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Identification of Concurrent Harmonic and Inharmonic Vowels: A Test of the Theory of Harmonic Cancellation and Enhancement

Alain de Cheveigné (CNRS, URA1028), Stephen McAdams, Jean Laroche (ENST/CNRS), Muriel Rosenberg (ENST/CNRS)

Journal of the Acoustical Society of America, 97, 3736-3748 (1995)
Copyright © ASA 1995


The improvement of identification accuracy of concurrent vowels with differences in fundamental frequency (F0) is usually attributed to mecanisms that exploit harmonic structure. To decide whether identification is aided primarily by the harmonic structure of the target ("harmonic enhancement") or that of the ground ("harmonic cancellation"), pairs of synthetic vowels, each of which was either harmonic or inharmonic, were presented to listeners for identification. Responses for each vowel were scored according to the vowel's harmonicity, the harmonicity of the vowel that accompanied it, and F0. For a given target, identification was better by about 3% for a harmonic ground unless the target was also harmonic with the same F0. This supports the cancellation hypothesis. Identification was worse for harmonic than for inharmonic targets by 3-8%. This does not support the enhancement hypothesis. When both vowels were harmonic, identification was better by about 6% when the F0s differed by 1/2 semitone. However, when at least one vowel was inharmonic, F0 had no significant effect. Identification of constituents of pairs was generally not the same when the target was harmonic and the ground inharmonic or vice-versa. Results are interpreted in terms of harmonic enhancement and harmonic cancellation, and alternative explanations such as phase effects are considered.


When two voices are present at the same time, differences in fundamental frequency (F0) can help listeners attend to one or the other voice and understand what is being said. This has been verified for natural and synthetic speech (Brokx and Nooteboom 1982) and for pairs of synthetic vowels (Scheffers 1983; Culling and Darwin 1993a). One interpretation is that differences in F0 allow the voices to segregate from each other. Various models and methods have been proposed to explain or reproduce this process (see de Cheveigné 1993a, for a review). Some make use of the harmonic structure of a voice to identify its components within the composite spectrum. The voice is then isolated by enhancing those components relative to the ground. Others make use of the harmonic structure of the interfering voice, which is then removed by cancelling its components. Either strategy (or both) can be used if both voices are harmonic, as long as they have different F0s. Both strategies fail if the vowels have the same F0, which explains why performance in double vowel identification experiments is not as good in this case.

Each strategy has its advantages and disadvantages. Harmonic enhancement allows harmonic sounds such as voiced speech to emerge from any type of interference (except harmonic interference with the same F0 as the target). Harmonic cancellation on the other hand allows any type of target to emerge from harmonic interference. Enhancement works best when the signal-to-noise ratio is high, because the F0 of the target is then relatively easy to estimate. However separation is probably most needed when the signal-to-noise ratio is low, in which case cancellation should be easier to implement. Cancellation removes all components that belong to the harmonic series of the interference, and may thus distort the spectrum of the target. Enhancement should cause no spectral distortion to the target, as long as it is perfectly harmonic. Cancellation of perfectly harmonic interference can be obtained using a filter with a short impulse response, whereas enhancement requires a filter with a long impulse response to be effective (de Cheveigné 1993a). The non-stationarity of speech may limit the effectiveness of such filters.

The aim of this paper is to study the degree to which each strategy is used by the auditory system in a double vowel identification experiment. An answer to this question may allow us to better understand auditory processes of sound organization, and refine our models of harmonic sound separation. We first review the literature on mixed vowel identification experiments and present the rationale and predictions for our experiment. We then present our experimental design and methods, report the results, and analyze them in relation to the predictions.

A. Double Vowel Identification Experiments

Bregman (1990) has suggested that, in order to understand speech in an environment with many competing sound sources, the auditory system must first analyze the acoustic scene and then build up an integral perceptual representation of the behavior of a voice over time. A mixture of several voices poses what Cherry (1953) called the "cocktail party problem". Cherry showed that among the cues useful to the listener trying to track a source is its spatial position, which creates binaural information that the auditory system uses to segregate the source. Another important cue for the separation of natural speech is the fundamental frequency. Brokx and Nooteboom (1982) found that this cue helped listeners separate competing speech streams and better reproduce the message carried by one or other stream. Fundamental frequency differences are especially effective when reinforced by onset asynchronies (Darwin and Culling 1990) or binaural cues (Summerfield and Assmann 1991; Zwicker 1984).

Another cue that might be expected to reinforce F0 differences is frequency modulation, particularly if competing streams are modulated incoherently. McAdams (1989) and Marin and McAdams (1991) demonstrated that frequency modulation increased the perceptual prominence of a vowel presented concurrently with two other vowels at relatively large F0 separations (5 semitones, or 33%). However, they also found that this increase was independent on whether the vowels were modulated coherently or not. Subsequent studies confirmed that the effects of frequency modulation incoherence can be accounted for by the instantaneous differences in F0 that it causes (Demany and Semal 1990; Carlyon 1991; Summerfield 1992; Summerfield and Culling 1992)

These results all suggest a crucial importance of harmonicity, exploited by the auditory system when there are differences in fundamental frequency (F0) between constituents of an acoustic mixture. The effects of F0 have been studied in detail by a number of authors (Assmann and Summerfield, 1989, 1990; Scheffers, 1983; Summerfield and Assmann, 1991; Zwicker 1984; Chalikia & Bregman, 1989, 1993; Darwin and Culling, 1990; Culling and Darwin, 1993a). In these studies, two synthetic vowels were presented simultaneously at various F0 values and subjects were requested to identify both vowels from a predetermined set of five to eight vowels. Identification scores reflecting the ability to identify both vowels (combinations-correct score) for several of these studies are plotted in Figure 1.

Fig. 1 Dotted lines: combination-correct identification rates as a function of F0 reported in previous studies. Continuous line: combination correctrates obtained in this study for mixtures of harmonic vowels (HH condition).

There are large differences in overall identification rate between studies that may be attributed to differences in training of subjects, presence or absence of feedback, size of vowel set, inclusion of pairs of identical vowels, stimulus duration, level, etc.. A common trend is a rapid increase in identification performance with F0 up to between 1/2 and 2 semitone separation (3-12% difference in F0), followed by an asymptote. This effect is usually explained by assuming that the mechanism that exploits the harmonic structure of the vowel spectrum is effective when the F0s are different but fails when they are the same and the harmonic series of both vowels coincide. However, a question that none of these studies has addressed is whether it is primarily the harmonicity of the vowel being recognized that aids its segregation and subsequent identification, or that of the background vowel. This leaves dangling many issues involved in the design of voice separation models. The primary aim of the present study is to directly test the effect of the harmonicity of both the target vowel and the background vowel on the target's identification.

