Te-form mnemonic (sung to Ba Ba Black Sheep):

i chi ri tte

bi mi ni nde

ki ite

gi ite

shi shite

I learned this 35 years ago to the tune of Clementine, youre using black sheep, my spouse uses another tune, but what funny is I learned it not with the 'i' endings, but with the dictionary form (sometimes called base-3) 'u' forms.

u tsu ru tte bu mu nu nde ku ite, gu ite

without the shi shite as that had been learned well ahead of the lesson adding ta/te forms.

I just think it's interesting how readily a little ditty tune helps people with recall, regardless of the actual tune.

I've generally found this kind of thing annoying in my various attempts to learn languages - in one of my high school spanish classes the teacher thought it was important to have us learn a little song to memorize the six present tense forms of the to-be verb ser: (yo) soy, (tu) eres, (el/ella) es, (nosotros) somos, (vosotros) sois, (ellos/as) son. My thinking was, there's only six forms to memorize, and the verb is an incredibly common one ("to be"!) so they'll get constantly reinforced anyway. The song is silly and isn't really helping anyway.

I feel similarly about the transformations for the Japanese -te forms and -ta past tense marker. The entire system is:

Ichidan: add -te/ta to stem Godan: -u/ru/tsu -tte/tta -su -shite/shita -mu/bu/nu -nde/nda -ku -ite/ita -gu -ide/ida

So basically ten patterns which group into 5 subpatterns. There's some logic behind them - the -te and -ta morphemes originally got added to the -i/pre-masu/ren'youkei stem and then underwent some idiosyncratic consonant reductions in godan verbs. But, really, it's only ten patterns, you can just memorize them; and these are incredibly common verb forms that get used all the time so you'll have them reinforced frequently if you are at all engaging with the language. It's a lot less to memorize than if you were learning Ancient Greek or Sanskrit or something.