitation. Journal of Phonetics, 40(1), 177-189.
7.  Major, R. C. (1987). English voiceless stop production by speakers of Brazilian Portuguese. Journal of Phonetics, 15, 197—
202.
8.  Rekart, D. M. (1985) Evaluation of foreign accent using synthetic speech. Ph.D. dissertation, the Lousiana State University.
9.  Boersma, P., & Weenink, D. (2014). Praat: Doing phonetics by computer (Version 5.4.04) [Computer program]. Retrieved
from www.praat.org.
10.  Hay, J., Podlubny, R., Drager, K., & McAuliffe, M. (under review). Car-talk: Location-specific speech production and
perception.
11.  Lane, H., & Tranel, B. (1971). The Lombard sign and the role of hearing in speech. Journal of Speech, Language, and
Hearing Research14(4), 677-709.

 

3pSC87 – What the f***? Making sense of expletives in The Wire – Erica Gold

3pSC87 – What the f***? Making sense of expletives in The Wire – Erica Gold

What the f***? Making sense of expletives in The Wire
Erica Gold – e.gold@hud.ac.uk
Dan McIntyre – d.mcintyre@hud.ac.uk

University of Huddersfield
Queensgate
Huddersfield, HD1 3DH
United Kingdom

Popular version of paper 3pSC87, “ What the f***? Making sense of expletives in ‘The Wire'”

Presented Wednesday afternoon, November 30, 2016
172nd ASA Meeting, Honolulu

season-1

In Season one of HBO’s acclaimed crime drama The Wire, Detectives Jimmy McNulty and ‘Bunk’ Moreland are investigating old homicide cases, including the murder of a young woman shot dead in her apartment. McNulty and Bunk visit the scene of the crime to try and figure out exactly how the woman was killed. What makes the scene unusual dramatically is that, engrossed in their investigation, the two detectives communicate with each other using only the word, “fuck” and its variants (e.g. motherfucker, fuckity fuck, etc.). Somehow, using only this vocabulary, McNulty and Bunk are able to communicate in a meaningful way. The scene is absorbing, engaging and even funny, and it leads to a fascinating question for linguists: how is the viewer able to understand what McNulty and Bunk mean when they communicate using such a restricted set of words?

bunkmcnulty

To investigate this, we first looked at what other linguists have discovered about the word fuck. What is clear is that it’s a hugely versatile word that can be used to express a range of attitudes and emotions. On the basis of this research, we came up with a classification scheme which we then used to categorise all the variants of fuck in the scene. Some seemed to convey disbelief and some were used as insults. Some indicated surprise or realization while others functioned to intensify the following word. And some were idiomatic set phrases (e.g. Fuckin’ A!). Our next step was to see whether there was anything in the acoustic properties of the characters’ speech that would allow us to explain why we interpreted the fucks in the way that we did.

The entire conversation between Bunk and McNulty lasts around three minutes and contains a total of 37 fuck productions (i.e. variations of fuck). Due to the variation in the fucks produced, the one clear and consistent segment for each word was the <u> in fuck. Consequently, this became the focus of our study. The <u> in fuck is the same sound you find in the word strut or duck and is represented as /ᴧ/ in the International Phonetic Alphabet. When analysing vowel sounds, such as <u>, we can look at a number of aspects of its production.

In this study, we looked at the quality of the vowel by measuring the first three formants. In phonetics, the term formant refers to acoustic resonances of sound in the vocal tract. The first two formants can tell us if the production sounds more like, “fuck” rather than, “feck” or “fack,” and the third formant gives us information about the voice quality. We also looked at the duration of the <u> being produced, “fuuuuuck” versus “ fuck.”

After measuring each instance, we ran statistical tests to see if there was any relationship between the way in which it was said, and how we categorised its range of meanings. Our results showed that if we accounted for the differences in the vocal tract shapes of the actors playing Bunk and McNulty, the quality of the vowels are relatively consistent. That is, we get a lot of <u> sounds, rather than “eh,” “oo” or “ih.”