One study that approached this question was conducted by Lea (1992; Lea and Summerfield 1992). He presented listeners with pairs of vowels of which each could be either voiced or whispered, and requested them to identify both vowels. He scored results according to the harmonicity of the vowel being answered (the target) and that of the other vowel (the ground). He found that targets were better identified when the ground was voiced than when it was whispered. There was no significant advantage when the target itself was voiced rather than whispered. However with a slightly different method, Lea and Tsuzaki (1993a,b) found that targets were better recognized when they were voiced.

A difficulty with this experiment is that it requires voiced and whispered vowels to be equivalent in both "phonetic quality" and "masking power" (except insofar as these depend on harmonicity). This is a difficult requirement because it is not evident how one should go about matching the continuous spectrum of a whispered vowel to the discrete spectrum of a voiced vowel. Lea (1992) used a model of basilar membrane excitation to match the vowels, but the possibility remains that some imbalance, for example of level, might have affected the results. Here we describe a similar experiment in which whispered vowels are replaced by inharmonic vowels with spectral structure and density closer to those of harmonic vowels.

B. Experimental Rationale and Predictions

We wish to determine whether the auditory system uses the harmonicity of the target or that of the ground to segregate the target from the mixture. For that purpose we used stimuli consisting of pairs of vowels, each of which was either harmonic or inharmonic. Inharmonic vowels were obtained by perturbing the frequencies of the components of a harmonic vowel by small random amounts, as explained in section I-B and Appendix A-2. In addition to the harmonicity state we introduced a difference in fundamental frequency (F0) in order to compare their effects and study their interaction, as well as to allow comparisons with previous studies. Pairs of vowels were presented simultaneously. Subjects were asked to identify both vowels and respond with an unordered pair of vowel names. For each vowel in the stimulus, the answer was deemed correct if the vowel's name appeared within the response pair. This answer was classified according to the harmonic state of that vowel (the target), the state of the other vowel (the ground), and the nominal F0 difference between them. This step was repeated for the second vowel in the pair, reversing the roles of target and ground.

In this paper, the notation 'HI', for example, indicates a harmonic target with an inharmonic ground, and 'R(HI)' indicates the identification rate for that target. Other combinations are noted IH, HH, and II. Where necessary, the relation between the F0s may also be specified: HI0 signifies the same F0 and HIx signifies a different F0 (HI implies that both F0 conditions are taken together). For each hypothesis concerning the strategy that is used by the auditory system to separate harmonic sounds, specific predictions can be made concerning the outcome of this experiment.

1. Enhancement

According to this hypothesis, harmonicity of the target promotes segregation (unless the ground is also harmonic and has the same F0). All else being equal, a target should be better identified if it is harmonic:

R(HI0) > R(II0),

R(HIx) > R(IIx),

R(HHx) > R(IHx).

If the hypothesis is false, these differences should be insignificant.

2. Cancellation

According to this hypothesis, harmonicity of the ground allows the target to be segregated (unless it is also harmonic and has the same F0). All else being equal, identification should be better when the ground is harmonic:

R(IH0) > R(II0),

R(IHx) > R(IIx),

R(HHx) > R(HIx).

If the hypothesis is false, the differences should be insignificant. In addition to these two hypotheses that our experiment was specifically designed to test, there are others that are worth considering.

3. Symmetric Mechanisms

According to Bregman (1990), a characteristic of primitive segregation is the symmetry of its effects: segregation causes both parts of a mixture to become equally accessible. We might thus expect vowels in a pair to be equally affected by factors that promote segregation such as differences in harmonic structure:

R(IH0) = R(HI0),

R(IHx) = R(HIx).

Specific cues or mechanisms that might show that behavior are:

a) Component Mismatch
According to this explanation, harmonicity per se is unimportant; segregation is limited by the proximity of components and increases when harmonic structures are different. In the HH0 condition harmonic series coincide, whereas all other conditions introduce a mismatch between component frequencies that should ease identification of both constituents:

R(all conditions other than HH0) > R(HH0).

b) Beating between Partials
Culling (1990) and Culling and Darwin (1993a,b) suggested that beating between partials in the F1 region might explain improvements in identification with F0. Beating occurs for example if two partials belonging to different vowels fall within the same auditory filter: the output fluctuates at a rate that depends on the difference in frequency between the partials. Fluctuations may allow the amplitudes of the two partials to be better estimated, as long as they are neither too slow to be appreciable within the duration of the stimulus, nor too fast to be resolved temporally by the auditory system. Beating is likely to affect identification in a complex fashion, but insofar as it depends on frequency difference between partials of both vowels, both should be equally affected.
c) Quality Differences (pitch, timbre)
Vowels that share the same pitch and harmonic nature (such as constituents of the HH0 and II0 conditions) may "sound alike" and thus be difficult to segregate when mixed. Differences in quality should promote segregation:

R(all conditions other than HH0, II0) > R(HH0,II0).

In contrast to the predictions of the component-mismatch hypothesis, the II0 condition does not promote segregation here (assuming that all of the inharmonic stimuli used are percieved as having a similar quality).

4. The Effect of F0

For all models, F0 effects are likely to be smaller when either vowel is inharmonic than when both are harmonic. For example in the IH condition the effectiveness of enhancement would be reduced, whereas that of cancellation should change relatively little with F0 (much of the F0 effect in the HH condition is due to the fact that when F0=0 all target components fall precisely on the ground vowel's harmonic series, and are cancelled together with those of the ground). Component mismatch or beating should also be less affected by F0 than in the HH condition, leading to smaller effects when either vowel is inharmonic. On the other hand when both vowels are harmonic, all models predict alike:

R(HHx) > R(HH0).

It is or this reason that classic double-vowel experiments do not allow us to choose between hypotheses.

I. Stimuli

A. Spectral Envelopes

Vowels belonged to a set of French vowels -- /a/, /e/, /i/, /o/, /u/ -- which are also common to many different languages. The spectral envelopes were derived from natural voiced speech by a screening procedure that produced a set of 10 allophones for each vowel (see Appendix A-1). Envelopes for each experimental condition were drawn at random from the allophone set. By using random allophones, we hoped a) to reduce the likelihood that a listener might learn the spectra of particular combinations of synthetic vowels and respond correctly without using separation mechanisms, b) to make the task more difficult in conditions such as equal F0 and thus obtain larger effects when the F0s differed, and c) to lower the overall recognition rate to avoid ceiling effects. We reasoned that intraclass variability would make the task more typical of situations in which human beings recognize speech.

