The fundamental frequency (f0) distribution of American speakers in a spontaneous speech corpus^*

The Buckeye Corpus of conversational speech comprises recordings from 40 American speakers, both male and female, who were born in or near Columbus, Ohio (Pitt et al., 2007). The study enlisted 20 men and 20 women, segregated into younger and older groups based on a threshold age of 40 years, each consisting of 20 participants. The participants engaged in hour-long friendly conversations with either a male postdoc or a female graduate assistant, covering topics such as politics and sports. To ensure a homogeneous target population, the corpus team screened individuals carefully through brief telephone interviews. Then, the team meticulously listened to the recordings, transcribing not only the interviewees' actual pronunciation using phonetic symbols but also capturing non-speech sounds like laughter, silence, noise, and the interviewer's voice.

Fundamental frequency values were gathered using Praat (v.6.3.14, Boersma & Weenink, 2023), and their distribution was subjected to statistical analyses using R (v.4.3.1, R Core Team, 2023).

Several Praat scripts were developed to refine the sound files and obtain accurate and reliable f0 values. Initially, a script was employed to silence non-speech sounds and the interviewer's voice by setting them to zero amplitude, referencing the labels of these segments in each transcript file. Another script measured f0 values for all files at 20 ms intervals within a range of 75 Hz to 600 Hz, storing the values on a notebook computer.

The initial f0 values of the forty speakers exhibited a broad distribution with numerous outliers. To address this, the author generated a boxplot in R and determined the interquartile range (IQR) for each dataset. Subsequently, the initial dataset underwent filtration to eliminate values falling below and beyond 1.5 times the IQR. The following code illustrates this process, demonstrating the application to the original f0 values of the first participant (S01) in the data frame (S01df) to create a new data frame (S01df_new) without outliers.

Figure 1 displays two boxplots representing the original data and the filtered data. Outliers are depicted as overlapped circles outside the second and third quartiles. While a few outliers are still noticeable in the filtered data, they appear negligible compared to those in the original dataset.

Figure 1. Boxplots of S01’s original fundamental frequency (f0) values (left) and outlier-filtered values (right).

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Statistical analyses of the f0 distribution were executed using R. An R code, proposed by Lennes et al. (2016), was adapted to generate probability density curves illustrating the f0 distribution concerning age and sex groups. Key statistical parameters, including mode, median, mean, standard deviation (SD), and the minimum and maximum values were compiled to discuss both group and individual variability. Additional statistical measures, such as skewness and kurtosis, were acquired to assess group characteristics.

Table 1 provides a statistical summary of all the f0 values from American speakers, comprising a final dataset of 1.774 million values.

The mode in the Buckeye Corpus was observed at 114 Hz, with a median of 145 Hz and a mean of 149 Hz. Although the mean was the highest among the three major measurements, the difference between the median and mean values was small (4 Hz). In contrast, the difference between the mode and median was more substantial at 31 Hz, akin to the Korean corpus with a 46 Hz difference (Yang, 2021). These differences may be linked to the right-skewed f0 values in the higher frequency region, where higher f0 values could have influenced the mean and median. Yang (2021) reported a median f0 value of 148 Hz from the Korean corpus, with a range from the maximum to the minimum f0 values at 559 Hz. He reported 102 Hz for the Korean mode and 160 Hz for the Korean mean. Here the f0 range of the American corpus records 320 Hz. The wide range difference between the American and Korean corpora might be related to the removal of the American outliers considering each individual IQR. On the other hand, Lennes et al. (2016:44) provided a statistical summary of the forty individual speakers. The average of their median values was 147 Hz spanning from 70 Hz to 199 Hz. The mode and mean of the Finnish speakers recorded 139 Hz, and 154 Hz. Considering extreme outliers derived from acoustic measurement errors, median values might best represent the inherent f0 for a given language corpus. The skewness of the American corpus was 0.78, which indicated the frequent f0 values at the lower end, and the tail pointed toward the higher end of the scale (Field, 2013). In addition, the kurtosis was 0.86 and there were three pointy peaks below 200 Hz. On the other hand, the skewness of the Korean corpus was 0.92, which represented a positive skew while that of the kurtosis was 0.94, which yielded a leptokurtic or pointy distribution.

