Howling, but with a different vocal
Solution 1:
It sounds like you're talking about the noun vocalise (the last syllable is pronounced to rhyme with Chinese and Japanese):
a musical composition consisting of the singing of melody with vowel sounds or nonsense syllables rather than text
or
any such singing exercise or vocalized melody.
(source: dictionary.reference.com)
It is not the same word as the verb vocalize (used in past tense in the second definition above), which is sometimes spelled vocalise in British English.
Solution 2:
The vocal on ‘The Beginning of a Journey’ sounds like Enya. I'd say 'mezzo-soprano vocalist in the New Age genre'. If pressed I might use the word 'choral'; in respect of ‘Naia’ the word 'celtic' comes to mind..
In my opinion what she is doing is 'singing', in spite of the lack of lyrics (or rather, the lack of consonants in the lyrics - she seems to have plenty of vowels).
See also:
http://en.wikipedia.org/wiki/Non-lexical_vocables_in_music
http://en.wikipedia.org/wiki/Loxian
http://en.wikipedia.org/wiki/Puirt_%C3%A0_beul
Non-lexical vocables, which may be mixed with meaningful text, are a form of nonsense syllable used in a wide variety of music. A common English example would be "la la la".
Solution 3:
I should have been paying more attention. If I had actually read the page I was linking to to provide an example, a part of the answer I was looking for is written right there on the page.
At least concerning that particular ‘iiih’ sample, the correct term apparently is kulning, i.e. ‘a high-pitched vocal technique … that can be heard or be used over long distances … [with a] fascinating and haunting tone, often conveying a feeling of sadness’ (my emphasis).
Fits perfectly.
This will do for this specific example. I guess I will have to settle on chant for the other vowels; ululate actually fits some narrow edge cases. Ultimately, trying to categorise different kinds of chants on the vowels sung is probably misguided.
For the rest, A E’s links seem to have enough pointers to allow me to circumscribe, together with the whole semantic field around kulning, joik, puirt à beul, loxian and so on. It’s an outlandish aspect of an absurd hobby project anyway, and I feel that I have sunk far too much time into it already. ^^