The 555 costs just a few pennies/cents.
When you said transistor, you didn't specify what type of transistor.
(By the way, these types of posts are not suitable for "Digital Signal Processing", they
are more elementary questions.
If you really really do want to do it with just BJTs, then there was a URL pointed out to you
many many times, with purely transistor circuits.
If you go to
this link
and just CTRL-F and search for the word "tone", you'll find a "capacitor tester" which makes
tones. It is clear that if you insert a capacitor, then you have got a tone generator.
It uses only transistors and no i.c., and drives a speaker. Then, if you clicked at the
link near the top of the page to go to
this page then
you can type CTRL-F again, search for "tone" and you'll find and other tone circuit which makes siren sounds.
Again just using transistors.
I think 99.9% of the circuits you ask for are on those two web pages.
Furthermore, when you have a 555 as tpetar suggests, you can click at another link near the top of that page and
find
50 555 circuits
and search for "tone" by doing CTRL-F again.....