The Pneumatic Sweep: Formant Trajectories in Three Sacred Vowel Sequences

Three historically independent traditions prescribe ordered vowel sequences performed as sustained vocal gestures on controlled exhalation, each traversing the cardinal vowel triangle of the human vocal tract: the seven-vowel sequence ΑΕΗΙΟΥΩ (/a ɛ e i o u ɔ/) of the Greco-Egyptian Papyri Graecae Magicae (PGM, 2nd–4th c. CE), the five-vowel kototama Futonorito sequence A–I–E–O–U (/a i e o u/) of the Japanese Shinto tradition, and the Vedic syllable AUM (/ɑ u m/). To the author’s knowledge, this paper presents the first comparative spectrographic analysis of these three sequences (performed by a single trained vocalist at a fundamental frequency of ~110 Hz and analysed with VoceVista Video). The results reveal a shared acoustic principle: each sequence, regardless of its particular vowel ordering, traverses the vowel space of the vocal tract, visiting the three corner vowel regions (/a/, /i/, /u/) that anchor human vowel perception across languages, performed on sustained phonation at a steady fundamental. This paper terms this principle the pneumatic sweep. The PGM seven-vowel sequence exists in cyclic rotation (as attested in the Miletus theatre inscription, 4th–5th c. CE), where each of seven archangels is invoked by the same sequence starting from a different vowel; the kototama tradition preserves three distinct vowel orderings (Sugaso, Kanagi, Futonorito). Despite different paths, all orderings activate the same resonant territory, visiting the three corner vowel regions (/a/, /i/, /u/) that define the vowel chart. AUM traverses this space in its vowel segment (/ɑ/ → /u/) and, as the paper reports, extends its formant trajectory during the sustained nasal murmur /m/, where F2 rises from ~600 Hz toward ~2200 Hz. This suggests that the phonetic notation “AUM” may underrepresent the acoustic content of the syllable as performed, and that the nasal closure may function as a latent continuation of the formant sweep. To the author’s knowledge, no prior study has mapped the A→U→M transition as a continuous F1×F2 trajectory or compared it within a unified vowel space across multiple sacred vowel traditions. The convergence suggests that the acoustic function of these practices is not a particular formant contour but the complete traversal of the formant space on sustained breath. Keywords: formant trajectory, pneumatic sweep, Papyri Graecae Magicae, kototama, AUM, vocal tract acoustics, spectral perception, comparative vocology, overtone singing, VoceVista