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Figure 4. Schematic illustration of singer AMH’s overtone singing performance of a Mozart song. A: the musical score. B: partials used for the melody tones (red lines) and for the drone (blue and black lines). C: wideband spectrogram of the performance.
In everyday listening, overtones are not perceived indi- vidually. Instead, the patterning of their amplitudes, determined by the resonance characteristics of the VT, collectively contributes to what our auditory system per- ceives as the “timbre” or vocal “color” of what is sung or spoken. The reason why overtones normally escape us is linked to the way our hearing works. It processes spectral contents by averaging the information in broad frequency bands, the so-called critical bands (Moore, 2012).
Characteristics of Overtone Singing
Against this background, we may be forgiven for finding overtone singing a rather puzzling phenomenon. Here we present an attempt to shed some light on its phonatory, articulatory, and acoustic bases.
We begin with a sample from AMH’s rendering of the Mozart melody. Figure 4A presents the first few bars of the beginning of Mozart’s theme in musical notation. Let us take a moment to consider what it would take to sing this sequence using overtones?
Figure 4 gives an answer in-principle. The format of the musical score is used to indicate the timing and pitch of each overtone. Along the frequency scale, the first eight harmonics are drawn at equidistant intervals. Hypotheti- cally, let us suppose that the singer selects a fundamental frequency near 300 Hz for the drone. That implies a
“keyboard” of the following frequencies of the first eight overtones: #2, 600 Hz; #3, 900 Hz; #4,1,200 Hz; #5,1,500; #6, 1,800 Hz; #7, 2,100 Hz; and #8, 2,400 Hz.
Note the following ratios: (1) 1,500/1,200 = 1.25; (2) 1,800/1,200 = 1.5; (3) 2,400/1,200 = 2. Relative to the first note at 1,200 Hz, the ratios correspond to a major third, a perfect fifth, and an octave, respectively. Those intervals are the ones needed to produce the notes of the first two bars.
For readers who find that result just a little too convenient, we should point out that it is no accident. Our musical scales and their intervals bear a very close evolutionary relationship to the physical structure of periodic sounds. Such sounds are constituted by the partials, the frequen- cies of which form a harmonic series (Gill and Purves, 2009). This implies that the musical intervals octave, fifth, fourth, major third, and minor third appear between the six lowest spectrum partials. Hence, it is possible to play melodies with the partials of a constant drone tone.
However, in the third bar in Figure 4A with chord tones C E G Bb, the pitch G appears. The series just mentioned does not provide an equally convenient choice for that note. Looking ahead to AMH’s performance (Figure 4B), we see how she handles the situation: She lowers the fundamental of the drone so as to produce an overtone whose relation- ship to 1,200 Hz is that of a major second or about 1,125 Hz! Our harmonic score includes that approach as illustrated by a shift in the fundamental and harmonics of the drone.
Figure 4C shows real data, a spectrogram of one of AMH’s overtone singing versions of the song. To enhance
the display of the overtones, we show a wideband filter- ing that portrays the overtones as dark patches. To help interpret their positions, we added black short lines that indicate the expected frequency values on the assump- tion that the 4th, 5th, 6th, and 8th harmonics of a 300-Hz fundamental serve as the melodic building blocks.
We note that these predictions parallel AMH’s overtones rather well. However, the black marks slightly underesti- mate the observed values. Why? AMH used a fundamental frequency slightly lower than our hypothetical 300 Hz.
This example illustrates the fact that overtone singing derives from the lawful way in which the harmonics are organized in periodic sounds. Overtone singers are able to exploit this patterning. They have developed a
Spring 2021 • Acoustics Today 45