Anne Fabricius, Roskilde University
Dominic Watt, University of York and J.P French Associates
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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
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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
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Adapted from Fabricius 2007: 300
Angle configurations and the S-centroid
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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
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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.
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(From Wikipedia)
Angle configurations and the S-centroid
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Peeters 2004
Angle configurations and the S-centroid
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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
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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
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Make no claims here about the centroid’s
perceptual significance (although the concept
does feature in some
perception/normalisation research, eg
Deterding 1990)
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Used here as a geometric point to investigate
and illustrate properties of vowel
distributions in F1/F2 space
Angle configurations and the S-centroid
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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 & KewleyPort, 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)
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Angle configurations and the S-centroid
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R-algorithm developed by Daniel Ezra
Johnson after an idea by Anne Fabricius
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Available here (The Modern RP Page)
Angle configurations and the S-centroid
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F2
90°
180°
S-centroid point
0°
F1
-180°
-90°
Angle configurations and the S-centroid
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F2
90°
u
i
180°
S-centroid point
0°
F1
-180°
-90°
a
Angle configurations and the S-centroid
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Angle configurations and the S-centroid
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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
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Angle configurations and the S-centroid
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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
Angle configurations and the S-centroid
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Female
speakers,
1998 cohort
(Data from
Fabricius
2009)
Angle configurations and the S-centroid
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Female
speakers,
2008 cohort
(Data from
Fabricius
2009)
Angle configurations and the S-centroid
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Male
speakers,
1998 cohort
(Data from
Fabricius
2009)
Angle configurations and the S-centroid
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Male
speakers,
2008 cohort
(Data from
Fabricius
2009)
Angle configurations and the S-centroid
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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
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Angle configurations and the S-centroid
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FLEECE stable over time:
OM, OF: older generation;
YM, YF: younger generation
YF5 flee
YF4 flee
YF3 flee
YF2 flee
YF1 flee
OM1 flee
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120
-140
-160
-180
OM2 flee
OM3 flee
OM4 flee
OM5 flee
OF1 flee
YM5 flee
Series1
OF2 flee
YM4 flee
OF3 flee
YM3 flee
OF4 flee
YM2 flee
OF5 flee
YM1 flee
Angle configurations and the S-centroid
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F2
90°
FLEECE
180°
S-centroid point
0°
F1
-180°
-90°
Angle configurations and the S-centroid
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FOOT moving over
time
OM1 foot
YF5 foot
YF4 foot
YF3 foot
YF2 foot
YF1 foot
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120
-140
-160
-180
OM2 foot
OM3 foot
OM4 foot
OM5 foot
OF1 foot
YM5 foot
Series1
OF2 foot
YM4 foot
OF3 foot
YM3 foot
OF4 foot
YM2 foot
OF5 foot
YM1 foot
Angle configurations and the S-centroid
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F2
90°
FOOT, YF3
FOOT,
older
180°
S-centroid point
0°
F1
-180°
-90°
Angle configurations and the S-centroid
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LOT variability,
mostly among
younger female
speakers
YF5 lot
YF4 lot
YF3 lot
YF2 lot
YF1 lot
OM1 lot
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120
-140
-160
-180
OM2 lot
OM3 lot
OM4 lot
OM5 lot
OF1 lot
YM5 lot
Series1
OF2 lot
YM4 lot
OF3 lot
YM3 lot
OF4 lot
YM2 lot
OF5 lot
YM1 lot
Angle configurations and the S-centroid
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STRUT in this perspective also
variable; nb Reduced scale here
YF5 strut
OM1 strut
0
OM2 strut
-20
YF4 strut
OM3 strut
-40
-60
YF3 strut
OM4 strut
-80
-100
-120
YF2 strut
OM5 strut
-140
-160
YF1 strut
OF1 strut
-180
YM5 strut
Series1
OF2 strut
YM4 strut
OF3 strut
YM3 strut
OF4 strut
YM2 strut
OF5 strut
YM1 strut
Angle configurations and the S-centroid
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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.
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 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
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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
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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
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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/analysesynthese/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.
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Angle configurations and the S-centroid
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Daniel Ezra Johnson
Tyler Kendall
Nicholas Flynn
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Nicolai Pharao
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Angle configurations and the S-centroid
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