Bandwidth Acoustic evidence of phonemes

84 Plot of a Speaker D’s back mid are areas of overlap bet

3.5.4 Bandwidth

Tongue root position is alone. X-ray and ultras e.g. Ladefoged 1964; the funds to do broad-s measurements lies in th tongue body and advan vocal tract, and this lar though F1 is the primar f all vowel tokens Speaker D id vowels are strangely lower than her front mid between both sets of mid vowels. th and [ATR] is difficult to determine on the basis of acousti rasound studies address the question from an art Gick et al. 2006, which is quite helpful, but f scale ultrasound experiments. The difficulty in the fact that two different articulatory gestures ancing the tongue root, result in a larger pharyn larger back cavity correlates with a lower F1 fre ary acoustic correlate of [ATR], it is also the p 103 id vowels. Also, there stic measurements articulatory perspective ut few researches have y in acoustic res, both raising the ryngeal cavity of the frequency. Therefore, e primary correlate of 104 tongue height. This lack of one-to-one mapping means that a change is F1 is ambiguous in terms of its articulatory origin. Because of these difficulties, researchers have sought other acoustic measures aside from F1 which would be an indicator of [ATR] but not tongue height. One of the most promising measures is the bandwidth of the first formant B1 39 , noted early by Lindau 1979. If tongue root position can be determined by measuring bandwidth, then bandwidth is potentially a useful acoustic measurement for distinguishing [ATR] contrasts. The question for Ikoma is Are bandwidth measurements a reliable indicator of mid-vowel [ATR] contrasts? If so, this could solve two tricky problems. First, it could be an indicator of whether or not the second degree vowels are [+ATR] or [-ATR], which would clarify what type of vowel inventory Ikoma has. Second, bandwidth measurements could be used to determine the quality of vowels which are both perceptually and acoustically in terms of F1 measurements in the overlap area between e o and . Before evaluating bandwidth in Ikoma, it is helpful to review Hess’s 1992 study which explored the correlation between a vowel’s first formant bandwidth B1 and its [ATR] value. This sets some expectations and parameters for evaluating the results for Ikoma. Hess investigates a number of acoustic measurements in pursuit of a reliable indicator of tongue root activity, which would be a helpful clue in understanding the nature of assimilation in Akan vowel harmony. Because the vowels overlap with e o in terms of their formant values, the first formant F1 alone is not sufficient to distinguish the two [ATR] harmony sets. 39 As defined by Baart 2010 60 “The bandwidth of a formant is a measure that indicates how wide the sphere of influence of a formant is how wide the range is of frequencies that are affected.” In a spectrogram display, a formant with a wider bandwidth is visibly broader, whereas a formant with a narrower bandwidth appears more thin. 105 Hess notes that formants of [+ATR] vowels have a narrower bandwidth than those of [-ATR] vowels, resulting in consistent differences in F1 bandwidth between high [-ATR] and mid [+ATR] vowels. The efficiency of this measurement can be seen when compared to measures of F1 alone. For example, in Akan she found only a 10 difference in F1 between the o pair, but a 66 difference between F1 bandwidths between these two vowels. Hess concludes that the bandwidth of the first formant is a reliable indicator of [ATR] harmony sets in Akan and can be used to determine the nature of assimilation of Akan vowels, which she argues is based on tongue root advancement, not gradient raising and lowering. This study was perhaps the most successful one to show clear results based on bandwidth. For evaluating bandwidth in Ikoma, I have once again used measurements from Speaker B. The averages in 85 below are based on the same group of initial root vowel V1 measurements as were used for the formant analysis in §3.5.2, which includes both nouns and verbs. The figures below show the average B1 bandwidth of F1 and the standard deviation SD of B1 measurements for each vowel. 85 Average bandwidth of initial root vowels in Hz Speaker B B1 average SD B1 average SD i 32.8 7.5 u 33.2 8.3 e 41.6 9.4 o 39.8 11.1 53.8 32.3 52.4 23.3 a 96.8 47.1 Note that the [-ATR] vowels have significantly higher SD than the [+ATR] vowels. The difference in B1 and SD between both mid vowel pairs is shown in 86 below. 106 86 B1 and SD difference between mid vowel pairs in Hz B1 average SD B1 average SD e 41.6 9.4 o 39.8 11.1 53.8 32.3 52.4 23.3 diff 12.2 22.9 diff 12.6 12.2 Because a formant’s bandwidth is largely dependent on its frequency, it is important to take a vowel’s F1 into consideration when evaluating its B1. In order to directly compare the bandwidth of two vowels, they must have approximately the same F1. Otherwise, adjustments must be made in order to make them comparable. One formula for doing this, which is the one used by Hess 1992, is from Fant 1972, which is given in 87 below. 