Singing two notes at the same time

Once, an operatic singer came to visit me. He was going to show me a very particular technique through which he would have sung two notes at the same time. He said that this kind of singing produces very high and inaudible overtones. Therefore, I had to make sure that no dogs would be nearby. Otherwise they would have acted crazy. Moreover, he added that this type of singing can call all the dogs from the street.
It is so that I learned diphonic singing, also known as harmonic, overtones, xoomi, sygyt, throat, and Tuva singing. In this technique, the singer emphasises one high harmonic of the voice to such an extent that it is heard separately from the low pitched note being sung. Different notes in the harmonic series may be chosen by changing the frequency of the resonance in the vocal tract that gives rise to it.
Therefore, we should not imagine a counterpoint made of two disting melodies. We will hear a fixed fundamental note, as it were a continuous bass, and a second note that can only move through certain natural harmonics of the fundamental. Therefore, the second note can embellish the fundamental with a melodic construct.
I eventually learned the technique and I saw that shifting harmonics is not that difficult. Practically, it is enough to change vowel, while keeping your mouth in a fixed position. Therefore, you do not articulate the vowel in your mouth. You sing a sort deep "O" for the fundamental. Then, you only move your larynx slightly to adjust for the change in vowel. As you practise, you will see that each vowel produces a different harmonic.
This consideration is very important, as most singers are not aware of it. Many vocal techniques rely on using the position of a certain vowel to sing anything. For example, the lunge technique uses the vocal "U". Some other singers recommend the vocal "E", as they find it reacher in harmonics and more brilliant. Unconsciously, they do this for a simple reason: If each vowel is a harmonic and you sing it with its associated note as it is, you obtain notes that have the sound and character of harmonics. This impairs the melody, as other sounds are perceived instead of the melodic line. If one bases his singing over a certain vowel, instead, the sung vowels over a base vowel retain their reference to the base sound. Thus, the melodic line seems consistent and anchored to the base vowel, while the actually sung vowels take on the character of nuances.
If you want to practice harmonic singing, one way to strengthen the second resonance - at the expense of the others - is to make a small mouth opening and also a relatively tight constriction between the tongue and the roof of the mouth. You will need feedback to perceive a difference. Usually, the feedback comes from finding a reasonably reverberant environment (bathroom, stairwell) and listening for the individual harmonics.
Therefore, hold the sung pitch (fundamental) constant, and then tune the vocal tract resonances to choose one or another harmonic. You will end up singing just as players of the natural trumpet or horn do. Skilled practitioners can vary the voice pitch and the resonant frequency independently.
The following graph shows what happens in diphonic singing.
Harmonic Singing
 Harmonic singing is still practised in Sardinia (Italy) and some regions of Russia.
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