The productions of fucks that were associated with the category of realization were found to be very similar to those associated with disbelief. However, disbelief and realization did contrast with those that were used as insults, idiomatic phrases, or functional words. Therefore, it may be more appropriate to classify the meaning into fewer categories – those that signify disbelief or realization, and those that are idiomatic, insults, or functional. It is important to remember, however, that the latter group of three meanings are represented by fewer examples in the scene. Our initial results show that these two broad groups may be distinguished through the length of the vowel – short <u> is more associated with an insult, function, or idiomatic use rather than disbelief or surprise (for which the vowel tends to be longer). In the future, we would also like to analyse the intonation of the productions. See if you can hear the difference between these samples:

Example 1: realization/surprise

Example 2: general expletive which falls under the functional/idiomatic/insult category

 

Our results shed new light on what for linguists is an old problem: how do we make sense of what people say when speakers so very rarely say exactly what they mean? Experts in pragmatics (the study of how meaning is affected by context) have suggested that we infer meaning when people break conversational norms. In the example from The Wire, it’s clear that the characters are breaking normal communicative conventions. But pragmatic methods of analysis don’t get us very far in explaining how we are able to infer such a range of meaning from such limited vocabulary. Our results confirm that the answer to this question is that meaning is not just conveyed at the lexical and pragmatic level, but at the phonetic level too. It’s not just what we say that’s important, it’s how we fucking say it!

*all photos are from HBO.com

 

 

5aSCb17 – Pronunciation differences: Gender and ethnicity in Southern English – Wendy Herd, Devan Torrence, and Joy Cariño

5aSCb17 – Pronunciation differences: Gender and ethnicity in Southern English – Wendy Herd, Devan Torrence, and Joy Cariño

5aSCb17 – Pronunciation differences: Gender and ethnicity in Southern English – Wendy Herd, Devan Torrence, and Joy Cariño

 

Wendy Herd – wherd@english.msstate.edu

Devan Torrence – dct74@msstate.edu

Joy Carino – carinoj16@themsms.org

 

Linguistics Research Laboratory
English Department
Mississippi State University
Mississippi State, MS 39762

 

Popular version of paper 5aSCb17, “Prevoicing differences in Southern English: Gender and ethnicity effects”

Presented Friday morning, May 27, 10:05 – 12:00 in Salon F

171st ASA Meeting, Salt Lake City

 

We often notice differences in pronunciation between ourselves and other speakers. More noticeable differences, like the Southern drawl or the New York City pronunciation yuge instead of huge, are even used overtly when we guess where a given speaker is from. Our speech also varies in more subtle ways.

If you hold your hand in front of your mouth when saying tot and dot aloud, you will be able to feel a difference in the onset of vocal fold vibration. Tot begins with a sound that lacks vocal fold vibration, so a large rush of air can be felt on the hand at the beginning of the word. No such rush of air can be felt at the beginning of dot because it begins with a sound with vocal fold vibration. A similar difference can be felt when comparing [p] of pot to [b] of bot and [k] of cot to [ɡ] of got. This difference between [t] and [d] is very noticeable, but the timing of our vocal fold vibration also varies each time we pronounce a different version of [t] or [d].

Our study is particularly focused, not on the large difference between sounds like [t] and [d], but on how speakers produce the smaller differences between different [d] pronunciations. For example, an English [d] might be pronounced with no vocal fold vibration before the [d] as shown in Figure 1(a) or with vocal fold vibration before the [d] as shown in Figure 1(b). As can be heard in the accompanying sound files, the difference between these two [d] pronunciations is less noticeable for English speakers than the difference between [t] and [d].

Figure 1. Spectrogram of (a) dot with no vocal fold vibration before [d] and (b) dot with vocal fold vibration before [d]. (Only the first half of dot is shown.)

We compared the pronunciations of 40 native speakers of English from Mississippi to see if some speakers were more likely to vibrate their vocal folds before [b, d, ɡ] rather than shortly after those sounds. These speakers included equal numbers of African American participants (10 women, 10 men) and Caucasian American participants (10 women, 10 men).