B. Harmonic Structure

Vowels were synthesized in one of two harmonicity states (harmonic and inharmonic) and at three nominal fundamental frequencies (125 Hz and ± 1/4-semitone, or ± 1.45% of the F0). Harmonic vowels had component frequencies equally spaced at multiples of the F0. For inharmonic vowels, each component frequency was shifted from the harmonic series by an amount drawn at random from a uniform distribution bounded by ±3% of the harmonic frequency, or half the spacing between adjacent harmonics, whichever was smaller (see Appendix A-2 for more details). The "nominal F0" of an inharmonic vowel is by definition that of the harmonic series before modification. We chose to use a rather mild perturbation to ensure that the spectral density was similar to that of a harmonic vowel shaped by the same envelope. A different component frequency pattern was used for each inharmonic allophone (however this pattern remained the same at different nominal F0s). Inharmonic patterns are illustrated in Fig. 2, together with a histogram illustrating the distribution of inter-component spacings in the F1 and F1-F3 regions.

The F0 values we chose allow F0s of 0 and 2.9% (1/2 semitone) to be investigated. Based on previous studies (Fig. 1), such values should ensure an effect large enough to be significant while leaving room for improvement with other factors. The range corresponds approximately to the maximum frequency shift of the partials of our inharmonic vowels, and to the mistuning up to which individual partials still make a full contribution to virtual pitch, as estimated by Moore et al. (1985)

Fig. 2 (a) Top: harmonic series; middle: range of frequencies from which inharmonic partials are drawn; bottom: a particular inharmonic series. (b) Histogram showing the distribution of inter-component spacings (divided by F0) for inharmonic series. Full line: spacings between components up to 750 Hz (F1 region). Dotted line: spacings between components up to 3 kHz (F1-F3 region).

C. Synthesis

Individual vowels were generated by 16-bit additive synthesis at a sampling rate of 16 kHz. Their spectra comprised 45 components with amplitudes determined by interpolated look-up in a spectral envelope table corresponding to a given envelope. There was an additional -5 dB/component de-emphasis from the 30th to the 45th component. All components started in sine phase. Stimuli were 200 ms in duration including 25 ms raised cosine onset and offset ramps.

II. Pre-test: Single Vowel Identification

The purpose of the pre-test was to screen listeners for their ability to identify the synthesized vowels used in the experiment. We were also interested in whether there were any systematic effects of harmonicity or F0 on the identifiability of vowels, as such effects might interfere with the effects studied in the main experiments.

A. Subjects

Subjects were 21 male and 11 female caucasian homo sapiens volunteers recruited from the staff and students at IRCAM and ENST (including the four authors). Their ages ranged from 23 to 50 years (mean 31.4). None of the subjects reported having a hearing disorder. The subjects had French as either their mother tongue (23) or as a highly fluent second language which they practised on a daily basis in their professional lives (9). The large majority had extensive experience producing and listening to synthesized sounds. Nineteen of the subjects had participated in a similar pilot experiment about two months prior to this one.

B. Stimuli

Ten allophones of the vowels /a/, /e/, /i/, /o/ and /u/ were each synthesized at the three F0s to be used in the main experiment (123.208, 125.0, 126.818 Hz). Each of these 30 combinations was synthesized in both harmonic and inharmonic versions. All stimuli were equalized for rms level.

C. Procedure

Subjects were seated in a Soluna SN-1 double-walled sound-proof booth, in front of a computer terminal that was used for prompting and to collect responses. Digital stimuli stored on hard disk were upsampled to 44.1 kHz, sent through the NeXT Cube D-A converters and presented diotically over Sennheiser HD 520 II earphones. The sound system was calibrated using a flat-plate coupler connected to a Bruel & Kjaer 2209 sound level meter to obtain a level of approximately 60 dBA.

Subjects were informed that they would hear individual vowel sounds and were to identify them as one of /a/, /e/, /i/, /o/, /u/ by typing the appropriate key on the computer keyboard (a, e, i, o, u, respectively). They were informed that they needed to attain a criterion performance level of 95% to continue on to the main experiment. The computer logged the spectral envelope, F0, harmonicity and response to each stimulus in a separate file for each subject. Each combination of allophone, nominal F0, and harmonicity was presented once for a total of 300 trials that were presented in random order (Appendix 4).The pre-test lasted 15 minutes on average.

D. Results

All but two of the subjects attained 95% criterion performance and continued on to participate in the main experiment. The identification rates for those subjects were 91% and 94%. Overall performance for a given subject varied from 91% (27 errors) to 100%. The global mean was 98% (11.2 errors; s.d. = 1.85%). Performance varied for different vowels: the order according to identification rate was /a/ (99%), /i/ (99%), /u/ (98%), /e/ (97%), and /o/ (97%). The only allophones whose performance fell below 90% were an /e/ and an /o/. The performance of one allophone (a /u/) fell between 90% and 95%. The remaining allophones were identified at better than 95%. The confusion matrix indicating the frequency of each response category assigned to each stimulus was examined. The only confusions that represented more than 1% of the judgments were confusions between /e/ and /i/ and between /o/ and /u/. These confusions accounted for 1.5% and 3.9% of the identification errors, respectively.

A multivariate repeated measures analysis of variance on factors vowel class (5) X harmonicity (2) X F0 (3) was performed with, as the dependent variable, proportion correct identifications across allophones by each subject within a given condition. Each data point was based on 10 judgments. The analysis revealed that the main effect of vowel noted above was significant (F(4,124)=3.5, p=0.016, GG=0.78). [1] There was no significant effect of fundamental frequency nor any significant interactions involving this factor. There was no main effect of harmonicity but the interaction between vowel and harmonicity was highly significant (F(4,124)=6.4, p=0.0002, GG=0.88) indicating an effect of harmonicity on vowel identification that is limited to certain vowels. Contrasts between harmonic and inharmonic versions for each vowel class showed that the effect of harmonicity was only significant for /e/ and /u/ vowels. Harmonic stimuli were better identified than inharmonic ones for /e/ by 2.8% (F(1,124)=19.5, p<0.0001, GG=0.88) and the reverse was true by 1.4% for /u/ (F(1,124)=4.5, p=0.041, GG=0.88). We can summarize these results by noting that there were small, though significant, effects of harmonicity for some stimuli and no effect of F0 for any stimuli. The general level of performance is quite good for the large majority of allophones in both harmonic and inharmonic versions.

III. Main Experiment: Double Vowel Identification

A. Subjects

Subjects were the 30 who attained criterion performance on the pre-test. Nineteen of these had participated in a similar pilot experiment about two months prior to this one.

B. Stimuli

The stimulus set consisted of pairs of synthesized vowel allophones belonging to the set: /a/, /e/, /i/, /o/, /u/. Vowels within a pair were always different, yielding 10 unordered combinations. Each vowel within a pair was either harmonic or inharmonic, yielding four combinations of harmonicity. Finally, there were two conditions of F0 difference: 0 and 1/2-semitone (2.9%). All factors, vowel pair (10), harmonicity (4) and F0 (2), were crossed giving 80 different combinations.

