The fundamental frequency - subglottal pressure ratio

It is known that subglottal pressure (Psb) is a major factor in the control of fundamental frequency (Fo) in speech. Yet, the details of this relation remain unclear. Estimates of the Fo to Psb ratio (FPR) from speech and special phonation tasks yield values between 5 and 15 Hz/cmH20 [1,2,3,4]. In another type of experiments pressure variations are induced externally, either subglottally or supraglottally. TheFPR's measured in these experiments tend towards values of2-5 Hz/cmH20 [5,6,7,8]. There seems to be no a priori reason for the FPR to be different in both kinds of experiments. Mter all, the voice source is the same and why should it behave differently during both kinds of phonation tasks? Therefore we carried Outexperiments that aimed at resolving this discrepancy. I. THE FPR IN EXPERIMENTS WITH INDUCED PRESSUREVARIATIONS INTRODUCTION The FPR in experiments with artificially induced pressure variations was studied first, because we had some ideas why estimates of the FPR in these experiments could be too low. These ideas are described below, and are formalized in three hypotheses. Except for Psb there are other factors that control Fo. lf we want to know the effect ofPsb alone on Fo then we must check whether all other factors are constant. It is known that Fo is also controlled by the laryngeal muscles. Baer [5] studied the influence of the laryngeal muscles on the FPR in an experiment in which the subject is pushed on the ehest to increase Psb. He found a consistent increase in the EMG activity of vocalis (VOC) and interarytenoid 30-40 ms after each push. Even for the fastest laryngeal musdes it takes about 15-20 ms before a change in the activity of a muscle is followed by a change in Fo [9,10]. So the first 45-60 ms following a push the laryngeal musdes probably do not affect Fo. Baer calculated the FPR during the frrst 30 ms and found a value of2-4 Hz/cmH20 in the ehest register, a value that did not deviate from the values reported earlier by others. W e did not reexamine the effect of the laryngeal muscles on the FPR. The frrst hypothesis: a sudden rise in Psb is followed by a rise in Psp. In most experiments either subor Supraglottal pressure (Psp) is measured and varied, while the other pressure signal (Psp resp. Psb) is not measured. During sustained phonation of a vowel the impedance of the glottis is high but fmite. A change of the pressure on either side of the glottis could leak through the glottis. If this would happen the change in transglottal pressure {Pt) is smaller than the change in the measured pressure signal. Because it is really Pt that controls Fo [11], it is also the change in Pt that has to be related to a change in Fo. The effect would be that the estimated FPR is smaller than the ratio between change in Fo and Pt. The second hypothesis: a change in Fo lags a change in Psb. The scatter plots of Fo versus Psb in Baer's artide [5] exhibit hysteresis. The hysteresis is already visible during the frrst 45 ms, so before laryngeal musde activity could influence Fo. This could be an indication that the Fo change lags the Psb change. During the sustained vowel the vibratory system is in a steady state. When Psb is changed it takes some time for the vocal folds to reach a new steady state. The time constant of this adaptation process depends on the total Psb change. Furthermore, this lag would only show up if the time constant of the Psb change is less than the time constant of the adaptation process. In speech the rate ofPsb change during an utterance of about 1-8 cmH20/s is probably slow enough for the vocal folds to adjust almost instantaneously to the new vibratory conditions. Both Ladefoged [6] and Baer [5] used short pushes to vary Psb. During these pushes the estimated rate of Psb change is substantially larger than the aforementioned rate of Psb change in speech. If the changes in Fo would lag the changes in Psb, then the duration of their pulsatile Psb changes could be too short for the vocal folds to reach a new steady state. The result would be an underestimation of dFo, and hence an underestimation of dFoldPsb. The third hypothesis: the FPR is different in Psb rising and lowering. In utterances that exhibit declination both Fo and Psb decrease during the course of the utterance. This is most clearly seen in dedarative utterances with a single accent early in the utterance. In these cases the FPR is calculated for decreasing Fo and Psb. On the other hand, in experiments where Psb is changed by pushing on the ehest the FPR is calculated for increasing Fo and Psb. Differences between Fo rising and Fo falling have been reported and Breckenridge [12] summarizes them by stating that "it has been found that falling tones are more common in the world's languages than rising tones, can be produced faster, and furthermorefall more than rising tones rise." Maybe the FPR is different for Psb rising and lowering, i.e. the ratio in lowering is higher. In short, three hypotheses were postulated that could explain why estimates of the FPR in experiments with induced pressure changes are too low: 1. a rise in Psb is followed by a rise in Psp 2. a change in Fo lags the change in Psb 3. the FPR is different in Psb rising and lowering These three hypotheses were tested with the data of an experiment.