The newsletter of The Acoustical Society of America Volume 17, Number 3 Summer 2007 Source-Filter Interaction in Speaking and Singing is Nonlinear Ingo R. Titze Many aspects tal flow) or the of speech produc- intraglottal pressure tion have been suc- (which drives the cessfully described vocal folds). For by a linear source- nonlinear source- filter theory. Linea- filter coupling, the rity implies that the glottal impedance is source-filter combi- adjusted to be com- nation, which pro- parable to the vocal vides the acoustic Fig. 1. Human male vocal tract compared to trumpet tract input imped- output at the mouth, ance, making the can be characterized by mathematical convolution in the time glottal flow highly dependent on acoustic pressures in the domain (or by multiplication in the frequency domain) of two vocal tracts (above and below the glottis). This is accomplished independent functions representing the source and the filter. by setting specific adduction levels of the vocal folds that With this assumption, the filter cannot influence the source to match a narrower epilarynx tube. The epilarynx tube serves the produce new frequencies or change the overall energy level of same function as the mouthpiece of a trumpet to match the the source. It has recently been shown, however, that this impedance of the main tube to the flow impedance of the lips. assumption is generally not valid, and only under certain condi- Singing styles (operatic, musical theatre, belting, yodel- tions is at best an appropriate simplification. The linear theory is ing) are based on the concept that certain vowels and voice applicable to male speech, less to female and child speech, and qualities work best with certain pitches, a concept that would much less to singing. As long as the dominant source frequen- have no explanation if the source-filter system were linear. The cies lie well below the formant (resonance) frequencies of the entire voice register terminology is based on observed phe- vocal tract (which occurs in male speech), glottal airflow is influ- nomena related to interaction within the source-filter building enced only in simple ways by the filter, mainly in terms of flow blocks, which includes the trachea. Vocal pedagogues who pulse skewing and pulse ripple. But when formants and har- invented terms like chest voice and head voice were not so monics cross, bifurcations in the glottal airflow and the dynam- naïve to suggest that the source of sound moves from location ics of vocal fold vibration can occur that may generate second- to location, but rather that interactions with certain parts of the ary frequencies and even change the energy level at the source. airway are stronger with certain source-filter adjustments and It is hypothesized that humans (and perhaps many ani- lead to special sensations along the airway. mals) have the ability to operate their source filter system with Because the vocal tract is relatively short (about 17 cm in either linear or nonlinear coupling. One way to express the comparison to more than 2 m for a stretched-out trumpet horn) degree of coupling is through the relative impedances of the and because a speaker or singer wishes to convey all the pho- source and filter. For linear source-filter coupling, the source netic variations of a spoken language, the length and shape of impedance is kept much higher than the input impedance to the the vocal tract cannot be adjusted to resonate many of the vocal tract. This linear coupling is accomplished by adducting source frequencies simultaneously. Thus, unlike in most musi- the vocal folds firmly and widening the epilarynx tube (a nar- cal instruments, for which the length and shape of the horn or row region of the vocal tract above the vocal folds, also known bore is carefully designed to resonate the dominant source fre- as the laryngeal vestibule; see arrow in Figure 1). The glottal quencies simultaneously, lining up source frequencies with flow is then determined strictly by aerodynamics, while vocal tract filter resonances is rarely effective in human phona- acoustic pressures above and below the glottis have little influ- tion. In fact, singers deliberately avoid the formant regions ence on either the transglottal pressure (which drives the glot- continued on page 2 We hear that . James West received the 2006 National Medal of Technology Source-Filter Interaction in Speaking and at the White House on July 27. Jim, who is a professor at Johns Singing is Nonlinear continued from page 1 Hopkins University and a former president of ASA, was recog- nized “for co-inventing the electret microphone while working with harmonic placement. Apparent “formant-harmonic tun- with Gerhard Sessler at Bell Labs in 1962. Ninety percent of the ing” occurs in high