In human speech, the production of vowels consists in strengthening some specific areas of the harmonic spectrum, known as formants, by adjusting vocal-tract acoustical resonances with articulators such as tongue, lips, velum, jaw, and larynx. In singing, a compromise is often sought between the frequency of harmonics and resonance frequencies, sometimes at the expense of vowel perception. In some vocal cultures, this link between harmonic frequency and resonance frequency is skilfully adjusted. A melody is generated independently of the tonal melody related to vocal-fold vibrations.

This is the case of harmonic singing, overtone singing or Xhoomij, practiced in Central Asia, but also of singing by Xhosa women in South Africa. In this paper, the adjustmentsbetween harmonics and formants are explored on a wide range of commercial singing recordings and experimental recordings in laboratory. Three main strategies are described from both acoustical and musical point of view. In a first case, the spectral melody is produced by a play on the first formant (F1). The first harmonic frequency is often kept constant and at low values due to period doubling induced by a ventricular vibration. In a second case, the spectral melody is produced by a play on the second formant (F2), with a higher frequency of the first harmonic. Complex spectral melody can also be developed by a vocal game on the first two formants. In particular, we will illustrate and discuss the cases where the two first formants evolve while remaining in an octave ratio (F2 = 2F1).1Introduction When producing vowels in speech and singing, the fluid-structure interaction between air expelled from the lungs and moving walls induces vocal-folds vibration. This vibration generates a harmonic acoustic source, which propagates through the vocal tract (laryngeal and pharyngeal cavities, mouth and nasal cavities). The vocal-tract area function from glottis to lips is controlled by the speech articulators (tongue, lips, jaw, velum, larynx), which contributes to the adjustment of vocal-tract resonances (Ri). The resonances shape the harmonic voiced sound spectrum, in boosting acoustical energy in frequency bands designated in acoustics by the term formants (Fi). The frequency ratio between the first two formants F1 and F2 is perceptually coded into vowels.C7C6C5C4C3Hz10020030040050080010002000150025003000ii200 HzF2()56789101265 Hz567891012F1Figure 1: Mean values of formant frequencies F1 (blue) andF2 (red) on a musical scale. On left panel, the vowels have been grouped for which the two formants vary conjointly.Several singing techniques illustrate harmonic-resonance adjustments. Possible interactions depending on sung pitch are shown in Figure 1, which presents the mean values of the two first formant frequencies for a male speaking voice. The vowel location on the diagram is only indicative. It depends on individual peculiarities and the chosen language. Besides, values are given for male speech, as the songs studied here are mainly produced by male singers. The first formant F1 ranges from 300 Hz (/i/) to 800 Hz (/a/), which corresponds on a musical scale to E4-G5. It covers the high range in male voices, the medium and high range in female voices. In western classical singing, a tuning between the vocal-folds vibratory frequency (f0 = H1) and vocal-tract first-resonance frequency (R1) is sometimes mandatory to allow a loud and comfortable voice production, such as in the case of soprano high range [1, 2, 3] or, more generally when the sung pitch gets close to R1 [3]. To find a good balance between resonance adjustments and clarity of vowels constitutes a great part of the classical singer’s training. Such singers have to be able to sing a text on a wide range of pitches. In traditional Croatian folk singing [4], in Bulgarian women’s singing [5] or in Broadway Musicals [6], a systematic tuning is observed between the second harmonic (H2=2f0) and R1 for those vowels which do not have a too low first-resonance frequency. This practice gives power and clarity to the voice. It is produced by means of vowels /o/ /ɔ/ /ɛ/ /a/ in a limited pitch range: 220 to 320 Hz for male singers, 350-500 Hz for female singers (see Figure 2).Figure 2: Illustration on a musical scale of vowels and pitches for which a tuning R1:2f0 is possible. The blue notes present the musical pitches.The second formant F2 ranges from 600 Hz for vowel /u/ to 2400 Hz for vowel /i/ within the musical range E5-E7 ( seeFigure 1). Glottal fundamental frequency may come close to resonance frequency only for low-F2 vowels such as /u/ and /o/. In most cases, F2 lies well above f0, and it globally contributes to the voice quality. F2:f0 tunings have been observed in the soprano high range [2]. But most F2:Hi (i>1) tunings observed in the literature are reported for techniques of harmonic singing, which we shall now address. The literature will first be briefly reviewed. The tuning strategies will then be discussed on the basis of a wide range of commercial recordings. These observations will be supplemented by a case study of a Mongolian singer by means of simultaneous acoustical recordings and ultrasound observations of tongue motion. 2Harmonic singing : the state of the art A spectral melody and low-pitch tone – In the singing techniques mentioned above, a melody is produced by varying the vocal-folds vibratory frequency and the resonances are tuned depending on vowel and sound quality. Roles are reversed in harmonic singing.