Abstract
This paper contributes insight into the sources of variability in vowel formant estimation, a major analytic activity in sociophonetics, by reviewing the outcomes of two simulations that manipulated the settings used for linear predictive coding (LPC)-based vowel formant estimation. Simulation 1 explores the range of frequency differences obtained when minor adjustments are made to LPC settings, and measurement timepoints around the settings used by trained analysts, in order to determine the range of variability that should be expected in sociophonetic vowel studies. Simulation 2 examines the variability that emerges when LPC settings are varied combinatorially around constant default settings, rather than settings set by trained analysts. The impacts of different LPC settings are discussed as a way of demonstrating the inherent properties of LPC-based formant estimation. This work suggests that differences more fine-grained than about 10 Hz in F1 and 15–20 Hz in F2 are within the range of LPC-based formant estimation variability.
Acknowledgement
The data used for this project were collected with support from grants # BCS-0518264, BCS-1123460, and BCS-1122950 from the National Science Foundation.
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Appendix: Full results from Simulation 1
Tables A1 and A2 provide the vowel category average medians for F1, F2, and F3 of the 4 tokens per vowel category from Simulation 1, with speakers grouped by sex (Table A1 for males, Table A2 for females). The tables also provide the average IQRs (over the 4 tokens) and the average absolute differences between the medians for each vowel token and the gold standard vowel measurement.
Inspecting the variability via average IQRs in these tables, it is evident that some speaker-vowel category pairings obtain somewhat unstable estimates. The individual speakers’ IQRs range for F1 from a low of 3.4 Hz (Ryan3381’s /i/) to a high of 135.5 Hz (Ann5805’s /ɑ/) (mean = 37.5 Hz) and for F2 from a low of 19.7 Hz (Bryan2168’s /ɪ/) to a high of 1567.1 (Paige5200’s /e/) (mean = 162.2 Hz). Further, we find some support for Harrison’s (2013) observation that formant estimation error is not uniform across the vowel space. High vowels tend to obtain tighter distributions for F1 while low vowels obtain the widest distributions (as visible in Figure 2 in the main text). For F2, less consistent patterns emerge. For instance, /ɑ/ and /ɔ/ obtain some of the smallest IQRs, but /æ/, also a low vowel, obtains some very large IQRs. Generally, /e/ obtains the highest IQRs for F2. And, although /ɪ/ has some of the lowest F2 IQRs for some speakers, it also has some of the highest for others (941.6 Hz for Natalie2800 and 1174.2 Hz for Paige5200). The range of variability across individual speakers and vowel classes reinforces the fact that LPC results are dependent on speaker-level and vowel token-level factors, but does not highlight specific patterns for the sources of that variability. We do find systematic patterns, however, by comparing the average IQRs across speaker sex (male: F1 = 32.4, F2 = 80.9; female: F1 = 42.7, F2 = 243.4), individual speakers (F1 = 37.5 [range = 18.0–50.7]; F2 mean = 162.2 [range = 63.2–491.1]), and vowel categories (F1 = 37.5 [range = 13.5–68.3]; F2 mean = 162.2 [range = 49.0–402.9]), showing that indeed higher formant frequencies (i.e. female voices and formants above F1) track less well with LPC and result in less stable estimates (Vallabha and Tuller 2002; Zhang et al. 2013). Speakers and vowel categories, however, yield roughly similar IQR ranges, indicating that they contribute equivalently to LPC-based estimation variability.
Simulation 1 results for individual male speakers.
