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is there any difference between the two? is it even possible to produce an alveolar trill with a single vibration of the tongue?

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    No difference, except that if there's only one contact it's not a trill, just a tap.
    – jlawler
    Aug 11 at 16:58
  • It’s not possible to produce a trill with just one vibration/contact, because that is a tap. The definition of a trill is multiple taps in rapid succession; if there’s only one, it fails the definition. Aug 11 at 17:56
  • What you're asking is like asking about a difference between a one-storeyed cottage and a one-storeyed skyscraper. :-)
    – Yellow Sky
    Aug 11 at 18:40

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I suggest consulting Ladefoged & Maddieson The sounds of the world's languages, p. 217 ff for the distinction. They state that

The primary characteristic of a trill is that it is the vibration of one speech organ against another, driven by the aerodynamic conditions. One of the soft moveable parts of the vocal tract is placed close enough to another surface, so that when a current of air of the right strength passes through the aperture created by this configuration, a repeating pattern of closing and opening of the flow channel occurs

...

a sufficiently narrow aperture must be created and an adequate airflow through the aperture must occur. The aperture size and airflow must fall within critical limits for trilling to occur, and quite small deviations mean that it will fail

Therefore, they note that

trills tend to vary with non-trilled pronunciations. So with trills, as with voicing, there is a potential conflict between an acoustic definition (more than one period of actual vibration) and an articulatory definition (positioning of the articulators in a configuration such that, given the right aerodynamic conditions, vibration would occur).

They then resolve this conflict, saying that

we will consider trills to be sounds made with an articulatory configuration appropriate for vibration, regardless of whether vibration actually occurs.

Accordingly, a single-trill trill is not the same as a flap/tap, but only if you accept their articulatory definition of a trill. As for flaps and taps,

a flap is a sound in which a brief contact between the articulators is made by moving the active articulator tangentially to the site of the contact, so that it strikes the upper surface of the vocal tract in passing; a tap is a sound in which a brief contact between the articulators is made by moving the active articulator directly towards the roof of the mouth.

So it depends on how you define tap, flap and trill.

Catford, in A Practical Introduction to Phonetics, does not "define" trills, but his description of them (p. 66) is based on articulation, not acoustic result – I would say that there is no disagreement between Catford and Ladefoged & Maddieson on what a trill is.

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