In addition to the factors that interest us, the design contained others that might also influence the phonetic quality of the target or the masking power of the ground: absolute F0, choice of inharmonic pattern, choice of allophone, or presentation order. To avoid any systematic bias due to these factors, the following precautions were taken: a) Pairs were duplicated so that each vowel of each pair occurred once at the higher and once at the lower F0 when F0!=0. b) For each inharmonic allophone, the same component pattern was used to synthesize different F0 conditions. c) Allophones were assigned in a balanced fashion across conditions. For example the subset of allophones representing the eight repetions of the vowel /a/ (2 positions X 4 other vowels) in the HH0 condition within a presentation of the stimulus set also represented that vowel in all other main conditions (HHx, HI0, etc.). Other subsets were used for other presentations. d) Stimuli were presented in random order, and this order was renewed for each run and each subject.

In the inharmonic state each allophone used a different component pattern. Since vowels within a pair were different, component patterns within an inharmonic-inharmonic pair were also different. As noted above, the same subsets of allophones appeared in all conditions, but for practical reasons it was not possible to guarantee that the occurence of allophone pairs was similarly balanced. Allophones were paired at random, and the pairing was renewed for each presentation and subject. Duplication of F0 conditions resulted in a 160-stimulus set.

Preliminary experiments had shown that when vowels are mixed at equal rms signal levels, one vowel might dominate the pair due to unequal mutual interference, as noted by McKeown (1992). In that case, the identification probability of one vowel is likely to be at its "floor" and the other at its "ceiling", both being thereby insensitive to the conditions of interest. To avoid such a situation, we performed a preliminary experiment to determine levels of equal "mutual interference" (see Appendix A-3). From these results we derived a level correction factor for all pairs, such that identification rates for both vowels were the same. Vowel levels were adjusted according to this factor, the vowels were summed, and the rms signal level of the sum was set to a standard level for all pairs.

C. Procedure

The experimental apparatus was the same as in the pre-test. The double vowel stimuli were presented at a level of about 60 dBA. Subjects were informed that they would hear a complex sound composed of two different vowels from the set /a/, /e/, /i/, /o/, /u/. Each vowel pair was presented once, followed by a visual prompt on the terminal screen. Subjects were required to hit two keys in succession, corresponding to the two vowels heard (two of a, e, i, o, u)--or else Q to quit temporarily. Any other response produced a message reminding the subject of the options, and requesting a new response. A response with two identical vowels produced a message reminding the subject that the vowels were different, and requesting a new response. Aside from information about response constraints, no feedback was given concerning the correct response. Subjects were presented with three consecutive runs of all combinations of vowel, harmonicity, and F0 in randomized order for a total of 480 stimuli.

Responses for each subject were gathered in a file. Each response was scored twice, once for each vowel present within the stimulus. The vowel was deemed correctly identified if its name appeared within the response pair. This partial response was classified according to the harmonic state of that vowel (the target), the state of the other vowel (the ground), the nominal F0 difference between them, and the names of both vowels. This procedure was repeated for the other constituent vowel, reversing the roles of target and ground, leading to a total of 960 "answers" for each subject. Figure 3 summarizes these conditions and their notation. This method of scoring is equivalent to that used by Lea (1992) to obtain "constituents-correct" scores.

Fig. 3 Response conditions: Target harmonicity X Ground harmonicity X F0 X vowel pairs.

D. Results

Within each harmonicity and F0 condition, proportion correct identification measures for each target vowel were calculated for each subject across all vowel combinations, yielding eight data points per subject. Each data point was based on 120 judgments (20 vowel pairs X 2 vowel identifications X 3 repetitions). A multivariate repeated measures analysis of variance was performed on factors F0 (2), target harmonicity (2), and ground harmonicity (2). All main effects and interactions were statistically significant (see Table I). Subsequent discussion will focus on tests of the various hypotheses outlined in the introduction.

Table I Analysis of variance table for the main experiment. Dependent variable: Mean Identification performance for target vowels across vowel pairs. Independent variables: fundamental frequency difference (F0), target harmonicity (Tar), ground harmonicity (Gnd).

1. Effect of F0

In Figure 4 the means across subjects are plotted as a function of F0. Each line represents one of the four combinations of target and ground harmonicity. Filled symbols represent harmonic targets and open symbols inharmonic targets. Squares represent harmonic grounds and circles inharmonic grounds. When both vowels are harmonic, performance increases with F0 by about 6%. Planned contrasts show that this effect is highly significant (F(1,29)=50, p<0.0001). When at least one vowel is inharmonic the effect is not significant (for HI: F(1,29)=0.1; for IH: F(1,29)=0.4; for II: F(1,29)=0.4). We take advantage of this fact to group these conditions across F0 in subsequent contrasts.

Fig. 4 Identification rate as a function of F0 for each of the harmonicity conditions. Error bars represent ± 1 standard error of the mean. The standard deviations vary between 0.066 and 0.081. Data points for HH and HI are displaced horizontally for visibility.

2. Effect of Harmonicity of Ground.

The data are replotted in Fig. 5 to emphasize the effects of ground and target harmonicity. Contrasts planned to test the cancellation hypothesis (Introduction, B.1) show that identification improves significantly when the ground is harmonic, unless the target is also harmonic and F0=0 (IH vs. II: F(1,29)=26, p<0.0001; HHx vs. HI: F(1,29)=14, p=0.0008). The improvement in identification rate is about 3%. These results are compatible with the cancellation hypothesis. An additional contrast shows that when the target is harmonic and F0=0, performance is significantly worse with a harmonic ground, also by about 3% (HH0 vs. HI0: F(1,29)=13, p=0.0009).

3. Effect of Harmonicity of Target.

Whatever the F0 and whatever the nature of the ground, identification is worse when the target is harmonic. Contrasts planned to test the enhancement hypothesis (Introduction, B.2) are highly significant (HI vs. II: F(1,29)=15, p=0.0004; HHx vs. IH: F(1,29)=13, p=0.0008), but the direction of the effects observed is opposite to that predicted by that hypothesis. The effect is similar in size, about 3%, to what was observed for ground harmonicity. An additional contrast shows that the larger effect (about 8%) obtained when the ground is harmonic and F0=0 is also significant (HH0 vs. IH0: F(1,29)=99, p<0.0001).

Fig. 5 Identification rate of target as a function of ground harmonicity, for harmonic and inharmonic targets and nominal F0 differences of 0 and 1/2 semitone.

