Tuvan Throat Singing and Harmonics
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IOP Physics Education Phys. Educ. 53 P A P ER Phys. Educ. 53 (2018) 035011 (6pp) iopscience.org/ped 2018 Tuvan throat singing © 2018 IOP Publishing Ltd and harmonics PHEDA7 Michael J Ruiz1 and David Wilken2 035011 1 Department of Physics, University of North Carolina at Asheville, Asheville, NC 28804, United States of America M J Ruiz and D Wilken 2 MusicWorks Asheville, Asheville, NC 28804, United States of America E-mail: [email protected] and [email protected] Tuvan throat singing and harmonics Abstract Printed in the UK Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian PED musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the listener hears two pitches 10.1088/1361-6552/aaa921 simultaneously. Harmonics such as H8, H9, H10, and H12 form part of a pentatonic scale and are commonly selected for melody tones by Tuvan singers. A real-time spectrogram is provided in a video (Ruiz M J 2018 Video: 1361-6552 Tuvan Throat Singing and Harmonics http://mjtruiz.com/ped/tuva/) so that Tuvan harmonics can be visualized as they are heard. Published Where is Tuva? Throat singing is known not only to the Tuvins, but also to several neighboring peo- 5 Richard Feynman, who shared the 1965 Nobel ples (Mongols, Oirats, Khakass, Gorno-Altais Prize in physics for his work on quantum electro- and Bashkirs). However, among the Tuvins it 3 dynamics, answered in a British documentary [1]: has been preserved in the most developed and ‘just outside of Outer Mongolia, in the middle of widespread form, … [3]. Central Asia, in the depths of Russia, far away from anything’. Feynman’s interest in Tuva (also Tibetan monks also have a tradition of throat called Tannu Tuva) dated back to when, as a child, singing with an extremely low fundamental pitch his father told him about interesting stamps from (first harmonic), close to 75 Hz [4]. In contrast, this captivating land. Later in life, he attempted the typical Tuvan fundamental is near 150 Hz, an to go to Tuva [2] with his friend Ralph Leighton octave higher, as demonstrated in this paper. (son of Caltech physicist Robert B Leighton3), Throat singing is also called overtone sing- but Feynman passed away before finally getting ing. Individual overtones (harmonics above the permission to travel there. fundamental) are enhanced in this type of sing- Not only is the location far out, but Tuva is ing, which is a beautiful demonstration of the also a very important region for throat singing. laws of physics. Students can visualize Fourier’s In throat singing, at least one overtone is empha- theorem, which states that any periodic tone with sized with the fundamental pitch. The composer frequency f can be constructed by adding sine and later ethnomusicologist A N Aksenov wrote: waves with frequencies f, 2f, 3f, and so on, the harmonics. 3 Leighton senior is coauthor of The Feynman Lectures on Physics (Richard P Feynman, Robert B Leighton, and Some students may already be familiar with Matthew Sands), first published in 1964. Tuvan throat singing from the popular television 1361-6552/18/035011+6$33.00 1 © 2018 IOP Publishing Ltd M J Ruiz and D Wilken show ‘The Big Bang Theory’, where the fictional somewhat and helps to create the resonance character Sheldon Cooper demonstrates the art chamber inside the mouth. in an episode. Students will find throat singing To produce the harmonics, the tongue must especially fascinating if the teacher begins by raise and lower inside the mouth in a manner sim- asking them if it is possible for the human voice ilar to whistling. The tip of the tongue is placed to sing two or three different notes at the same behind the upper teeth, as if saying the letter ‘L’ time. The skill employed in throat singing allows and the sides of the tongue are brought against the the singer to enhance harmonics above the fun- molars. By raising and lowering the middle of the damental, which creates the illusion that one is tongue while the tip and sides are in this position, singing a musical interval (two notes) or even a the harmonics are isolated and melodies can be chord (three or more notes). The practice for sing- sung. It takes some practice and experimentation ing a tune is to emphasize one overtone so that for the singer to learn the precise position of the by hearing the fundamental and the amplified tongue in order to isolate the specific partials and higher harmonic, one perceives two simultane- bring out the harmonics. ously sounding notes. The melody is carried by When initially learning to sing in this way the the overtone and the