| F1 | F2 | F3 | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Val | IQR | Dif | Val | IQR | Dif | Val | IQR | Dif | |
| aaron3265 | |||||||||
| /i/ | 271.5 | 26.5 | 7.2 | 2313.4 | 68.7 | 17.2 | 2800.4 | 408.6 | 44.3 |
| /ɪ/ | 390.0 | 40.9 | 8.1 | 1964.9 | 46.4 | 12.1 | 2598.2 | 125.1 | 13.7 |
| /e/ | 416.5 | 37.5 | 8.2 | 2094.1 | 79.8 | 25.6 | 2657.4 | 198.1 | 40.5 |
| /ɛ/ | 525.9 | 47.6 | 14.7 | 1791.7 | 45.8 | 13.5 | 2581.1 | 186.2 | 44.1 |
| /æ/ | 645.5 | 29.3 | 5.6 | 1661.6 | 53.2 | 8.5 | 2474.9 | 141.2 | 49.1 |
| /ɑ/ | 680.1 | 37.2 | 19.4 | 1137.8 | 40.4 | 26.0 | 2397.0 | 101.8 | 32.3 |
| /ɔ/ | 633.9 | 67.3 | 26.1 | 1043.3 | 105.4 | 21.9 | 2407.0 | 385.2 | 29.8 |
| /ʌ/ | 613.1 | 48.0 | 9.7 | 1297.7 | 50.8 | 14.3 | 2479.8 | 61.8 | 16.6 |
| /o/ | 494.8 | 53.0 | 18.6 | 1093.9 | 79.1 | 16.2 | 2352.2 | 90.9 | 15.6 |
| /u/ | 324.1 | 21.8 | 6.9 | 1585.9 | 109.2 | 23.1 | 2255.8 | 48.1 | 5.7 |
| Mn | 40.9 | 12.5 | 67.9 | 17.8 | 174.7 | 29.2 | |||
| SD | 13.6 | 6.9 | 24.9 | 6.0 | 126.7 | 15.3 | |||
| Bryan2168 | |||||||||
| /i/ | 286.4 | 6.4 | 0.4 | 2437.3 | 67.4 | 16.1 | 3016.0 | 326.2 | 47.4 |
| /ɪ/ | 392.8 | 9.6 | 2.6 | 2095.6 | 19.7 | 7.0 | 2885.9 | 51.1 | 14.9 |
| /e/ | 438.1 | 15.3 | 3.5 | 2191.5 | 154.8 | 15.0 | 2930.2 | 224.0 | 13.2 |
| /ɛ/ | 568.0 | 16.0 | 4.1 | 1880.8 | 29.7 | 2.7 | 2848.5 | 65.2 | 10.8 |
| /æ/ | 780.6 | 30.9 | 9.2 | 1711.7 | 145.1 | 10.3 | 2690.1 | 306.2 | 67.7 |
| /ɑ/ | 701.0 | 26.6 | 6.7 | 1051.4 | 22.5 | 5.4 | 2660.3 | 135.6 | 10.8 |
| /ɔ/ | 635.6 | 20.2 | 10.8 | 970.2 | 39.5 | 11.5 | 2668.0 | 901.9 | 25.8 |
| /ʌ/ | 643.1 | 14.5 | 5.0 | 1277.4 | 42.3 | 7.1 | 2753.6 | 60.1 | 16.3 |
| /o/ | 490.3 | 30.6 | 8.3 | 1101.6 | 77.5 | 9.5 | 2626.5 | 109.2 | 3.0 |
| /u/ | 340.2 | 10.3 | 3.3 | 1392.5 | 107.5 | 24.9 | 2374.5 | 103.0 | 13.4 |
| Mn | 18.0 | 5.4 | 70.6 | 11.0 | 228.3 | 22.3 | |||
| SD | 8.8 | 3.3 | 49.9 | 6.4 | 256.9 | 20.0 | |||
| Eric1510 | |||||||||
| /i/ | 260.5 | 5.6 | 0.9 | 2309.4 | 301.0 | 13.1 | 2831.5 | 418.5 | 118.7 |
| /ɪ/ | 446.2 | 12.4 | 2.7 | 1809.7 | 24.9 | 6.4 | 2682.2 | 71.6 | 6.9 |
| /e/ | 474.5 | 10.3 | 3.7 | 1987.3 | 340.7 | 6.0 | 2683.3 | 291.3 | 24.0 |
| /ɛ/ | 580.7 | 13.1 | 3.0 | 1717.0 | 31.3 | 6.5 | 2612.8 | 155.9 | 11.8 |
| /æ/ | 709.0 | 17.3 | 5.4 | 1581.4 | 141.8 | 11.4 | 2373.9 | 739.4 | 30.5 |
| /ɑ/ | 669.3 | 27.3 | 9.4 | 1129.2 | 23.2 | 12.3 | 2417.1 | 87.2 | 5.6 |
| /ɔ/ | 629.5 | 74.7 | 30.7 | 1062.6 | 118.7 | 30.4 | 2471.4 | 407.0 | 16.0 |