4. Evidence of Symmetrical Segregation.

A contrast planned to test the hypothesis of symmetrical segregation (Introduction, B.3) shows that, contrary to what this hypothesis predicted, performance is significantly better for IH than for HI conditions (HI vs. IH: F(1,29)=96, p<0.0001), by about 5% (Fig. 5). Symmetric segregation mechanisms cannot account for our results. They might however coexist with other asymmetric mechanisms, so it is of interest to consider contrasts specific to the various symmetric segregation hypotheses.

Performance for HH0 is worse than for all other conditions (HI vs. HH0: F(1,29)=19, p<0.0001; IH vs. HH0: F(1,29)=142, p<0.0001; II vs. HH0: F(1,29)=59, p<0.0001). This would be consistent with the component-mismatch hypothesis, were it not for the asymmetry between HI and IH mentioned above.

Performance is better for IH than for II (F(1,29)=26, p<0.0001) but worse for HI than for II (F(1,29)=15, p=0.0004). This is inconsistent with the quality differences hypothesis, already weakened by the asymmetry between HI and IH.

5. Confusion Matrix

The confusion matrix for vowel pairs is shown in Table II. There was a slight bias towards responses containing 'o' (22.0%) and 'e' (21.0%), rather than those containing 'i' (19.1%), 'u' (19.1%) or 'a' (18.8%). The unordered response pair 'ou' was recorded most often (14.2 %), and 'au' least often (7.1%). The vowel /u/ appears to be correctly identified most often (85%), followed by /o/ (80%), /e/ (76%), /a/ (73%) and /i/ (72%). Vowels paired with /a/ are identified correctly most often (91%) followed by those paired with /i/ (86%), /e/ (82%), /o/ (79%) and /u/ (49%). The poor rate for vowels paired with /u/ is most certainly due to the excessive level emphasis given to /u/ relative to other vowels (see Appendix A-3).


Table II Confusion matrix for vowel pairs (response orders are confounded). The total number of times each stimulus type was actually presented was 1440. The bottom two rows give the total number of responses of each kind, and the proportion of total responses they represent.

6. Dependency of Effects on Vowel Pair

Our experiment was designed assuming that data would be averaged over vowel pairs (and thus over allophone pairs and component pattern pairs). This was deemed appropriate because we had no theoretical reason to expect major differences in the way different vowel pairs, allophone pairs, or pattern pairs might affect the dependency of identification rate on our main conditions: ground harmonicity, target harmonicity, and F0. It is nevertheless of interest to note such effects. Figure 6 displays the identification rate as a function of ground harmonicity for each of the 20 vowel pairs, for both conditions of F0 and both conditions of target harmonicity. Vowel pairs differ considerably in overall identification rate, as well as in the size and direction of the effects of ground harmonicity. These differences might be due to genuine vowel specificities, or to some effect of the level correction factors that we applied, or possibly to differences between the component patterns used to synthesize each vowel pair (each allophone had its own inharmonic pattern when it was synthesized in an inharmonic state; each vowel was thus represented by a different set of patterns). Our experimental design does not allow us to decide which of these factors are responsible for the differences. It is however of interest to keep them in mind when interpreting our main effects. For example it may be that the population of "inharmonic" patterns that we treat as homogenous is actually made up of members with widely differing properties.

Fig. 6 Identification rate of target vowel as a function of ground harmonicity for each vowel pair and for all four conditions of F0 and target harmonicity. The thick lines without markers represent the effect averaged over vowel pairs, also plotted in Fig. 5.

IV. Discussion

A. Effect of F0 in Comparison with Previous Studies

Most previous studies report the proportion of responses for which both vowels in a pair were correctly identified (combinations-correct rates). To allow comparisons to be made, combinations-correct scores were calculated from our data for the HH condition and plotted in Fig. 1 together with data from those studies. The effect of F0 is quite similar. Although our task was relatively easy (chance level is 10%, as in Culling and Darwin (1993a) and Lea (1992), compared to 3.8% for Scheffers (1983), or 6.7% for Summerfield and Assmann (1991)), our rates are relatively low. This probably reflects the greater variability of our stimulus material, and differences in training (we used a large number of relatively untrained subjects).

B. Evidence for Cancellation

At a F0 of a 1/2-semitone, whatever the target, and at F0=0 when the target is inharmonic, identification is better when the ground is harmonic. This is consistent with the cancellation hypothesis. No advantage was to be expected for a harmonic ground in the fourth condition (F0=0 with a harmonic target), but identification was actually worse when the ground was harmonic than when it was inharmonic (an unexpected outcome). One possible explanation is that our inharmonic stimuli were approximately harmonic with a "pseudo period" that differed from their nominal period (on informal listening they often appeared to have a pitch different from that of a harmonic vowel of same nominal F0). A harmonic sieve tuned to reject the "peudo-period" might partially remove the inharmonic ground without completely removing the target, whereas that target would be eliminated if both vowels were harmonic and had the same F0. Another possible explanation is that other mechanisms are at work in addition to cancellation.

Lea (1992) also found evidence for cancellation: when the target was a 112 Hz voiced vowel, identification rates were better by 3% for a 100 Hz voiced ground than for a whispered ground. When the target was a whispered vowel, the advantage was 8%. Subsequent experiments (Lea and Tsuzaki 1993a,b) gave similar results. The largest effect found by Lea (1992) was greater by a factor of 2.7 than the ground harmonicity effects we found (~3%). The smaller size of our effects may be due to the fact that our inharmonic vowels were more "harmonic" than whispered vowels.

C. Evidence for Enhancement

Our results do not support enhancement. In fact identification rates are worse when the target is harmonic, whereas in the absence of enhancement we predicted a null effect. This result is unexpected. It is worth considering in more detail at this point the assumptions upon which we based our predictions. We assumed that both vowels could be retrieved simultaneously via independent processing channels involving enhancement and/or cancellation, and thus that both hypotheses could be tested independently. If instead the auditory system must choose between strategies, factors that favor one may penalize the other. If, for example, cancellation is used systematically, it may tend to "lock" onto whatever happens to be harmonic within the stimulus, and thus impair the identification of harmonic targets. Inharmonic targets would be relatively immune. Thus the unexpected outcome of our experiment may be due to the mutual interference between segregation mechanisms. If so, we cannot rule out the eventuality that enhancement is used, but its effects are swamped by the side effects of cancellation. Enhancement would eventually show up in tasks in which cancellation is less likely to come into play. Our results contrast with those of Lea (1992), who found no significant difference between whispered and voiced targets, and Lea and Summerfield (1992), who found an advantage for targets that were voiced rather than whispered.

