Table 6.
Measures of area, dispersion, or distance within the F1-F2 plane.
| Measure or plot | Formula or method | References |
|---|---|---|
| Point cloud | Plot of all F1-F2 points for a sample of vowels | Hillenbrand et al. (1995); Peterson & Barney (1952); Story & Bunton (2017) |
| Quadrilateral Vowel Space Area (qVSA or VSA-4) | qVSA =|0.5 * (F1/i/(F2/a/−F2/u/) + F1/a/(F2/u/−F2/i/) + F1/u/(F2/i/−F2/a/)| | Higgins & Hodge (2002) |
| Triangular Vowel Space Area (tVSA or VSA-3) | tVSA = |0.5 * [(F2/u/+F2/i/) × (F1/u/−F1/i/) – (F2/a/ +F2/u/) × (F1/u/−F1/a/) – (F2/a/+F2/i/) × (F1/a/−F1/i/)]| tVSA = [s(s−a) (s−b) (s−c)]½ Where s = ½ (a +b + c) and a, b, c are the lengths of the sides of the triangle. (Heron’s formula based on the perimeter s and the sides of the triangle) |
Bradlow, Torretta, & Pisoni (1996) Fox & Jacewicz (2008) |
| Vowel Articulation Index (VAI) | VAI = (F2/i/+F1/α/) / (F1/i/+F1/u/+F2/u/+F2/α/). | Roy et al., 2009) |
| Formant centralization ratio (FCR) | FCR =(F2/u/ + F2/ɑ/ + F1/i/ + F1/u/) / (F2/i/ + F1/ɑ/) Note: FCR is the reciprocal of VAI |
Sapir, Ramig, Spielman, & Fox (2010) |
| Vowel Formant Dispersion (VFD) | VFD = the Euclidean length of vectors for vowels originating from a defined center point of the vowel space fixed to a basic three-vowel frame. | Karlsson & van Doorn (2012) |
| Formant Spacing: compact-diffuse (C-D) and grave-acute (G-A). C-D are an index of tongue elevation and G-A is an index of tongue advancement. | C-D = F2 − F1 G-A = (F1 + F2)/2. |
Blomgren, Robb, & Chen (1998) |
| Area of convex hull encompassing all vowel tokens | Area contained within convex hull | de Boer (2009), McCloy, Wright, & Souza (2014), Story & Bunton (2017) |
| Mean vowel cluster size | Mean of the areas of the 95% confidence ellipses for each vowel category | McCloy et al (2014) |
| Mean Euclidean distance from center | The mean of the distances between vowel tokens and a point in the center of a speaker’s vowel space | Bradlow et al. (1996) |
| Repulsive force (or total energy) | Sum of inverse squared distances between all pairs of vowel tokens not belonging to the same vowel phoneme. | Liljencrants & Lindblom (1972), McCloy et al (2014) |
| F1 or F2 frequency range | Maximum range of formant frequency across vowel tokens or vowel category means | Bradlow et al. (1996), Hazan & Markham (2004) |
| F2/i//ssF2/u/ ratio | The ratio between the F2 frequencies for /i/ and /u/ | Moura et al. (2008), Sapir et al. (2007) |