2 1/2 beats duration without ties
I want to know if I can notate a note with duration 2 1/2 beats (half note + eighth note) without using ties. Is there a special augmentation dot or notation for this?
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Ah, something like the double dot, which extends the dotted value by half again? Except for this case you'd need something like a "half-dot" which AFAIK doesn't exist. I don't think there is any kind of "five-beat" marking in standard music notation.
Here is a great discussion from 2011 on this very topic: https://forum.makemusic.com/default.aspx?f=6&m=319987
There is no 5-beat (5/8 ths) symbol in standard western notation.
Whichever notation you do come up with will need an editorial note to explain it to your performers; which is likely just as much hassle as just using the standard tied notation.
Indeed, it's not a thing supported by standard notation. But for the record, but there have been a couple of composers who have proposed and used a symbol one of them invented, looks like a five-pointed star. Feel free to do a web search for more info if you're curious, and probably most fonts have a star-like symbol somewhere in them you could add as text, along with the text note you'd have to add for the benefit of the musicians reading the score who have never seen this notation before.