An explanation for the apparent preference of the auditory system for cancellation over enhancement may be found in an experiment by McKeown (1992). He requested subjects to identify both vowels within a pair, and at the same time judge which vowel was "dominant", and which was "dominated". Improvements in identification with F0 only concerned the dominated vowel. If we suppose that it is easier to estimate the F0 of a dominant vowel than that of a dominated vowel, it should follow that cancellation is easier to apply to segregate the dominated vowel (de Cheveigné 1993a). It is then reasonable that factors upon which cancellation depends should affect the scores. Another explanation may be found in an experiment of de Cheveigné (1993b, 1994). Harmonic enhancement and cancellation were implemented in a speech recognition system to reduce the effects of co-channel speech interference. Cancellation was more effective than enhancement, presumably because it was less affected by the non-stationarity of speech. The synthetic vowels used in our experiments are stationary so this consideration should not apply here. However, the auditory system may have evolved to use only strategies that are robust for natural stimuli.

D. Compatibility with F0-guided Models of Concurrent Vowel Perception

A variety of models make use of explicit F0 information. Some clearly take sides for either enhancement (Frazier et al. 1976) or cancellation (Childers and Lee 1987; Hanson and Wong 1984; Naylor and Boll 1987), but most other models are capable of both. Models come in three sorts: spectral, spectro-temporal, and temporal.

The harmonic sieve employed by spectral models based on Parson's harmonic selection method (Assmann and Summerfield 1990; Parsons 1976; Scheffers 1983; Stubbs and Summerfield 1988, 1990, 1991) can be used in either of two modes: to retain components that fall close to a harmonic series, or else to remove them. These modes correspond to enhancement and cancellation, respectively. The sieve may be applied in turn for each F0, correlates of one voice being selected among those rejected by the sieve tuned to the other. In that case each voice retrieved is actually a product of both strategies. Similar remarks can be made concerning models derived from Weintraub's spectro-temporal model (Assmann and Summerfield 1990; Lea 1992; Meddis and Hewitt 1992; Weintraub 1985): channels dominated by the period of a voice can be retained (enhancement) or else removed (cancellation). If both operations are applied in turn, each voice retrieved is really the product of both strategies. In the model of Meddis and Hewitt (1992), only one F0 was used, so one voice (the dominant one) was purely the product of enhancement, whereas the other voice was purely the product of cancellation. However nothing in the model prevents it from being extended to use both strategies to segregate both voices. Finally, de Cheveigné (1993a) proposed a time-domain comb-filtering model implemented by neural circuits involving inhibition that was capable of either enhancement or cancellation.

Since most models allow both strategies, our results do not allow us to choose among them, but they do allow us to better understand how each model functions.

E. Compatibility with other Models of Concurrent Vowel Perception

A number of models that do not require explicit extraction of F0 have been proposed to explain improvement of identification with F0. Summerfield and Assmann (1991) suggested that such an improvement might be explained by misalignment between partials of constituent vowels. At unison the partials of both vowels coincide, and their relative contributions to the combined spectrum are obscured by phase-dependent vector summation. Misaligned partials on the other hand may show up as independent peaks within a high-resolution spectrum and thus template-matching strategies might be more successful. Summerfield and Assmann (1991) found some evidence for an effect of component misalignment for vowels with widely-spaced components (200 Hz), but none for monaurally presented vowels at 100 Hz. On the other hand in a masking experiment in which thresholds were determined for synthetic vowels masked by vowel-like maskers, Summerfield (1992) attributed up to 9 dB of a 17 dB release from masking to component misalignment. The remaining 8 dB were attributed to F0-guided mechanisms. Our results certainly cannot be explained solely in terms of component misalignment. HI and IH conditions involve the same inter-component intervals, yet they produce identification rates that are very different. However if harmonic misalignment were involved together with other mechanisms, it might help explain for example why the HH0 condition was significantly worse than the HI0 condition. Our experiments used II pairs in which the inharmonic patterns of the vowels were different, and thus partials did not coincide at nominal F0=0. It would be worth investigating a similar condition in which both vowels have the same inharmonic pattern. Comparisons between the two would allow us to factor out eventual effects of component misalignment.

If the period of a vowel is long relative to time constants of integration within the auditory system, the vowel's auditory representation may fluctuate during the period. Mutual interference between concurrent vowels may be more or less severe according to whether the fluctuations of their respective representations line up in time or not. A small F0 difference is equivalent to a gradually increasing delay of one vowel relative to the other, and this might allow the auditory system to select some favorable interval on which to base identification. Differences in F0 might thus enhance identification. Summerfield and Assmann (1991) investigated the effects of pitch period asynchrony on identification rate using vowels with same F0 but varying degrees of phase shift. They found a significant effect at 50 Hz, but none at 100 Hz, presumably because the integrating properties of the auditory representation smooth out fluctuations at this rate. Our vowels had even higher F0s, so this explanation is unlikely to account for our data.

Slower fluctuations may occur in the compound representation of the vowel pair. Two partials falling within the same peripheral channel produce beats with a depth that depends on their relative amplitudes, and a rate equal to their difference frequency. Three or more partials produce yet more complex interactions. These fluctuations may cause the auditory representation to take on a shape that momentarily allows one vowel or the other, or both together, to be better identified. Culling and Darwin (1993a,b) suggested that such beats might explain increases of identification rate with differences in F0. Assmann and Summerfield (1994) found that successive 50 ms segments excised from a 200 ms stimulus composed of two vowels with different F0s were not equally identifiable. For small F0, identification of the whole stimulus could be accounted for assuming it was based on the "best" of the segments that composed it. This result is compatible with the notion that F0 differences cause the auditory representation to fluctuate (as does, indeed, the short-term spectrum itself), and provide the auditory system with various intervals upon which to base identification, one of which may be particularly favorable to either vowel or both.

Inharmonicity or F0 differences between vowels can be interpreted as slowly varying phase relationships between partials of harmonic vowels with a same F0. The "best interval" provided by beating can be interpreted simply as a phase relationship that is particularly favorable for identification. The harmonic vowels used in our experiments were all synthesized in sine phase, whereas the partials of inharmonic vowels can be interpreted as progressively moving out of this phase relationship. If the masking power of vowels in sine-phase is relatively small and the resistance to masking of vowels in sine-phase is relatively poor, then harmonic vowels will appear to be both less well recognized and less effective as maskers, as indeed we found. Phase effects thus constitute a possible alternative explanation of our results.

