Introducing A Music Notation Scheme for Pitch-Vowel Interaction

(ProQuest: ... denotes formulae omitted.) PITCH-VOWEL INTERACTION INVOLVES relations between harmonics and formants. A formant is an acoustic resonance of the vocal tract. It is a wave phenomenon in which forward and backward travelling sound waves between the glottis and the lips reinforce each other. Resonance occurs only at specific sound frequencies known as formant frequencies. In a neutral vowel like /.../ or /Λ/, these formant frequencies occur around 500, 1500, 2500, 3500, 4500 Hz, all are about 1000 Hz apart from each other. The separation is different for every vowel, however. Most vowels are distinguished by the first two formant frequencies, labeled Fl and F2. Compared to the neutral vowels, the vowel /a/ has a high first formant (around 700 Hz) and low second formant (around 1100 Hz), the vowel /i/ has a low first formant (around 300 Hz) and a high second formant (around 2100 Hz), and the vowel /u/ has both formants low (about 300 Hz and 800 Hz). It is important to keep clear that the vocal tract does not produce these frequencies; it only resonates them. They must be produced by a source of sound, such as the glottal airflow between the vocal folds during vibration. The source generally produces many sound frequencies, simultaneously. If the sound is continuous, steady, and not noisy, the frequencies are harmonically related. There is a fundamental FO, a second harmonic 2FO, a third harmonic 3FO, and so on. Individually, each harmonic can be considered a tone, a pure whistle-like sound to which we would assign a pitch if it were heard in isolation. We can also assign a tone and pitch to a formant, with the understanding that it exists only as a tone location, a place in tonal space where a harmonic can be resonated (or boosted). If we use traditional clefs for musical notation, harmonics and formants can be shown to coexist. The notation can be quite confusing and cluttered, however, unless a clear symbolic notation is used. To date, I have not found such a symbolic notation, but will propose one for discussion. Let the second harmonic of any note be written as a small diamond ([diamonds]) and the third harmonic as a small rectangle ([white square]). Higher harmonics could be given additional symbols, but let that be a future discussion. With regard to formants, let the first formant Fl be a single symbol (Example 1) and the second formant F2 a double version of the symbol (Example 2). Most of the interesting interactions occur between the first two harmonics (FO and 2FO) and the first formant (Fl). Example 3 shows a vowel sequence /.../ to be sung on the pitch intervals D^sub 4^-A^sub 4^-D^sub 4^-A^sub 4^. Here we see that the fundamental (normal quarter note notation, ...) and the second harmonic ([diamonds]) alternate in both, being below Fl for D^sub 4^ and both being above Fl for A^sub 4^. …