87 Fant’s 1972 formula from Hess 1992 486 B 1 = 15500F 1 2 + 20F 1 500 12 + 5F 1 5500 2 Hz Using this formula, I calculated the expected B1, based on each vowel’s average F1 taken from 70 in §3.5.2 above. The table in 88 below shows Speaker B’s average F1, the average B1 which was actually measured, the expected B1 which was calculated using Fant’s formula, and the difference between the actual and expected B1. 88 F1, measured B1 and expected B1 Speaker B M MM M C C C C C M C M C M C M P . P . P . P . 3 7 70 70 7 7 0 70 7 7 7+ 7 70 070 + 07 70 +7 7 37 7 + 07 37 7 107 In the Difference column, negative figures represent those which are lower than Fant’s predictions, whereas positive figures are those which are higher than Fant’s predictions. As recalled from Hess’s study above, we expect that [+ATR] vowels will have a narrower B1 than corresponding [-ATR] vowels, and that is in fact what we find in Ikoma. All four [+ATR] vowels have a narrower i.e. lower B1 than expected, whereas the three [-ATR] vowels have a wider i.e. higher B1 than expected. Easier viewing of the B1 difference for each vowel is in 89 below. 89 Difference between expected and measured B1 B1 Difference B1 Difference i -23.89 u -29.69 [+ATR] e -4.59 o -7.11 12.47 11.55 [-ATR] a 56.3 This can be visually represented in the plot in 90 below. 108 90 Plot of measured B1 and predicted B1 The squares represent the B1 predicted by Fant’s formula for each vowel’s average F1, whereas the diamonds show the actual, measured average B1. As shown above, each height[ATR] pair has a similar F1 and B1. The high vowels and [+ATR] mid vowels have a lower-than-predicted B1, whereas the [-ATR] vowels are above the line, showing a higher-than-predicted B1. This conforms to our expectations that [+ATR] vowels have a narrower F1 bandwidth than corresponding [-ATR] vowels. These results suggest that the degree 2 vowel e o are indeed likely to be [+ATR], not [ ], since if they were [-ATR] they would be more likely to be above Fant’s prediction line. Though the average B1 values of different harmony sets are helpful for determining the general quality of these vowels in terms of their [ATR] values, additional graphs show that bandwidth might not always be a reliable indicator of the [ATR] value of specific questionable vowels. For example, the graph in 91 below u o ɔ i e ɛ a 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 F 1 B a n d w id th H z F1 Frequency Hz Measured and Predicted B1 Measured Predicted Fant 109 shows 33 individual tokens of the back vowel o and 32 tokens of plotted based on their F1 and B1. Once again, I also include Fant’s predicted B1 based on Ikoma’s average F1 values, which allows us to see the individual tokens which fall above and below the predicted values. 91 B1 of o and - Individual tokens Likewise, the graph in 92 does the same for the front vowel pair, showing 30 individual tokens of e and 29 tokens of . 20 40 60 80 100 120 140 200 300 400 500 600 700 F 1 B a n d w id th H z F1 Frequency Hz B1 of o and ɔ o ɔ Fant 110 92 B1 of e and - Individual tokens As the charts above show, many individual [+ATR] tokens fall below the line, as expected, whereas many of the [-ATR] tokens are above the line, also as expected. At the same time, however, some individual tokens of e o have similar and overlapping B1 values with their [-ATR] counterparts . And for the front vowel pair in particular, 92 shows some overlap along both axes in the range of 400-450 Hz on the F1 axis and 40-50 Hz on the B1 axis. The figures in 93 below help us to better understand this trend. For each of the four mid vowels, I show the percentage of individual tokens which are above and below the predicted B1 based on the average F1 for each vowel. 10 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 F 1 B a n d w id th H z F1 Frequency Hz B1 of e and ɛ e ɛ Fant 111 93 Percentage of measurements above and below predicted B1 value Total tokens Predicted B1 above predicted B1 below predicted B1 e 30 46 Hz 33 67 o 33 47 Hz 24 76 32 41 Hz 66 34 29 41 Hz 62 38 For all four vowels, we see that the majority of [+ATR] vowels have a lower-than- expected B1, whereas the majority of [-ATR] vowels have a higher-than-expected B1. These figures are perhaps less conclusive than we might hope, and the level of overlap of B1 values among the [ATR] sets would make it difficult for bandwidth to be a conclusive measure when uncertain about an individual vowel’s [ATR] value. Nonetheless, these results are still highly suggestive that the degree 2 vowels are e o, not . We can conclude that the average B1 values for different [ATR] sets show tendencies as we would expect, with [-ATR] vowels having a higher bandwidth, on average, than their [+ATR] counterparts.

3.6 Phonetic realization of phonemes