 

Previous research found that men were more likely to vibrate their vocal folds before [b, d, ɡ] than women, but we found no such gender differences [1]. Men and women from Mississippi employed vocal fold vibration similarly. Instead, we found a clear effect of ethnicity. African American participants produced vocal fold vibration before initial [b, d, ɡ] 87% of the time while Caucasian American participants produced vocal fold vibration before these sounds just 37% of the time. This striking difference, which can be seen in Figure 2, is consistent with a previous smaller study that found ethnicity effects in vocal fold vibration among young adults from Florida [1, 2]. It is also consistent with descriptions of regional variation in vocal fold vibration [3].

 

Figure 2. Percentage of pronunciations produced with vocal fold vibration before [b, d, ɡ] displayed by ethnicity and gender.

The results suggest that these pronunciation differences are due to dialect variation. African American speakers from Mississippi appear to systematically use vocal fold vibration before [b, d, ɡ] to differentiate them from [p, t, k], but the Caucasian American speakers are using the cue differently and less frequently. Future research in the perception of these sounds could shed light on how speakers of different dialects vary in the way they interpret this cue. For example, if African American speakers are using this cue to differentiate [d] from [t], but Caucasian American speakers are using the same cue to add emphasis or to convey emotion, it is possible that listeners sometimes use these cues to (mis)interpret the speech of others without ever realizing it. We are currently attempting to replicate these results in other regions.

Each accompanying sound file contains two repetitions of the same word. The first repetition does not include fold vibration before the initial sound, and the second repetition does include vocal fold vibration before the initial sound.
 

  1. Ryalls, J., Zipprer, A., & Baldauff, P. (1997). A preliminary investigation of the effects of gender and race on voice onset time. Journal of Speech Language and Hearing, 40(3), 642-645.
  2. Ryalls, J., Simon, M., & Thomason, J. (2004). Voice onset time production in older Caucasian- and African-Americans. Journal of Multilingual Communication Disorders, 2(1), 61-67.
  3. Jacewicz, E., Fox, R.A., & Lyle, S. (2009). Variation in stop consonant voicing in two regional varieties of American English. Language Variation and Change, 39(3), 313-334.

 

 

3pSC10 – Does increasing the playback speed of men’s and women’s voices reduce their intelligibility by the same amount? – Eric M. Johnson, Sarah Hargus Ferguson

3pSC10 – Does increasing the playback speed of men’s and women’s voices reduce their intelligibility by the same amount? – Eric M. Johnson, Sarah Hargus Ferguson

Does increasing the playback speed of men’s and women’s voices reduce their intelligibility by the same amount?

 

Eric M. Johnson – eric.martin.johnson@utah.edu

Sarah Hargus Ferguson – sarah.ferguson@hsc.utah.edu

Department of Communication Sciences and Disorders
University of Utah
390 South 1530 East, Room 1201
Salt Lake City, UT 84112

 

Popular version of poster 3pSC10, “Gender and rate effects on speech intelligibility.”

Presented Wednesday afternoon, May 25, 2016, 1:00, Salon G

171st ASA Meeting, Salt Lake City

Older adults seeking hearing help often report having an especially hard time understanding women’s voices. However, this anecdotal observation doesn’t always agree with the findings from scientific studies. For example, Ferguson (2012) found that male and female talkers were equally intelligible for older adults with hearing loss. Moreover, several studies have found that young people with normal hearing actually understand women’s voices better than men’s voices (e.g. Bradlow et al., 1996; Ferguson, 2004). In contrast, Larsby et al. (2015) found that, when listening in background noise, groups of listeners with and without hearing loss were better at understanding a man’s voice than a woman’s voice. The Larsby et al. data suggest that female speech might be more affected by distortion like background noise than male speech is, which could explain why women’s voices may be harder to understand for some people.

We were interested to see if another type of distortion, speeding up the speech, would have an equal effect on the intelligibility of men and women. Speech that has been sped up (or time-compressed) has been shown to be less intelligible than unprocessed speech (e.g. Gordon-Salant & Friedman, 2011), but no studies have explored whether time compression causes an equal loss of intelligibility for male and female talkers. If an increase in playback speed causes women’s speech to be less intelligible than men’s, it could reveal another possible reason why so many older adults with hearing loss report difficulty understanding women’s voices. To this end, our study tested whether the intelligibility of time-compressed speech decreases for female talkers more than it does for male talkers.

