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I introduce this question with something I'll amateurishly call "Slavic sung vibrato", because I don't know of a better term. It's a sort of recognizable extendeded and pronounced vibrato that proliferates in traditional and popular sung music of the region.

Although more-typical vibrato also occurs often in the music of that region, this sounds different to me, and it also seems different from vibratos and glissandi in traditional Perso-Arabic and Carnatic music.

(If you want more clarification, youtube: 1 2)

It is stylistic, but like other 'styles' it often seems to work in step with harmonic and melodic considerations. After listening to much music from the area over the past year and a half, it seems more subtle now but still powerful and affecting. I am guessing something of this spirit is in the 'terrible Soviet singing' Xenakis critiques at the end of this [informal interview]

(http://ada.evergreen.edu/~arunc/texts/music/xenakisFeldman.pdf) (I like Xenakis's music very much, by the way). I began to wonder, though, how this style fit within traditional Western music instrumentation and notation. In the same way the Georgian neutral third may have a harmonic function within 31-EDO or 11-limit (or maybe even 7-limit) JI - I wondered if extended vibratos might actually have some functional place in modern Western art music as more than just a simple ornamentation one day.

Sorry for the ramblings; my question is actually whether there was ever much of a known codification or notation of Slavic styles, beyond just the recording and arranging of individual folk tunes, or the writing and reviewing of new works in a 'nationalistic' style.

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You need to back up a bit, to see the wood and not the trees, you can't break it down like that, you can't do one without the other nor t'other without the one, so because it's not logical to talk of it distinctly, there's no term for it. It all comes from beat, where interference patterns make new tones in the harmonics.

Xenakis is talking about one of the oldest known musical practices: the caves where cave paintings are found also usually have excellent acoustics for overtone enharmonic singing. Most caves either echo wildly or not at all: it's therefore thought this is not coincidental.

The way to access this in voice is to listen carefully for the harmonics of a group of singers supposedly aiming for the same note: normally someone'll be out and you'll hear the beat come in at about 10 cents off pitch. Repeat on your own in the bathroom using the echo of your own voice to work with.

The physics of it is wave interference, where two waves of slightly different wavelength meet, the wave heights add, crests and dips becoming bigger where they meet their same, and zeroing out where they meet the opposite. The result is another hypertone forming, a harmonic. And that can sound like a vibrato, but a vibrato it isn't.

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I have never heard of special notation for styles of Slavic music. I do not believe a notation specific to it in regards to stylistic differences exist.

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