| /ʌ/ | 611.3 | 20.6 | 4.6 | 1327.8 | 47.4 | 6.4 | 2476.8 | 330.7 | 19.2 |
| /o/ | 515.7 | 32.2 | 5.5 | 1149.0 | 54.4 | 8.7 | 2379.4 | 217.4 | 25.7 |
| /u/ | 337.9 | 11.1 | 4.3 | 1362.1 | 151.1 | 27.4 | 2214.1 | 268.3 | 23.9 |
| Mn | 22.5 | 7.0 | 123.5 | 12.9 | 298.7 | 28.2 | |||
| SD | 20.1 | 8.6 | 114.8 | 8.9 | 196.0 | 32.8 | |||
| Johnny4055 | |||||||||
| /i/ | 245.0 | 7.6 | 2.2 | 2475.1 | 63.7 | 12.3 | 3067.0 | 284.5 | 78.4 |
| /ɪ/ | 373.1 | 30.0 | 3.9 | 1969.6 | 48.6 | 18.6 | 2681.0 | 57.4 | 19.3 |
| /e/ | 403.9 | 32.0 | 4.1 | 2163.5 | 115.4 | 15.8 | 2635.5 | 91.8 | 53.8 |
| /ɛ/ | 563.1 | 44.2 | 20.4 | 1706.9 | 40.9 | 9.5 | 2627.6 | 57.9 | 36.0 |
| /æ/ | 771.0 | 37.6 | 6.3 | 1565.7 | 64.2 | 12.7 | 2485.9 | 162.2 | 21.9 |
| /ɑ/ | 657.9 | 124.4 | 31.8 | 998.7 | 102.8 | 25.4 | 2216.5 | 381.5 | 10.6 |
| /ɔ/ | 634.1 | 63.0 | 30.0 | 962.6 | 53.8 | 17.0 | 2208.7 | 54.6 | 22.7 |
| /ʌ/ | 607.2 | 55.2 | 14.0 | 1290.2 | 53.7 | 10.0 | 2466.4 | 87.9 | 20.3 |
| /o/ | 442.5 | 37.3 | 13.1 | 1050.1 | 62.6 | 24.6 | 2465.9 | 101.6 | 13.1 |
| /u/ | 266.2 | 9.9 | 3.0 | 1373.8 | 190.5 | 21.8 | 2392.8 | 68.3 | 16.1 |
| Mn | 44.1 | 12.9 | 79.6 | 16.8 | 134.8 | 29.2 | |||
| SD | 33.1 | 11.2 | 45.6 | 5.8 | 111.5 | 21.4 | |||
| Ryan3381 | |||||||||
| /i/ | 257.5 | 3.4 | 1.5 | 2334.7 | 57.1 | 7.3 | 3070.3 | 168.2 | 16.4 |
| /ɪ/ | 405.5 | 22.6 | 4.4 | 2044.0 | 37.9 | 8.5 | 2683.8 | 89.0 | 17.5 |
| /e/ | 422.2 | 11.2 | 3.5 | 2175.8 | 102.2 | 19.1 | 2700.1 | 238.7 | 28.4 |
| /ɛ/ | 529.3 | 17.9 | 5.2 | 1857.6 | 50.5 | 10.8 | 2570.9 | 143.4 | 18.5 |
| /æ/ | 730.4 | 24.3 | 4.5 | 1743.0 | 47.7 | 8.3 | 2434.1 | 157.0 | 10.3 |
| /ɑ/ | 742.3 | 134.0 | 21.6 | 1133.7 | 67.9 | 15.5 | 2165.3 | 352.3 | 41.2 |
| /ɔ/ | 696.2 | 77.7 | 17.2 | 1067.5 | 27.3 | 8.9 | 2296.2 | 256.7 | 17.0 |
| /ʌ/ | 613.3 | 35.3 | 8.2 | 1308.5 | 58.6 | 12.0 | 2496.0 | 199.9 | 37.0 |
| /o/ | 467.2 | 25.0 | 8.5 | 1131.1 | 72.1 | 17.8 | 2183.0 | 34.0 | 8.1 |
| /u/ | 293.2 | 12.5 | 3.9 | 1480.4 | 110.3 | 29.2 | 2245.4 | 57.3 | 6.0 |
| Mn | 36.4 | 7.9 | 63.2 | 13.7 | 169.7 | 20.0 | |||
| SD | 39.9 | 6.5 | 26.3 | 6.8 | 97.2 | 11.9 | |||
Mean for each vowel category for individual token medians (Val), mean interquartile ranges for individual token distributions (IQR), and mean absolute differences from gold standard values (Dif), separated by formant, for F1, F2, and F3. All values in Hz. Means and standard deviations provided for IQRs and differences.