fundamental serves as a con- singer’s throat can itch, causing a coughing fit. stant pedal bass tone. Singers in training must be careful not to sing too Coauthor David Wilken first learned how to loud and when the throat itches, the singer should sing the base pedal-tone pitch with a particular stop, drink some water, and take a break to avoid sort of constriction that closes the ventricular damaging the vocal folds. The above description folds, sometimes called the ‘false folds’. These is informational and not intended to be instruc- false vocal folds are ‘paired tissues that occur tional. As with any advanced vocal technique, it directly above the true folds’ [5]. This practice is best to learn with a professional voice teacher. helps the oral cavity resonate more and brings There are other variants to throat singing out the overtones. Then he learned to employ a among the indigenous populations of Siberia two-cavity technique by creating a second reso- (Tuvans), Mongolia, and Tibet. In all cases, the nance chamber by raising his tongue up to the physics of resonance is important. The two reso- roof of the mouth. The cavity configuration is nances described earlier lead to the listener’s per- varied by adjusting the position of the tongue ception of two distinct tones. Levin and Edgerton against the roof of the mouth. In this manner describe the lower pedal tone as ‘a low, sustained higher harmonics can be selected for emphasis. fundamental pitch, similar to the drone of a bag- A single harmonic has an ethereal whistle qual- pipe’ [5]. They describe the whistle-like overtone ity characteristic of sine waves with midrange to as a sound in ‘a series of flutelike harmonics, high frequencies perceived by humans. Melodies which resonate high above the drone and may with tones that fit the pitches available in the over- be musically stylized to represent such sounds as tone series can then be sung. Since your students the whistle of a bird, the syncopated rhythms of a are likely to ask about the mechanism by which mountain stream or the lilt of a cantering horse’ throat singing works, we include a more detailed [5]. Later we will show why these higher tones are description in the following section. typically between three and four octaves above the fundamental. To read more about the different styles of throat singing with accompanying dia- The mechanism of throat singing grams of the vocal system, the reader is encour- The Tuvan style of throat singing, known generi- aged to consult the excellent references [5, 6]. cally as khoomei, begins with applying a special type of constriction of the vocal folds in order to help isolate the harmonics inside the oral cavity. Formants It can be learned by softly singing a low pitch Before analyzing the harmonics of throat sing- using the lowest register of the voice (the vocal ing, first consider speech and usual singing. The fry). Maintaining the vocal folds in the same posi- resonances in the vocal system, unique to each tion add a bit of volume and tone to the voice. individual due to variation in biological structure, This throat constriction closes the vocal folds enhance some frequency regions of the speech or May 2018 2 Phys. Educ. 53 (2018) 035011 Tuvan throat singing and harmonics Figure 1. Coauthor Michael Ruiz (with no voice training) singing the vowels A, E, I, O, and U. Note the harmonics and the brighter areas. These enhanced brighter regions are called formants or formant regions. song. These enhanced regions are called formants O, and 2nd and 3rd for the U. Therefore, strong or formant regions. Throat singing is a skillful overtones are present in normal singing. In Tuvan control of these enhancements. singing, the strength of individual overtones can See figure 1 for a spectrogram of coauthor be expertly controlled by the singer. In this light, Michael Ruiz singing the vowels A, E, I, O, and Tuvan throat singing is not so strange after all. All U with no voice training. The raw spectrogram of us naturally have enhanced harmonics in our for figure 1 came from the PC desktop software voice and song. Mark van Tongeren emphasizes called ‘Spectrogram 16’, developed by Richard this connection in his book Overtone Singing [6]. Horne years ago. A spectrogram is a plot of sine frequencies against time. Note the presence of The throat singer ‘Michael Vetter has said many harmonics with various degrees of bright- that when we speak we produce sequences ness. The stronger the presence of the harmonic, of chords. These are not the triads that our the more pronounced the harmonic appears in the beloved great composers used, of course.