Figure 2 presents a box plot of f0 values collected from all the American speakers every 20 ms from nearly 40 hours of the American English corpus.

Figure 2. Boxplot of f0 values (Hz) of forty speakers in the Buckeye Corpus.

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In the boxplot, outliers are generally identified beyond these limits of a lower bound at 75 Hz and an upper bound at 291 Hz. The frequency band, spanning 216 Hz between these bounds, characterizes the typical f0 range of American English speakers. Notably, there is a comparatively short tail of outliers around 100 Hz above the upper bound, which is half of the outlier range depicted in Figure 1. This limited range of outliers is likely a result of filtering individual data. The lower quartile registers at 109 Hz, while the upper quartile reaches 182 Hz, yielding an IQR of 73 Hz. To eliminate outliers further, an upper bound can be approximated by multiplying the IQR by 1.5 and adding the third quartile value, resulting in 291.5 Hz, which is only 0.5 Hz above the upper bound.

Table 2 lists basic statistical measures of the American English data grouped by sex.

The mode for male speakers registered at 114 Hz, aligning with the overall mode across all the speakers. Combining male and female data, the prevalence of higher peaks in the male data resulted in a shared mode for both groups. Specifically, female speakers exhibited a mode of 175 Hz, indicating a distinct 61 Hz contrast between the two groups.

In contrast, Korean speakers, as reported by Yang (2021), showcased a median of 111 Hz for the male group and 200 Hz for the female group. Also, the median of the twenty Finnish male speakers amounted to 110 Hz while that of the female speakers listed as 184 Hz (Lennes et al., 2016). These figures suggest slightly higher or lower values compared to their American counterparts. It is noteworthy that the Finnish participants predominantly consisted of young adults, and the potential clipping of f0 values below the threshold might have occurred due to the Praat software's lower limit of 75 Hz. This crosslinguistic distinction may stem fundamentally from anatomical differences between Americans and Koreans. Notably, the greater f0 in the female group could be linked to anatomical sex differences in the length and mass of vocal folds (Boothroyd, 1986).

Figure 3 illustrates two boxplots presenting the fundamental frequency values of male and female speakers collectively. A noticeable and substantial difference is apparent between the two groups. The boxplot for female speakers reveals a broader distribution range, featuring additional outliers identified by small circles positioned either above or below the quartile division.

Figure 3. Boxplot of f0 values (Hz) of female (left) and male (right) groups in the Buckeye Corpus.

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Additionally, the f0 range for the female group appeared wider than that of the male group. For a meaningful crosslinguistic comparison, it is advisable to recruit participants within the same age range and control for speech style, be it reading or conversational. Failure to do so might introduce biases in any crosslinguistic comparison, influenced by these intervening factors.

Table 3 provides a summary of the basic statistics for each American speaker.

The mode range spans 124 Hz, ranging from 76 Hz (S24) to 200 Hz (S12). The lowest median, observed in S24, is 82 Hz, while the highest median, found in S12, reaches 229 Hz. Positioned between the mode and mean, the median offers a central tendency measure. In this context, the mean range is slightly broader than the preceding measures, extending from 84 Hz (S13) to 240 Hz (S12). The average SD is 21 Hz, ranging from 5 Hz (S13) to 63 Hz (S07). The relatively narrow SD may be attributed to the outlier filtering procedure using the IQR specific to each individual speaker. In comparison, Yang (2021) reported an SD range of 55 Hz, varying from 16 Hz to 71 Hz for the Korean corpus. Also, Lennes et al. (2016) provided an average SD of 31 Hz, covering from 17 Hz to 49 Hz.