F. Harmonicity and the Cohesion of Sound

The lack of a positive effect of harmonicity on target vowel identification is the most surprising result of this study. It has been suggested that harmonicity labels parts of a sound as belonging together in several ways: continuity of F0 indicates that successive parts of speech belong to the same voice, the same F0 indicates that different formants belong to the same vowel, a common F0 signals that partials within a formant belong together (Bregman 1990; Broadbent and Ladefoged 1957; Darwin 1981). Without this "harmonic glue" components would fall apart, and the sound might lose its intelligibility or be more easily masked. Nevertheless Darwin (1981) found that speech sounds synthesized with different formants on different F0s retained their phonetic quality. Culling and Darwin (1993a) synthesized vowels with a difference in F0 between their first and higher formants, and paired them so that the components making up the first formant of one vowel belonged to the same harmonic series as the higher formants of the other. In other words, the F0s were swapped between vowels in the F1 region. Identification was as good as for vowels with unswapped F0s for all but the largest F0s, from which Culling and Darwin concluded that a common F0 between formants does not affect how they are grouped together. Our results go a step further. They suggest that a common F0 between partials has no positive effect (and apparently even a negative effect) on the identification of the sound that they form. This result is counter-intuitive, and is contradicted by some other studies. For example, Darwin and Gardner (1986) found that mistuning a single partial within a formant affected the phonetic quality of a vowel. However the effect of mistuning (which was phase-dependent) was not always in the direction expected on the basis of harmonic grouping.

A common F0 does have one important effect: it produces the impression of a single source. The presence of multiple F0s within a sound, what Marin (1991) calls "polyperiodicity", produces the impression of multiple sources, and thus signals to the auditory system that segregation is called for. This signal might have great value for sound organization, and yet have no effect in psychoacoustic experiments for which the listening frame is already determined by the task.

V. Summary and Conclusion

1) Listeners identified vowels within synthetic pairs better by about 3% when they were inharmonic than when they were harmonic, except when the ground was harmonic and F0=0, in which case the advantage was 8%. This result is contrary to what one would expect if a strategy of harmonic enhancement was used to segregate the vowels.

2) Listeners identified vowels within synthetic pairs better by about 3% when the vowels accompanying them were harmonic than when they were inharmonic, except when the target vowel was also harmonic and F0=0, in which case they were less well identified by about 3%. These results are consistent with the hypothesis of harmonic cancellation.

3) When both vowels within a pair were harmonic, they were better identified by about 6% when there was a difference in F0 of 1/2 semitone. This is consistent with results of previous studies. When either vowel was inharmonic, a difference in F0 did not affect identification.

4) When one vowel within a pair was harmonic and the other inharmonic, the inharmonic component was identified significantly better than the harmonic component. Effects do not follow the symmetric pattern that is sometimes assumed to be characteristic of primitive segregation.

5) Our experiments employed a particular starting phase pattern (sine) to synthesize all vowels. In the light of recent results that demonstrate the role of beats in the identification of concurrent vowels (Assmann and Summerfield 1993, Culling and Darwin 1993b), we cannot rule out the possibility that our results are partly specific to this phase pattern.

Fundamental frequency had two putative roles for Darwin (1981): to "group consecutive sounds together into the continuing speech of a single talker" and to "group together the harmonics from different formants of one talker, to the exclusion of harmonics from other sources" (p. 186). Our results suggest that these roles are minor in comparison to a third: to group together components that belong to an interfering source to better eliminate it. The lack of benefit of target harmonicity for identification is surprising, as target harmonicity can in principle be exploited by a majority of harmonic sound separation models. The question merits further examination, perhaps using tasks that do not trigger cancellation.


Thanks to Gérard Bertrand for technical assistance, to Laurent Ghys for guiding some of us through the mysteries of the NeXT Machine, and to Nina Fales for assistance during the experiments. Thanks to John Culling and Quentin Summerfield for providing data on which Fig. 1 was based, and to Andrew Lea for useful discussions. This research was supported by a grant from the "Cognitive Sciences" program of the French Ministry of Research and Space.

Appendix A-1: Preparation of Spectral Envelopes

We wished to use stimuli with high intra-class variability in order to make the identification task more difficult and more typical of real speech communication. We reasoned that the best place to look for such variability is in natural, continuous speech. We systematically extracted voiced (quasi-periodic) tokens from a multi-speaker speech database to obtain samples of a wide range of spectra. We then screened them in several stages to obtain a set of spectral envelopes that were consistently identifiable as given vowels after resynthesis. The thresholds of acceptance in these screening tests were chosen to strike an (arbitrary) balance between the goals of variability and consistent identifiability.


The database consisted initially of 50 phonetically balanced French sentences pronounced by 11 adult speakers (5 male, 6 female), belonging to the CD6_GRECO1 disk of the GRECO1 database (GRECO 1987). To this initial database we later added 16 sentences containing mainly /u/ vowels and a set of CVCV (V=/u/) words from the same database. Data were sampled at 16 kHz with 16-bit resolution.

Estimation of Period and Periodicity, Extraction of Tokens

The initial database was processed by an F0 estimation algorithm based on the Average Magnitude Difference Function (AMDF) algorithm (described in Appendix B-2 of de Cheveigné 1993a), that produces as a by-product a measure of periodicity. The F0 and periodicity measure were used to label portions of voiced speech as follows: wherever the periodicity measure was above an arbitrary threshold (2.0) for more than 50 ms, and the F0 was within the range 111 Hz - 141 Hz, an index was set every 50 ms. A total of 1788 indices were thus set.

First Screening

For each index, a 50 ms stimulus was synthesized by extracting a single period of the wave form and repeating it by concatenation at the original F0. These stimuli were screened by informal listening by one of the authors (M.R.). Stimuli that did not sound like vowels were rejected and the others were labelled with a vowel name. 572 vowel tokens were kept (107 /a/, 180 /e/, 113 /i/, 94 /o/, 78 /u/).

Spectral Analysis

Spectral analysis was performed according to the following procedure: for each labeled token, a single period was extracted and a DFT was performed on this period to obtain a magnitude spectrum. A 512-point, 0-8 kHz spectral envelope was derived by linear interpolation between the magnitude spectrum coefficients (each representing a harmonic of the original vowel) [2]. An envelope file was produced for each token.

Second Screening

For each envelope file, a periodic synthetic stimulus was produced by additive synthesis. Forty-five harmonics of 125 Hz were added in sine phase with amplitudes determined by the envelope, with a 5 dB/component de-emphasis from the 30th to the 45th component to reduce edge effects. Stimuli were 400 ms in duration, including 50 ms raised-cosine onset and offsets. Subjects were the four authors. All stimuli were presented three times in random order, diotically via headphones in an office environment. Subjects could listen repeatedly to each stimulus and were required to press a key representing the vowel, or "x" if the stimulus was not identifiable as one of the target vowels. Stimuli that were consistently identified as the same vowel (independently of their initial label) at least 11 times out of 12 were kept. We thus retained 79 /a/, 54 /e/, 73/i/ and 20 /o/, but only 3 /u/. To obtain more /u/ tokens, we extended the analyzed database and repeated the previous analysis/synthesis steps to obtain 58 more /u/ tokens.

