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When is a triplet not actually played as three equal-duration note lengths?

If I may use ratio notation -- I have always understood the only acceptable interpretation of a triplet notation to be the following:

1:1:1

In particular, when the rhythm is misinterpreted as a sort of clave:

3:3:2

... that's always been a good indication to me that the person executing the triplet is not processing it correctly.

However, I have recently seen it claimed that Baroque-era triplets (like the alternate version of Bach's 1st Invention) would correctly be interpreted (when making use of historical performance practice) in one of two duple rhythms:

2:1:1
1:1:2

I would like to see a summary with references of the prevailing wisdom on this issue -- some preliminary searching seems to indicate it is at least not so simplistic as claimed.

  • An interesting thought. Not so much triplets, per se, as the rhythm split into 4 (or 8), with a very slightly different take on the resulting rhythmic feel. Sadly, many years too late to get any original definition thereof. – Tim Mar 8 '15 at 18:53
  • Not sure if this helps, but have you had a look at Notes inégales. Unfortunately, the Wikipedia article doesn't seem to be one of their best, at least in terms of inline citations, but it does have a decent list of references. – Old John Mar 8 '15 at 21:43
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    Marginally related: fives and sevens should be played absolutely uniformly, but far too many (especially grade school&high school) conductors tell the ensemble to play them as 2-3 or 3-2, which is a completely different rhythm. – Carl Witthoft Mar 9 '15 at 14:13
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I am rather sceptical of that claim since changes between rhythms like 4/2 and 3/1 are rather old practice and I distinctly remember some Missa from Josquin Desprez where there were there was one voice with three notes over 2 or even 4 bars.

I'd be rather surprised if baroque composers fell apart with smaller subdivisions where things actually become simpler to execute.

However, when triolic patterns are played against dotted rhythms in Bach, it is actually rather the dotted rhythms which are to be interpreted triolic. The dotted rhythms are used both for long-short and short-long, and if there were a fixed interpretation for the parallel trioles, it would not end consistently. Trying to play both the dotted rhythms as well as the trioles "accurately" tends to cause rhythmic unrest not really serving a discernible purpose.

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