Angle configurations and the S-centroid: modeling changing planar locations in the vowel space

Anne Fabricius, Roskilde University Dominic Watt, University of York and J.P French Associates

Angle configurations and the S-centroid 2

Outline

Background to the paper Aim of the research Introducing the S-centroid anchor

method Application to some vowel data from

British English (SSBE/Modern RP)

Discussion and further implications

Angle configurations and the S-centroid 3

Background

Quantitative methods in a quantitative discipline The art and science of vowel change (Labov 1994) Earlier work this study is based on

Watt and Fabricius S-centroid method (Watt and Fabricius 2002)

TRAP/STRUT rotation in RP (Fabricius 2007) and angle methods using vowel juxtapositions

Testing normalisation methods (Fabricius, Watt and Johnson 2009) for geometrically-related properties

Here: Combining the two (normalization and modelling changing vowel loci distributions around the centroid)

Angle configurations and the S-centroid 4

A summary of the original S-centroid normalization method

Adapted from Fabricius 2007: 300

Angle configurations and the S-centroid 5

Modified W&F (tested in Fabricius, Watt and Johnson 2009)

Flynn 2010: slide 16

For variety-specific modifications of the Watt and Fabricius S-centroid method, see also Durian, forthcoming and Bigham 2008. mW&F uses F1 of [a] only

Angle configurations and the S-centroid 6

(Geometrical) Centroid ≠ Spectral Centroid

In geometry, the centroid, geometric center, or barycenter of a plane figure or two-dimensional shape X is the intersection of all straight lines that divide X into two parts of equal moment about the line. Informally, it is the "average" (arithmetic mean) of all points of X.

(From Wikipedia)

Angle configurations and the S-centroid 7

(Geometrical) Centroid ≠ Spectral Centroid

Peeters 2004

Angle configurations and the S-centroid 8

Aim of this paper

To present the method To investigate the methodological

advantages for sociophonetics of representing relative planar locations as vectors vis à vis a pre-defined geometrical centroid of the vowel space

To ask whether this supports other arguments in favour of a centroid-based normalisation method? (in the spirit of Fabricius, Watt and Johnson 2009)

Angle configurations and the S-centroid 9

The definition of the S-centroid point

Make no claims here about the centroid’s perceptual significance (although the concept does feature in some perception/normalisation research, eg Deterding 1990)

Used here as a geometric point to investigate and illustrate properties of vowel distributions in F1/F2 space

Angle configurations and the S-centroid 10

Some previous phonetic studies using the centroid concept

Effect of speech disorders on the vowel space and distance of vowels from the centroid (e.g. in stuttering: Blomgren, Robb and Chen 1998)

Pickering 1986 formalised peripherality measured as dispersion from a centroid, context speech perception research

Hyper- and hypo-articulation, ie clear and indistinct speech: (Lindblom 1990, 1996, Ferguson & Kewley-Port, 2002; Picheny, Durlach, & Braida, 1986)

Whiteside 2001; NB definition of centroid used here differs from this presentation since axes are derived differently (using Bark differences)

Angle configurations and the S-centroid 11

Announcing the S-centroid anchor method

R-algorithm developed by Daniel Ezra Johnson after an idea by Anne Fabricius

Available here (The Modern RP Page)

Angle configurations and the S-centroid 12

0°

180°

-180°

90°

-90°

S-centroid point

F1

F2

Angle configurations and the S-centroid 13

0°

180°

-180°

90°

-90°

S-centroid point

F1

F2

i u

a

Angle configurations and the S-centroid 14

Angle configurations and the S-centroid 15

So far….

Documenting changes by measurements in degrees vis a vis a stable point, rather than eyeball judgments of relative placement

Could also be used in combination with Euclidean/Cartesian distances (as in Fabricius 2007, Richards, Haddican and Foulkes 2009)

Quantification enables further statistical testing Has potential applications in determining the

nature of centre versus periphery in the vowel space (Labov 1994) in a more reproducible way

Angle configurations and the S-centroid 16

Demonstration of planar locations and their relationships

RP generational vowel data from Hawkins and Midgley 2005 and Moreiras 2006, plus Fabricius 2009

using R script devised by Daniel Ezra Johnson

This example: short vowel system with lines connecting average vowel loci

17

Female speakers, 1998 cohort

Angle configurations and the S-centroid

(Data from Fabricius 2009)

18

Female speakers,2008 cohort

Angle configurations and the S-centroid

(Data from Fabricius 2009)

Angle configurations and the S-centroid 19

Male speakers, 1998 cohort

(Data from Fabricius 2009)

Angle configurations and the S-centroid 20

Male speakers, 2008 cohort(Data from Fabricius 2009)

Angle configurations and the S-centroid 21

The new alternative: the S-centroid anchor method

To make these types of configurations more easily comparable

By using the S-centroid point as anchor deriving angles vis-à-vis the centroid point The S-centroid point is common to ALL

speakers in the sample since they are all normalised using the W&F (or mW&F) method

