I've been reading up on Tippett's Concerto for Double String Orchestra and came across the two terms 'additive rhythm' and 'asymmetrical grouping'. I would assume they are synonymous...
Is there a difference between the two?
They don't seem to be completely synonymous. Instead, it seems like an asymmetric time signature implies an additive rhythm, but an additive rhythm can exist in a "traditional" time signature.
It appears that the word asymmetric is commonly used to describe meter, while additive is used to describe a rhythm. Rhythm and meter are related, but are not the same thing.
A meter is an aspect of notation and is not necessarily a component of the music itself. A rhythm is a musical component that is played and heard, even if it is never written down. One way to see the difference is to understand that two different meters could be used when transcribing the same rhythm. While there may be subtle performance differences between the two, a 4/4 meter with triplets can be used to notate the same rhythm as a 12/8 meter with no triplets.
In this particular case, it is possible for an additive rhythm to exist in a simple meter, such as 4/4. If the rhythm is a group of five eighth notes (quavers) followed by three eigth notes (quavers), then that would be considered an additive rhythm even though it might be notated in 4/4 time.
For whatever reason, the term asymmetric seems to be exclusively applied to meters, and refers to meters with odd, or more commonly prime, numerators. So 5/4 time and 7/8 time would be called asymmetric meters. Of course, music in 5/4 or 7/8 time would almost certainly also have additive rhythms, but an additive rhythm does not require the use of an asymmetric meter.