Using 32 listeners with normal hearing, we measured how much the intelligibility of two men and two women went down when the playback speed of their speech was increased by 50%. These four talkers were selected based on their nearly equivalent conversational speaking rates. We used digital recordings of each talker and made two different versions of each sentence they spoke: a normal-speed version and a fast version. The software we used allowed us to speed up the recordings without making them sound high-pitched.

Audio sample 1: A sentence at its original speed.

Audio sample 2: The same sentence sped up to 50% faster than its original speed.

 

All of the sentences were presented to the listeners in background noise. We found that the men and women were essentially equally intelligible when listeners heard the sentences at their original speed. Speeding up the sentences made all of the talkers harder to understand, but the effect was much greater for the female talkers than the male talkers. In other words, there was a significant interaction between talker gender and playback speed. The results suggest that time-compression has a greater negative effect on the intelligibility of female speech than it does on male speech.

johnson & ferguson fig 1

Figure 1: Overall percent correct key-word identification performance for male and female takers in unprocessed and time-compressed conditions. Error bars indicate 95% confidence intervals.

Figure 1: Overall percent correct key-word identification performance for male and female takers in unprocessed and time-compressed conditions. Error bars indicate 95% confidence intervals.

 

These results confirm the negative effects of time-compression on speech intelligibility and imply that audiologists should counsel the communication partners of their patients to avoid speaking excessively fast, especially if the patient complains of difficulty understanding women’s voices. This counsel may be even more important for the communication partners of patients who experience particular difficulty understanding speech in noise.

 

  1. Bradlow, A. R., Torretta, G. M., and Pisoni, D. B. (1996). “Intelligibility of normal speech I: Global and fine-grained acoustic-phonetic talker characteristics,” Speech Commun. 20, 255-272.
  2. Ferguson, S. H. (2004). “Talker differences in clear and conversational speech: Vowel intelligibility for normal-hearing listeners,” J. Acoust. Soc. Am. 116, 2365-2373.
  3. Ferguson, S. H. (2012). “Talker differences in clear and conversational speech: Vowel intelligibility for older adults with hearing loss,” J. Speech Lang. Hear. Res. 55, 779-790.
  4. Gordon-Salant, S., and Friedman, S. A. (2011). “Recognition of rapid speech by blind and sighted older adults,” J. Speech Lang. Hear. Res. 54, 622-631.
  5. Larsby, B., Hällgren, M., Nilsson, L., and McAllister, A. (2015). “The influence of female versus male speakers’ voice on speech recognition thresholds in noise: Effects of low-and high-frequency hearing impairment,” Speech Lang. Hear. 18, 83-90.

 

 

4pMU4 – How Well Can a Human Mimic the Sound of a Trumpet? -Ingo R. Titze

4pMU4 – How Well Can a Human Mimic the Sound of a Trumpet? -Ingo R. Titze

How Well Can a Human Mimic the Sound of a Trumpet?

Ingo R. Titze – ingo.titze@utah.edu

University of Utah
201 Presidents Cir
Salt Lake City, UT

Popular version of paper 4pMU4 “How well can a human mimic the sound of a trumpet?”

Presented Thursday May 26, 2:00 pm, Solitude room

171st ASA Meeting Salt Lake City

 

Man-made musical instruments are sometimes designed or played to mimic the human voice, and likewise vocalists try to mimic the sounds of man-made instruments.  If flutes and strings accompany a singer, a “brassy” voice is likely to produce mismatches in timbre (tone color or sound quality).  Likewise, a “fluty” voice may not be ideal for a brass accompaniment.  Thus, singers are looking for ways to color their voice with variable timbre.

Acoustically, brass instruments are close cousins of the human voice.  It was discovered prehistorically that sending sound over long distances (to locate, be located, or warn of danger) is made easier when a vibrating sound source is connected to a horn.  It is not known which came first – blowing hollow animal horns or sea shells with pursed and vibrating lips, or cupping the hands to extend the airway for vocalization. In both cases, however, airflow-induced vibration of soft tissue (vocal folds or lips) is enhanced by a tube that resonates the frequencies and radiates them (sends them out) to the listener.