Advantage: the S-centroid does not move over time

Angle configurations and the S-centroid 22

Illustration

Angle configurations and the S-centroid 23

OM1 flee

OM2 flee

OM3 flee

OM4 flee

OM5 flee

OF1 flee

OF2 flee

OF3 flee

OF4 flee

OF5 fleeYM1 flee

YM2 flee

YM3 flee

YM4 flee

YM5 flee

YF1 flee

YF2 flee

YF3 flee

YF4 flee

YF5 flee

-180

-140

-100

-60

-20

20

60

100

140

180

Series1

FLEECE stable over time: OM, OF: older generation; YM, YF: younger generation

Angle configurations and the S-centroid 24

0°

180°

-180°

90°

-90°

S-centroid point

F1

F2

FLEECE

Angle configurations and the S-centroid 25

OM1 foot

OM2 foot

OM3 foot

OM4 foot

OM5 foot

OF1 foot

OF2 foot

OF3 foot

OF4 foot

OF5 footYM1 foot

YM2 foot

YM3 foot

YM4 foot

YM5 foot

YF1 foot

YF2 foot

YF3 foot

YF4 foot

YF5 foot

-180

-140

-100

-60

-20

20

60

100

140

180

Series1

FOOT moving over time

Angle configurations and the S-centroid 26

0°

180°

-180°

90°

-90°

S-centroid point

F1

F2

FOOT, older

FOOT, YF3

Angle configurations and the S-centroid 27

OM1 lot

OM2 lot

OM3 lot

OM4 lot

OM5 lot

OF1 lot

OF2 lot

OF3 lot

OF4 lot

OF5 lotYM1 lot

YM2 lot

YM3 lot

YM4 lot

YM5 lot

YF1 lot

YF2 lot

YF3 lot

YF4 lot

YF5 lot

-180

-140

-100

-60

-20

20

60

100

140

180

Series1

LOT variability, mostly among younger female speakers

Angle configurations and the S-centroid 28

OM1 strut

OM2 strut

OM3 strut

OM4 strut

OM5 strut

OF1 strut

OF2 strut

OF3 strut

OF4 strut

OF5 strutYM1 strut

YM2 strut

YM3 strut

YM4 strut

YM5 strut

YF1 strut

YF2 strut

YF3 strut

YF4 strut

YF5 strut

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

Series1

STRUT in this perspective also variable; nb Reduced scale here

Angle configurations and the S-centroid 29

To sum up

What are the methodological advantages to representing relative planar locations as vectors vis a vis the centroid location of the vowel space?

Quantifiability, reproducibility, visual evidence backing auditory perceptions

Does this argue for the advantages of a centroid-point based normalisation method?

Yes, and the method could also be adapted to work from the centroid-based Lobanov normalisation algorithm. But Lobanov’s normalisation method is in some cases too

powerful (close to a standard statistical normalisation technique) and performs less well overall (in several testing parameters) than mW&F in Flynn’s comparison of 20 normalisation algorithms (Flynn 2010)

Angle configurations and the S-centroid 30

Conclusion

Method offered here as an aid to the sociophonetic community

The illustrative chart template will also be available online ( MS Excel.crtx file)

NB A Euclidean distance metric could be included as well

R-code will be available and can be adjusted

Angle configurations and the S-centroid 31

References 1

Bigham, Douglas. 2008. Dialect contact and accommodation among emerging adults in a university setting. Ph.D. thesis. The University of Texas at Austin.

Deterding, David. 1990. Speaker Normalisation for Automatic Speech Recognition, Unpublished PhD Thesis, Cambridge University.

Fabricius, Anne. 2007. Variation and change in the TRAP and STRUT vowels of RP: a real time comparison of five acoustic data sets. JIPA 37:3: 293-320.

Fabricius, Anne. 2009. Short vowels in real time: TRAP, STRUT and FOOT in the South of England. Paper presented at ICLaVE 5, Copenhagen. June 27th 2009. (www.ruc.dk/~fabri )

Fabricius, Anne H., Dominic Watt and Daniel Ezra Johnson. 2009. A comparison of three speaker-intrinsic vowel formant frequency normalization algorithms for sociophonetics. Language Variation and Change, 21,3:1-23.

Flynn, Nicholas. 2010. Comparing vowel formant normalisation procedures. Talk given at York Postgraduate Mini-conference, June 10th, 2010.

Hawkins, Sarah and Jonathan Midgley. 2005. Formant frequencies of RP monophthongs in four age groups of speakers. JIPA 30: 63-78.

Labov, William. 1994. Principles of Linguistic Change volume 1: Internal Factors. Oxford: Blackwell.

Angle configurations and the S-centroid 32

References 2

Lindblom, B. 1990: Explaining phonetic variation: A sketch of the H&H theory, in Speech Production and Speech Modeling, edited by W. J. Hardcastle and A. Marchal. Kluwer Academic, Netherlands, pp. 403–439.

Lindblom, B. 1996: Role of articulation in speech perception: Clues from production. Journal of the Acoustical Society of America, 99, 1683–1692.

Moreiras, C. 2006. An acoustic study of vowel change in female adult speakers of RP. Unpublished undergraduate dissertation, University College London.

Peeters, Geoffroy. 2003. A large set of audio features for sound description (similarity and classification) in the CUIDADO project. http://recherche.ircam.fr/equipes/analyse-synthese/peeters/ARTICLES/Peeters_2003_cuidadoaudiofeatures.pdf

Pickering, J.B. 1986. Auditory vowel formant variability. Unpublished doctoral dissertation, Oxford University.

Richards, Hazel, Bill Haddican and Paul Foulkes. 2009. Exhibiting standards in the FACE of dialect levelling. Paper presented at ICLaVE 5, Copenhagen, June 2009.

 Watt, Dominic and Anne Fabricius. 2002. Evaluation of a technique for improving the mapping of multiple speakers’ vowel spaces in the F1-F2 plane. Leeds Working papers in Linguistics and Phonetics. 9: 159-173.

Angle configurations and the S-centroid 33

Acknowledgements

Daniel Ezra Johnson Tyler Kendall Nicholas Flynn

Nicolai Pharao

Thank you for listening!