How to Compose for Overtone Singing, Experimental, Polyphonic Style for Choir

Overtone singing, for the uninitiated, is the ability to clearly produce two or more pitches simultaneously from a single voice.
The implications of this phenomenon, when applied to four separate ranges of voices (soprano, alto, tenor, bass) in a choral context are quite monumental.
Of course, this would mean that if all four voices are overtone singing at the same time, you arrive at eight tones.
The chordal possibilities become complex.

Being limited by the law of the harmonic series tends to complicate the issue of choice.

In order for the vertical relationships to work, it involves the consideration that certain combinations of fundamental pitches and corresponding overtones will invariably clash with others.

These interval relationships refuse to be altered in and of themselves, so it is necessary to use complementary fundamentals (each with their own series of available pitches) in building harmonies. In the case of overtone choir pieces where there is an unmoving drone pitch for the fundamental, the task is fairly simple. Even if the singers are instructed to 'move up and down' the harmonic series over a given ground pitch, in an improvisational manner, there is little chance of dissonance.

However, when the composer intends any degree of polyphony, the above mentioned complexities come into account.
Of course, there are always those composers who prefer a little dissonance in their writing! If two or more of the four voices are singing overtones, then it may become preferable to at least use octave displacement. (i.
e.
alto and bass might use the same fundamental pitch an octave apart). The numbers given to show which harmonics are being isolated will generally be higher for the basses, and lower for the altos. Tenor tends to be the ideal range for overtone singing in the context of overtone choirs.

It is not so low as to create somewhat muffled harmonics in the lower regions of the harmonic series, and can still be quite effective even up to the 12th harmonic. This is not to leave out the sopranos.

For although they are more limited as to the area of the harmonic series they can successfully produce (the lower portion), they may create a lovely effect with their natural 'falsetto' or head voice.

The resulting overtone pitches are 'sky high', but the listener's ears tend to perceive overtones as lower than they actually are anyway. As long as there are melodies in the other voices being sung with regular singing technique, this allows some space for an overtone soloist.

In many cases, this may appear as an 'overtone optional' part.
This is advantageous if the conductor wishes to perform the piece, but does not have a capable overtone soloist available yet.
If the composer is clever, the vowel sounds in the regular voices can 'match' the vowel sounds used by the overtone singer(s). To some extent, certain vowels will be implied by the harmonics, though they do not sound like the normal vowels due to the special way in which the singer is filtering the sound, manipulating the tongue and resonant chambers.

This would be considered highly advanced composition for overtone choir.
With present day notation programs (Finale, Sibelius) making composition so much easier than the old days, there are still special factors to take into account. To have the overtones play back accurately is unrealistic, so compromise must be made- to write the pitches one or two octaves lower than the actual sounding range with a small 8 or 15 above the treble clef.

This is also more convenient to sight read.
With all this being said, more and more singers are becoming skilled at overtones, to bring these pieces into manifestation.
The field is wide open for experimentation.