Which of these notations is preferred?
- This is a bit pedantic, but it's sometimes seen. An experienced sight-reader should have no problem with this.
- This is the closest to a 'standard' notation, and the most usual one. Leonard Bernstein uses this in the Prologue from "West Side Story". Orchestras never have a problem reading it.
- This makes the intention a bit clearer. Richard Strauss often uses this. E.g. in "Die Frau ohne Schatten":
- One contributor claims this this is the 'theoretically correct' solution. I've never seen this in practice.
- This is messy and obscures the fact that both notes are the same. They will probably be played differently. Hardest to read.
- This is only a solution if the piece is more in 2/4 than 6/8. Notating a whole piece in 2/4 with triplets just to avoid a few duplets is an unnecessary complication.
The second way (but probably with a bracket as well as the number) is traditional. The first is gaining popularity. Both are acceptable.
A tuplet can usually be expressed as a whole-number ratio 'x in the time of y' where x is greater than y. I've heard the opinion that our example should be notated as duplet quarters, '2 in the time of 1½'. Presumably because they think the 'more in the time of less' thing is a 'rule'. I think not. This is an exception!
I don't like either one of these. Especially if I expect someone to sightread it. One possibility that would probably be understood at sight would be to use a dotted eighth followed by a sixteenth tied to an eighth. (I cannot seem to paste graphics yet.)
The real problem is that the pulse has changed from 2 beats to measure to 4 beats (for this measure). A measure of 6/8 implies that the next level from is a triple. It (6/8) signifies that the basic pulse is two triples. There's no nice division into fourths. The first second measure is awkward in that the dotted eighths do not represent the "normal" second level beat structure. The second measure could be done as Rosie notes; that's probably best though it does make the two halves of the measure have different secondary pulses. One could solve the problem by rewriting the measure as 2/4 or 4/4 (or 12/16) but any irregular change in time signature causes sight reading (aka rehearsal) delays.
Let's start fresh and use a 2/4 time signature instead of 6/8. Now we'll have triplets in the first beat of the first measure, followed by a quarter note. Then the second measure will have two eighth notes followed by a quarter note.
I think this will give you more flexibility to play with different subdivisions and patterns as things progress.
Also, this will make it easier for people to sightread -- which was an understandable concern, brought up in one of the answers.
After all, a 6/8 meter is mainly a convenience when you are dealing with a large number of triplets. But there's no objective need to notate in 6/8.