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This paper summarizes our research efforts in functional modelling of the relationship between the acoustic properties of vowels and perceived vowel quality. Our model is trained on 164 short steady-state stimuli. We measured F1, F2, and additionally F0 since the effect of F0 on perceptual vowel height is evident. 40 phonetically skilled subjects judged vowel quality using the Cardinal Vowel diagram. The main focus is on refining the model and describing its transformation properties between the F1/F2 formant chart and the Cardinal Vowel diagram. An evaluation of the model based on 48 additional vowels showed the generalizability of the model and confirmed that it predicts perceived vowel quality with sufficient accuracy.