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How exactly are vowel qualities of a particular speaker, or average qualities of the speakers of an accent, plotted on a neat quadrilateral chart like these (from the Wikipedia articles for Received Pronunciation and General American English):

https://upload.wikimedia.org/wikipedia/commons/3/37/RP_English_monophthongs_chart.svg (John C. Wells) https://upload.wikimedia.org/wikipedia/commons/0/0e/General_American_monophthong_chart.svg (Peter Roach)

I've never been able to figure this out. The quadrilateral chart resembles a plot of qualities based on F1 and F2, but it seems to be an idealistic transformation from such raw data. How exactly is the formant plot neatly transformed into a quadrilateral, whereby all the back cardinal vowel qualities align on a perfectly vertical line? And how are relative accent-based qualities transformed for that matter?

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There are many possible answers, and surprisingly, nobody ever says how they create the trapezium. In your example, we can't even identify an actual person who probably created it. You can find a similar chart for Gaza City Arabic, which present both the classical vowel chart and a graph of F1 vs F2 in Bark, from which you might interpolate specific measurements and relate that to the trapezium. There are also similar charts for Ambel, Dagaare, Kalasha and Mono Lake Paiute (there are hundreds of Illustrations of the IPA). The manuscript guidelines (§4) don't say anything specific about the positioning of vowels.

The traditional approach is to position vowels by reference to the IPA auditory standard, which is sampled here. If the author of the Gaza Arabic article was following that practice, that means that he judged the vowel [i:] in the language to be somewhat retracted and lower that IPA [i]. The author of the Ambel article would appear to have declined to make any finer-grained judgments (the Wiki graph-creator on the other hand does not decline). The only way to know how the vowels were positioned on the trapezium is to write to the author. One could position the vowels using formant values, though this is usually not done (except in formant charts, which are a different thing).

When vowels align perfectly, you can assume that the author is not being more specific than to say "close mid front vowel" which is the coarsest level of analysis. The Kalasha article does say that the vowels positions are "based on" formants, though they do not state what the equation is (exercise for the reader, I suppose) that relates their formant graphs to the trapezium. The Wikipedia graphs don't actually align perfectly, but there is no information on how the points were positioned in those two cases.

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  • I got those from Wikipedia. I edited the question for clarity. I thought there was a unified methodology to this so I neglected mentioning the sources. Sep 16, 2023 at 5:41

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