This paper presents part of an ongoing research program which aims to apply mathematical and geometrical analytic methods to vowel formant data to enable the quantification of parameters of variation of interest to sociophoneticians. We open with an overview of recent research working towards a set of desiderata for choice of normalization algorithm(s) based on replicable procedures. We then present the principles of centroid-based normalization and account for its performance in recent road

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... ts. In sections 4 and 5 we introduce a method that utilizes the centroid of the speaker's vowel space as an anchor point or vertex for calculation of planar locations on formant plots, permitting quantification of the distribution of vowel tokens within the space. This information, along with details such as Euclidean distances, can then be used to precisely pinpoint the trajectories of diachronic change, for instance over a set of speakers in different age groups within a defined speech community. This has the advantage of mathematical reproducibility, and reduces the level of subjectivity in visual analyses of formant plots used in investigations of vowel variability and change in progress.