I am learning the Blazhevic number 34 for tuba and it is in (9/8 3/4) time. What does that mean? It seems to me that some measures equate to be in 3/4 while others equate to be in 9/8. Very confused. Any explanation is greatly appreciated.
Two time signatures indicates alternation back and forth between the two. It's just shorthand for writing a new time sig at the start of every bar. The second sig is usually in parentheses, so, for example, 3/4(6/8) would have a bar of 3/4, then a bar of 6/8, then a bar of 3/4, etc. That exact example is from the "America" song from Bernstein's West Side Story, and is a pretty common situation: same number of subdivision notes (6 eighth notes) but divided differently in each measure (groups of two followed by groups of three in this example). Your specific example is different, but still works similarly: every measure has three beats, but the beats will have subdivisions of two alternating with subdivisions of 3. What is less clear to me is whether you should keep the beat the same and thus play the eighth notes faster in the 9/8 measures or if you should keep the eighth note the same thus making the 9/8 measures' sense of beat slower. Perhaps there's a clarifying marking on that topic as well?
Some composers use the marking when the switch between time signatures is more erratic than just every other bar. This only works if the visual difference makes the meter super clear, but I could see 3/4(9/8) working this way if necessary.
Without knowing the score it seems to me that this is a case of interchangeable metres/time signatures rather than alternating metres.
Eight note triplets in 3/4 could be equated with ordinary eights in 9/8. Thus can the two time signatures be seen as interchangeable (using three beats per bar). And the dual time signature can make the writing of the score more convenient: the triplet markings on the eights can be omitted in reference to the 9/8 time and the dots on quarters can be omitted in reference to the 3/4 time.
But if you have a more complex score (not only using quarters and three grouped eights) this is potentially confusing because when interchangeable the two time signatures are basically utilizing different duration values which can lead to quite serious ambiguity.
Presumably the piece is in triple time with three triplets per quarter note. One way of notating this is 3/4 (three quarter notes per bar), one way is 9/8 (three triplets per quarter note = nine triplets per bar).
On the assumption that each bar is as long as any other, the 3/4 will be a 'straight' feel, while the 9/8 bars will feel more 'swingy'. As in 3/4 the quavers will count as ONE-and-TWO-and-THREE-and-.,while the 9/8 bars will feel ONE-trip-let-TWO-trip-let-THREE-trip-let-, with 1.2 and 3 all being counted in the same timing. Another way to annotate it would be to stay in 3/4 and put triplet 'slurs' appropriately - as where it could have been written 9/8.
See a previous question from today for a similar explanation.