soprano singing (Sundberg, 1977; Joliveau two billion microphones produced annually and used in every- et al., 2004), but close inspection of the data reveals that F0 is day items such as telephones, hearing aids, camcorders, and slightly less than the formant frequency F1. The reason for this multimedia computers employ electret technology.” is that peak vocal tract inertance is sought out, which occurs ț Jan Achenbach received the National Medal of Science at below resonance. Exact formant-harmonic tuning seems to the White House on July 27. Jan, who is a professor at occur only in so-called harmonic singing or overtone singing, Northwestern University and an ASA Fellow, was recognized where a single harmonic is highly reinforced by a formant that for “seminal contributions to engineering research and educa- is tuned precisely to its frequency (Rachele, 1996). In this tion in the area of wave propagation in solids and for pioneer- exceptional case, peak vocal tract resistance seems to be ing the field of quantitative non-destructive evaluation.” sought out, which occurs exactly at the formant frequency. Patricia Kuhl, Professor of Speech and Co-Director of the Linear source-filter coupling is then likely. University of Washington Institute for Learning and Brain Nonlinear source-filter theory predicts a preference in Sciences, received an Outstanding Alumni Achievement award placing harmonics on the left side of a formant (in the inertive from the University of Minnesota. reactive region below the formant frequency) as opposed to the right side (in the compliant reactive region above the formant A letter from the editor: frequency). Fortunately, the vocal tract has more than one for- Once again, we received no Letters to the Editor, so this mant, so vowels can be chosen such that a “leap over a for- space will be filled by a Letter from the Editor, who is still get- mant” can be made by a harmonic to land on the upslope of an ting unpacked after moving to Los Altos Hills (that makes 3 adjacent formant. Thus, choosing favorable vowels on an moves in the past 3 years). But the view of the setting sun in ascending pitch scale, for example, is like walking up a tall the hills as I write this makes it all worthwhile! I invite my mountain that has multiple peaks and valleys along the way. acoustics friends to come by and enjoy this view with me. And You stay on the upslopes and try to leap over the valleys as someday soon I hope to find all those books and papers that quickly and effectively as possible. Figure 2 shows the process. Ten vowels are represented as have been packed away in boxes. nearly horizontal lines, with the peaks and valleys in the curves As you know, we publish an issue of ECHOES a month or representing the changes in vocal tract inertance (inertive reac- two before each ASA meeting, and another issue a month or so tance divided by angular frequency ω). Vocal tract inertance has after each meeting. This issue includes photos from the Salt been shown to enhance vocal fold vibration (Titze, 1988). The Lake City meeting as well as an article based on a paper at that greater the inertance, the more enhancement there will be for a meeting. We invite readers to submit photos and meeting notes harmonic of the source. Inertance changes rapidly only near the within a month after the New Orleans meeting. formants. For the uu = /u/ vowel, for example, the first formant Likewise, we can use photos and notes from the ICA is near C4; for the ih = / I / vowel, the first formant is near C5; (International Congress on Acoustics) and the various satellite for the ae = / æ / vowel, the first formant is between C and C meetings in Europe this September. The deadline for the Fall 5 6 (note the pitch labels C2, C3, C4, C5, and C6 on horizontal axes). issue is September 27, but in case we receive more submis- For any selected pitch, there will be a series of harmonics cre- sions than we have space, it may be “first come first served.” Newsletter of the Acoustical Society of America Provided as a benefit of membership to ASA members The Acoustical Society of America was organized in 1929 to increase and diffuse the knowledge of acoustics and to promote its practical applications. Echoes Editor . .Thomas Rossing ASA Editor-in-Chief . .Allan Pierce Advisors . .Elaine Moran, Charles Schmid Phone inquiries: 516-576-2360. Contributions, including Letters to the Editor, should be sent to Thomas Rossing, Stanford University, CCRMA Department of Music, Stanford, CA 94305 <[email protected]> Fig. 2. Vocal tract inertance for 10 vowels as a function of frequency 2 Source-Filter Interaction (a) (b) compliant region. Some evidence of chaotic vibration was seen around 4.0 s, where the lowest F0 and the highest vibration amplitude occurred.