Around 1840, theatrical singing by males went through a revolution.  Men wanted to portray more masculinity and raw emotion with vocal timbre. “Do di Petto”, which is Italien for “C  in chest voice” was introduced by operatic tenor Gilbert Duprez in 1837, which soon became a phenomenon.  A heroic voice in opera took on more of a brass-like quality than a flute-like quality.  Similarly, in the early to mid- twentieth century (1920-1950), female singers were driven by the desire to sing with a richer timbre, one that matched brass and percussion instruments rather than strings or flutes.  Ethel Merman became an icon in this revolution. This led to the theatre belt sound produced by females today, which has much in common with a trumpet sound.

Titze_Fig1_Merman

Fig.1.  Mouth opening to head-size ratio for Ethel Merman and corresponding frequency spectrum for the sound “aw” with a fundamental frequency fo (pitch) at 547 Hz and a second harmonic frequency 2 fo at 1094 Hz.

 

The length of an uncoiled trumpet horn is about 2 meters (including the full length of the valves), whereas the length of a human airway above the glottis (the space between the vocal cords) is only about 17 cm (Fig. 2). The vibrating lips and the vibrating vocal cords can produce similar pitch ranges, but the resonators have vastly different natural frequencies due to the more than 10:1 ratio in airway length.  So, we ask, how can the voice produce a brass-like timbre in a “call” or “belt”?

One structural similarity between the human instrument and the brass instrument is the shape of the airway directly above the glottis, a short and narrow tube formed by the epiglottis.  It corresponds to the mouthpiece of brass instruments.  This mouthpiece plays a major role in shaping the sound quality.  A second structural similarity is created when a singer uses a wide mouth opening, simulating the bell of the trumpet.  With these two structural similarities, the spectrum of tones produced by the two instruments can be quite similar, despite the huge difference in the overall length of the instrument.

 

Titze_Fig2_airway_trumpet

Fig 2.  Human airway and trumpet (not drawn to scale).

 

Acoustically, the call or belt-like quality is achieved by strengthening the second harmonic frequency 2fin relation to the fundamental frequency fo.  In the human instrument, this can be done by choosing a bright vowel like /ᴂ/ that puts an airway resonance near the second harmonic.  The fundamental frequency will then have significantly less energy than the second harmonic.

Why does that resonance adjustment produce a brass-like timbre?  To understand this, we first recognize that, in brass-instrument playing, the tones produced by the lips are entrained (synchronized) to the resonance frequencies of the tube.  Thus, the tones heard from the trumpet are the resonance tones. These resonance tones form a harmonic series, but the fundamental tone in this series is missing.  It is known as the pedal tone.  Thus, by design, the trumpet has a strong second harmonic frequency with a missing fundamental frequency.

Perceptually, an imaginary fundamental frequency may be produced by our auditory system when a series of higher harmonics (equally spaced overtones) is heard.  Thus, the fundamental (pedal tone) may be perceptually present to some degree, but the highly dominant second harmonic determines the note that is played.

In belting and loud calling, the fundamental is not eliminated, but suppressed relative to the second harmonic.  The timbre of belt is related to the timbre of a trumpet due to this lack of energy in the fundamental frequency.  There is a limit, however, in how high the pitch can be raised with this timbre.  As pitch goes up, the first resonance of the airway has to be raised higher and higher to maintain the strong second harmonic.  This requires ever more mouth opening, literally creating a trumpet bell (Fig. 3).

Titze_Fig3_Menzel

Fig 3. Mouth opening to head-size ratio for Idina Menzel and corresponding frequency spectrum for a belt sound with a fundamental frequency (pitch) at 545 Hz.

 

Note the strong second harmonic frequency 2fo in the spectrum of frequencies produced by Idina Menzel, a current musical theatre singer.

One final comment about the perceived pitch of a belt sound is in order.  Pitch perception is not only related to the fundamental frequency, but the entire spectrum of frequencies.  The strong second harmonic influences pitch perception. The belt timbre on a D5 (587 Hz) results in a higher pitch perception for most people than a classical soprano sound on the same note. This adds to the excitement of the sound.