Third Screening

The allophones were screened once more. The same four subjects judged the "quality" of the vowels on a 3-point scale (1-excellent, 2-average, 3-poor). With a rejection criterion of 1.5 (1.7 for the /u/), we retained 75 /a/, 49 /e/, 35 /i/, 13 /o/ and 13 /u/.


For each vowel we wished to obtain a set of 10 allophones with as much intra-set variability as possible. To obtain a better distribution than by random choice, we used a clustering algorithm based on the classic K-means algorithm, using Euclidean distance on the 512-point spectral envelopes. The algorithm performed the following steps:

1) Choose an initial 10-point reference set. The first point is chosen at random, each following point is chosen as far away as possible from previously chosen points.

2) Partition the set into clusters, assigning each data point to its closest reference.

3) Replace each reference by the centroid of its cluster, then loop to 2) until a convergence criterion is met.

4) For each centroid finally obtained, choose the closest original data point.

The result was a set of 50 allophones, 10 for each vowel.

Final Screening

A pilot version of our experiments served as a final screening test. Stimuli were 50 harmonic and 50 inharmonic allophones with a nominal F0 of 125 Hz, presented diotically via headphones in a sound-treated booth in random order. Subjects were 30 adults, of which 27 had French as their mother tongue and 3 used it as a highly fluent second language. A criterion was set to eliminate subjects whose identification rate fell below 92%. The analysis of the confusion matrix of the 20 subjects that remained showed a very high error rate for /u/ stimuli (18.6%). Errors for /u/ represented 62% of all errors, and 95% percent of these errors were /u/-/o/ confusions. Practically all errors occurred for four /u/ allophones that tended to be identified as /o/, even by subjects that had consistently classified them as /u/ in previous screening tests. This result no doubt illustrates effects of context on vowel identification. We eliminated these allophones, duplicated four of the remaining allophones, renamed them, and proceeded as if /u/ had the same number (10) of allophones as the other phonemes.

We repeatedly met difficulties with /u/. For some reason, very few portions of speech isolated from our database sounded like /u/ after resynthesis, even those taken from sentences labelled as containing mainly /u/ phonemes. A tentative explanation is that in French /u/ is articulated with a protrusion of the lips. The target position may require some time to be attained, and the resulting spectral transition may in fact be necessary for identification. Evidently no such transition is present in the resynthesized vowel. This does not explain however why a few tokens do sound reasonably /u/-like after synthesis. Overall, surprisingly few of the original voiced speech tokens were identified consistently as vowels after resynthesis: less than 10 % of the original tokens survived the final screening. In real speech vowel identity is probably largely determined by contextual or dynamic features that are absent from the resynthesized vowels (Hillenbrand and Gayvert 1993).

Appendix A-2: Synthesis of Inharmonic Component Patterns

We wished to obtain vowels that were inharmonic, but with a spectral density close to that of a harmonic vowel. The frequency of each component of a harmonic series was shifted by a random amount drawn from a uniform distribution bounded by ±3% of the harmonic frequency, or half the spacing between adjacent harmonics, whichever was smaller. We synthesized twice the required number of component patterns (50), then screened out the "least inharmonic" half by choosing those with the greatest values of the following measure of inharmonicity:

where fn is the frequency of the nth component.

Appendix A-3: Level Correction Factors

When vowels are mixed at equal rms signal levels, one vowel may dominate the pair due to unequal mutual interference. We wished to avoid this situation. Informal listening showed that equal rms level results in approximately equal loudness; we concluded that matching for equal loudness was unlikely to fulfil our goal. Instead we decided to determine experimentally a corrective factor to balance mutual interference.

We first determined informally, for each of the 10 vowel pairs, the rms level differences for which either vowel appeared to be absent. We then centered a scale with 4 dB steps and 10 levels on the mean of these two differences, and synthesized pairs of unison harmonic vowels according to this scale. There were 10 such scales, one for each different vowel pair. The stimuli were presented 5 times each in random order to four subjects (the four authors). At each presentation the stimulus was repeated twice; after each repetition the subject had to identify one constituent (SRSR pattern). A response could be any of the five vowels, or 'x' if no vowel could be heard, but the two responses had to be different. Psychometric functions were plotted for each component of a pair, and their intercept was taken as the corrective factor (more sophisticated interpolation techniques were judged unnecessary for our purpose of adjusting levels to avoid complete dominance within a pair). The corrective factors for all pairs are shown in Table A3-I


Table A3-I Level correction factors for vowel pairs, in dB. The level after correction of one vowel relative to another is shown at the intersection of the row and column that they label, respectively. For example to synthesize /ae/ the rms level of /a/ should be set to be 5.0 dB less than that for /e/. These results are roughly compatible with those reported by McKeown (1992) for three of his four subjects: /a/ tends to dominate all other phonemes, /u/ tends to be dominated by all others. Other phonemes are intermediate: /o/, /i/, /e/ in order of increasing dominance. However, our factors were determined before the final screening that eliminated four allophones of /u/. Levels are therefore certainly biased too far in favor of /u/ to compensate for their poor quality. This is evident in the rates as a function of ground vowel, particularly low when /u/ is ground (III-D-6), but it should not affect our main conclusions concerning the effects of harmonicity or F0: they remain quite similar when pairs containing /u/ are removed from analysis. We do not recommend that these particular level correction factors be used in other studies.

Appendix A-4: Randomization

It is worth stating explicitly what we mean by random order and quantities. Inharmonic vowel component patterns were "random" in the limited sense that a set of 50 inharmonic patterns was obtained by random perturbation of a harmonic series. This same set was used for all subjects and presentations. Stimulus presentation order was random in the sense that the stimulus set was shuffled before each run according to a fresh series of random numbers. The pairing of allophones representing a vowel pair was random in the sense that it depended on the random order with which allophones were called upon to represent a given vowel within a stimulus set. All series of random numbers were produced by the random() routine of the UNIX C library, after initialization by a call to srandom() with an argument derived from the system clock.


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In all reports of F statistics in this article the probabilities reflect, where necessary, an adjustment of the degrees of freedom by the Greenhouse-Geisser factor to correct for the inherent correlation of repeated measurements (Geisser and Greenhouse, 1958). GG indicates the epsilon factor by which degrees of freedom were multiplied to determine the probability level. This is a conservative correction factor.
We tried a cepstral smoothing technique in an early stage, but rejected it because we were dissatisfied with the quality of re-synthesized vowels. However we met similar problems with other methods we tried, so it seems likely that the poor quality was essentially due to variability and coarticulation effects in the speech we analyzed, and the harshness of purely periodic resynthesized speech. We nevertheless stuck to the present procedure that has the advantage that it makes no normative assumptions about the shape of the spectral envelope.

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