Simulation 1 results for individual female speakers.
| F1 | F2 | F3 | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Val | IQR | Dif | Val | IQR | Dif | Val | IQR | Dif | |
| Ann5805 | |||||||||
| /i/ | 364.2 | 11.8 | 2.7 | 2878.2 | 54.4 | 7.6 | 3298.2 | 182.0 | 28.2 |
| /ɪ/ | 490.2 | 18.5 | 3.4 | 2392.7 | 36.5 | 6.2 | 3167.9 | 120.7 | 18.1 |
| /e/ | 455.1 | 28.8 | 6.0 | 2619.7 | 88.7 | 10.5 | 3167.1 | 261.6 | 11.6 |
| /ɛ/ | 730.8 | 28.9 | 10.7 | 2173.0 | 145.9 | 12.2 | 2993.3 | 92.7 | 7.8 |
| /æ/ | 874.2 | 54.8 | 7.3 | 2088.8 | 147.5 | 60.9 | 2778.3 | 127.6 | 34.8 |
| /ɑ/ | 928.2 | 135.5 | 15.8 | 1301.0 | 49.9 | 7.6 | 2825.5 | 117.7 | 38.4 |
| /ɔ/ | 739.6 | 101.6 | 37.9 | 1096.4 | 61.4 | 22.0 | 3028.1 | 96.2 | 26.5 |
| /ʌ/ | 814.6 | 47.0 | 14.2 | 1727.9 | 58.2 | 11.3 | 2983.1 | 201.4 | 36.1 |
| /o/ | 547.9 | 25.8 | 7.5 | 1184.7 | 59.0 | 7.3 | 2972.5 | 108.5 | 10.6 |
| /u/ | 411.1 | 11.5 | 4.8 | 1770.2 | 86.1 | 19.7 | 2942.1 | 39.7 | 12.6 |
| Mn | 46.4 | 11.0 | 78.8 | 16.5 | 134.8 | 22.5 | |||
| SD | 41.2 | 10.4 | 39.0 | 16.5 | 63.5 | 11.7 | |||
| Jocelyn1675 | |||||||||
| /i/ | 352.6 | 25.7 | 1.2 | 2828.4 | 69.1 | 6.4 | 3167.1 | 133.1 | 38.9 |
| /ɪ/ | 507.6 | 19.6 | 2.4 | 2296.7 | 35.4 | 5.8 | 3142.1 | 67.8 | 13.3 |
| /e/ | 445.2 | 8.2 | 0.8 | 2569.1 | 80.9 | 6.5 | 3105.2 | 395.2 | 23.8 |
| /ɛ/ | 675.0 | 28.9 | 2.1 | 2069.4 | 161.4 | 9.8 | 3095.2 | 327.6 | 19.7 |
| /æ/ | 861.9 | 44.6 | 7.2 | 1838.2 | 76.9 | 3.7 | 2867.2 | 224.3 | 16.2 |
| /ɑ/ | 834.1 | 36.4 | 6.8 | 1264.9 | 30.3 | 6.6 | 3150.8 | 48.3 | 9.2 |
| /ɔ/ | 808.3 | 21.9 | 5.8 | 1268.9 | 31.5 | 2.9 | 3154.5 | 31.0 | 7.9 |
| /ʌ/ | 758.3 | 28.7 | 15.3 | 1714.6 | 44.1 | 19.9 | 2966.7 | 186.3 | 18.9 |
| /o/ | 563.0 | 25.8 | 11.8 | 1383.5 | 103.6 | 44.4 | 2845.3 | 173.8 | 39.0 |
| /u/ | 440.9 | 6.7 | 2.7 | 1954.8 | 233.6 | 43.0 | 2836.9 | 145.3 | 26.9 |
| Mn | 24.7 | 5.6 | 86.7 | 14.9 | 173.3 | 21.4 | |||
| SD | 11.5 | 4.8 | 65.5 | 15.9 | 118.0 | 11.0 | |||
| Lindsey1595 | |||||||||
| /i/ | 329.0 | 32.3 | 1.5 | 2815.5 | 52.4 | 3.7 | 3410.9 | 106.6 | 10.2 |
| /ɪ/ | 521.2 | 30.9 | 5.6 | 2234.5 | 57.0 | 13.0 | 3103.6 | 69.0 | 9.6 |
| /e/ | 414.2 | 32.6 | 9.4 | 2626.4 | 102.6 | 29.2 | 3168.4 | 195.7 | 39.8 |
| /ɛ/ | 698.5 | 43.9 | 15.6 | 2043.7 | 393.7 | 31.8 | 3082.9 | 325.0 | 8.9 |
| /æ/ | 870.0 | 134.0 | 36.4 | 1835.7 | 414.4 | 27.4 | 2991.2 | 538.3 | 28.8 |
