This morning I got up early so I could read an instruction manual on overtone singing. I then practiced into my computer from 10AM to 1 PM and discovered the following nifty details:
In overtone singing, you hold a steady pitch with your voice and change the the resonating space in your mouth by changing the shape of your lips (puckered to open) and your tongue (high or low). You can do this seperately or in combination. Each individual combination of tongue/lip positions changes the space in your mouth and resonates with a different overtone of the overtone series.
If you sing a "C" note with your vocal chords (called the fundamental), its ascending overtone series is (C, C an octave above, G, C, E, G, B (slightly low), C, D, E (slightly low), F (slightly high), G, A (slightly low), B (slightly low), B, C). The "slightly low/high" qualifications refer to their relationship to the tempored scale that they use on the piano. The overtone scale does not match the piano exactly, but the overtone scale is the one that comes from nature (and the one used in Norwegian folk music), so personally, I think it is the piano which is out of tune.
So, after many different trials, I was able to pinpoint exactly which vowels create which specific overtones! I can now sing overtone melodies of my choosing!
(These are vowels formed with the lips only. The tongue is down in a neutral position)
ooh/[u] : C- octave above the fundamental
oh/[o]: G- octave and a 5th above the fundamental
aww/[open o]: C- 2 octaves above the fundamental
ahhh/[a]: E- a major 3rd 2 octaves above the fundamental
To get higher overtones, it is necessary to involve the tongue. Start by making an American "r" sound. This causes your lips to pucker and the tip of your tongue to come up. It is very easy to hear overtones on this vowel, so it is a good one to start with. When you begin to get better, you can dispense with the "r", but use it for now.
Keeping the "r" position, form the following vowels with the middle (the blade) of the tongue. With each successive vowel, your tongue should be moving slightly higher:
ahhh/[a]: C- 2 octaves above the fundamental
aaaah/ [ae]: E- a major 3rd 2 octaves above the fundamental
eh/ [E]: G- a perfect 5th 2 octaves above the fundamental
(Somewhere between eh/[E] and ay/[e]): (low B- a low major 7th 2 octaves above the fundamental)
ay/ [e]: C- 3 octaves above the fundamental
(Somewhere between ay/[e] and eeee/[i]): D- a major second 3 octaves above the fundamental
eee/[i]: E- A low 3rd 3 octaves above the fundamental.
If you then un-pucker your lips from the "r" position and open your mouth really wide, saying [i] (the brightest vowel), you might be able to get a little higher- but it is really hard to hear in that range- and also very difficult to stabalize.
As the pitches go up in the overtone series, they become harder and harder to hear. Thus, the first ones (made by the lips) are the lowest and strongest, and the high ones (made by the tongue) will be the hardest to find and stabalize.
Anyway, I went through all of this so that I could see if the vowels that brought out the cool overtones were the same ones that were most often used in Norwegian improvised nonsense syllables.