I use integer notation a lot. My scale is 0 1 2 3 4 5 6 7 8 9 10 11 '0. To avoid double digits, X and H are used instead of 10 and 11. X is easy to remember, roman numeral 10. H looks like 11. So here's Mary Had a Little Lamb:

4 2 0 2 4 4 4 2 2 2 4 7 7
4 2 0 2 4 4 4 4 2 2 4 2 0
'0 7 7 9 7 H '0

It's easy to write down a quick tune I find in my head.

For a lower octave I use a comma, like ,7 and an apostrophe for a higher octave, like '5

Double quotes do fine for an even higher octave "2
I don't find any good symbol for an even lower one, I use ; until somethin' better comes along.

For chords, I just write 047 = tonic major. 037 = Tonic minor. 7H2 = dominant. 590 = subdom.

This can be quickly converted to ABC with a substitution table.

By the way, in ABC, I find this is cool:
L:1/1
Then a quarter note becomes c/4. An eighth note, c/8. So easy to understand quickly. Why struggle with TWO layers of complexity? based on a crazy system anyway, invented by (celibate) monks 700 years ago?

BTW-BTW, Colin Hume runs a pretty good online abc translator.