| /ɑ/ | 812.6 | 52.5 | 14.0 | 1119.3 | 80.9 | 24.0 | 2807.6 | 54.5 | 11.3 |
| /ɔ/ | 801.3 | 55.8 | 19.1 | 1205.1 | 115.0 | 43.6 | 2807.3 | 350.4 | 15.8 |
| /ʌ/ | 731.0 | 88.8 | 18.6 | 1435.4 | 380.3 | 96.6 | 2964.8 | 641.3 | 4.3 |
| /o/ | 527.6 | 29.4 | 10.2 | 1156.7 | 118.1 | 29.0 | 2869.3 | 90.5 | 13.6 |
| /u/ | 371.3 | 6.4 | 2.9 | 1816.6 | 207.5 | 57.2 | 2717.6 | 111.3 | 28.5 |
| Mn | 50.7 | 13.3 | 192.2 | 35.6 | 248.3 | 17.1 | |||
| SD | 36.4 | 10.2 | 147.3 | 26.0 | 208.5 | 11.4 | |||
| Natalie2800 | |||||||||
| /i/ | 364.8 | 47.3 | 12.7 | 3082.5 | 119.2 | 25.4 | 3625.5 | 284.8 | 26.0 |
| /ɪ/ | 485.7 | 30.0 | 22.6 | 2609.0 | 941.6 | 12.7 | 3412.7 | 853.3 | 36.8 |
| /e/ | 449.9 | 20.7 | 10.0 | 2939.7 | 1396.3 | 28.2 | 3303.2 | 511.8 | 83.7 |
| /ɛ/ | 749.0 | 37.6 | 15.4 | 2357.2 | 410.5 | 11.4 | 3341.1 | 879.7 | 46.4 |
| /æ/ | 966.4 | 113.7 | 22.7 | 2210.4 | 354.0 | 30.1 | 3093.5 | 764.7 | 61.3 |
| /ɑ/ | 808.5 | 80.6 | 41.2 | 1050.7 | 41.7 | 3.4 | 3027.3 | 132.2 | 31.2 |
| /ɔ/ | 817.2 | 78.0 | 22.9 | 1016.3 | 42.3 | 15.5 | 2967.7 | 547.7 | 41.8 |
| /ʌ/ | 803.7 | 42.0 | 9.7 | 1567.4 | 165.9 | 19.5 | 3139.7 | 863.3 | 40.9 |
| /o/ | 548.9 | 30.9 | 13.5 | 1221.8 | 99.2 | 19.1 | 3014.0 | 81.8 | 37.2 |
| /u/ | 424.0 | 11.1 | 6.9 | 1820.8 | 112.1 | 34.3 | 2912.3 | 70.7 | 23.0 |
| Mn | 49.2 | 17.8 | 368.3 | 20.0 | 499.0 | 42.8 | |||
| SD | 31.9 | 10.1 | 452.3 | 9.6 | 335.7 | 18.0 | |||
| Paige5200 | |||||||||
| /i/ | 274.2 | 27.9 | 12.2 | 2838.1 | 112.4 | 31.0 | 3355.5 | 396.3 | 364.2 |
| /ɪ/ | 475.9 | 30.7 | 23.5 | 2165.0 | 1174.2 | 11.3 | 2963.1 | 801.3 | 490.2 |
| /e/ | 485.7 | 25.8 | 28.0 | 2362.0 | 1567.1 | 27.0 | 2916.8 | 841.0 | 455.1 |
| /ɛ/ | 651.0 | 42.9 | 14.3 | 1907.1 | 787.3 | 7.4 | 2836.9 | 927.2 | 730.8 |
| /æ/ | 870.8 | 106.1 | 19.9 | 1733.7 | 456.6 | 26.7 | 2543.8 | 656.9 | 874.2 |
| /ɑ/ | 781.7 | 28.7 | 10.3 | 1154.3 | 30.8 | 8.6 | 2456.2 | 313.8 | 928.2 |
| /ɔ/ | 775.9 | 49.5 | 11.1 | 1145.0 | 50.8 | 18.1 | 2315.5 | 180.8 | 739.6 |
| /ʌ/ | 756.0 | 48.5 | 16.1 | 1419.2 | 362.1 | 34.8 | 2515.8 | 799.9 | 814.6 |
| /o/ | 580.5 | 29.5 | 16.7 | 1438.9 | 223.2 | 44.8 | 2488.1 | 342.3 | 547.9 |
| /u/ | 443.8 | 33.9 | 10.3 | 1795.7 | 146.7 | 15.0 | 2719.4 | 204.4 | 411.1 |
| Mn | 42.4 | 16.2 | 491.1 | 22.5 | 546.4 | ||||
| SD | 24.0 | 6.0 | 523.8 | 12.4 | 287.2 | ||||
© 2020 Walter de Gruyter GmbH, Berlin/Boston