In Figure 4, probability density curves delineate the f0 values of individual male and female speakers within the American English corpus. The author used distinct colors, with the f0 values of male speakers depicted in blue and those of female speakers in red. Generally the female data appear flat across a wide frequency range while those of the male speakers look more pointy peaks around 100 Hz, which we will check by the measure of kurtosis grouped by the sex and age factors in the following section.

Figure 4. Density plot of f0 values (Hz) of forty individual speakers colored by sex in the Buckeye Corpus.

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In the plot, the skewed distribution observed can be partly attributed to the length of vocal folds, which sets a natural lower limit to glottal frequency. However, speakers possess the capability to extend their vocal folds, enabling the production of higher f0 (Lennes et al., 2016). As a result, a prolonged tail is noticeable in each individual density curve. Yang (2021) advocated for the mode as a suitable measure to describe individual speaker characteristics but proposed the median as a better index, particularly considering the probability density graph.

Notably, two outliers are discernible within each sex group in Figure 4. Participant S33, a young male (YM), exhibits a median of 163 Hz, placing his data in the lower frequency range of the female group. Conversely, participant S27, an old female (OF), has a median f0 value of 116 Hz, aligning more closely with the male data range. Consequently, defining a normative f0 range for the two sex groups, inclusive of these outliers, might be misleading. It is recommended that further studies undertake a rigorous evaluation of the data before assigning a conclusive statistical summary to each group.

As the Buckeye Corpus did not specify participant ages numerically, we opted to explore the general association between age and f0 values. To achieve this, we categorized speakers by both age and sex within the American English Corpus. Table 4 presents the statistical details of f0 values for male and female speakers in these grouped categories.

The number of f0 values across the three groups appears comparable, except for the young female (YF) group, which registers ten thousand counts less. Among these groups, the YM group exhibits the lowest median, while the young female group demonstrates the highest median. All skewness values are positive, signifying right-skewed f0 values that taper toward the higher frequency region. The group difference range between young and old females is 0.54. Conversely, all kurtosis values are also positive. A kurtosis of zero typically indicates a bell-shaped or normal distribution, whereas the present kurtosis values exceeding one suggest a relatively peaked distribution. Figure 5 visually displays the density distributions for all four groups.

Figure 5. Probability density plot of f0 values (Hz) of forty speakers grouped by age and sex in the Buckeye Corpus.

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In Figure 5, it becomes apparent that the f0 values of the YM group are lower than those of the old male group. Conversely, the f0 values of the YF group are higher than those of the OF group. This age-group mismatch complicates any conclusive statement about older groups generally having higher f0 values. Notably, two outliers within each sex group have already been identified. Yang's (2021, 2023) studies have also tentatively explored the relationship between age and f0 values. These findings may be associated with the work of Hollien & Shipp (1972), who examined the correlation between age and f0 in a sample of 175 individuals aged 20 to 89. Their results indicated a gradual decrease in f0 values from 20 to 40 years, followed by an increase from 60 to 80 years. In contrast, male and female f0 values regressed to the mean of the two groups, as female f0 values decreased after middle age (Baken, 2005). Moreover, Reubold et al. (2010) investigated several aspects related to changes in fundamental frequency (f0) and formant frequencies (F1) over time and their effects on age perception. Their findings revealed that f0 and the first formant of schwas decreased over roughly 30 years in speakers, consistent with previous research indicating a decline in f0 with increasing age. Additionally, f0 and F1 changed at similar rates over a 50–60 year period in both male and female speakers, with evidence of a V-shaped trend in f0 and a similar pattern in F1. As highlighted by Yang (2023), more comprehensive data collection, including biological data, might clarify the relationship between age and f0 values.

One could deduce that the young groups are deviating from the group median value, while the old groups are converging towards the median. This trend might be more accurately described as a regression toward the center of the group mean.