we usually say voiceless stops are produced with vocal folds not vibrating. but when we introduce the idea of VOT, we say VOT is a specific feature for stop consonants that measures the amount of time between the release of obstruction and the onset of voicing (i.e. vocal folds vibration); and voiceless stops have a longer lag - onset of voicing comes after the release. isn't this contradictory? when we talk about the onset of 'voicing' for voiceless stops, do we mean 'voicing' of the subsequent vowel?
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There are numerous fine-grained problems with identifying the boundary between a consonant and a vowel, but setting that aside, yes, we generally define the consonant / vowel boundary in terms of the release of the consonant's constriction (the vowel is what follows), in which case VOT is a measure of the time until the vocal folds vibrate during the following vowel. If VOT is zero, the vowel is fully voiced, and if it is positive, the vowel is devoiced on some initial portion. The apparent contradiction stems from thinking that all of the properties of one segment get realized before any of the properties of the next segment: in reality, there is a lot of overlap (for example CV formant transitions where the tongue and lip configuration of the consonant persist for some time after the release of the constriction).
A "voiceless" stop can have a range of VOT values, from (small) negative to large positive, so characterizing voiceless stops as having "longer lag" isn't exactly true, since there may not be any lag. In North Saami, voicing at a very low amplitude precedes release by about 10 msc, in Thai voicing follows release by something less that 10 msc, and then you can find unaspirated stops with quite a range of VOT values (so the unaspirated stops of Navaho have a longer VOT than the aspirated stops of Thai). What counts is that voiceless unaspirated stops have a smaller VOT than do voiceless aspirated stops.
