In a first treatise on vowel acoustics, entitled Preliminaries, intellectual, methodological and empirical reasoning was exposed that gives rise to scepticism about the prevailing acoustic theory of the vowel, the formant theory. In this second treatise, pursuing the quest for the acoustic representation of vowel quality, the variability of the vowel spectrum and its dependence on fundamental frequency is revisited on the new empirical basis of the Zurich Corpus of Vowel and Voice Quality, with the aim of formulating knowledge-based statements concerning the spectral representation of vowel quality in general and of questioning the cause of the observable relation of the vowel spectrum to fundamental frequency. As a central result, three statements are presented that serve as primary indices for a future acoustic theory: The vowel sound is a kind of perceptual and acoustic foreground–background phenomenon, spectral representation of vowel quality is nonuniform and, most importantly, the recognition and spectral representation of the vowel does not relate to fundamental frequency but to pitch (or to a comparable perceptual reference). The treatise concludes with a reflection on the prerequisites and challenges of building a future acoustic theory of the vowel.