The key to the relationship between the on’yomi of “myriad” 万 (まん) and “diligence” 励 (れい) is the related character “scorpion” 虿 (たい), but it gets complicated to explain because both the characters and their readings have changed dramatically over time (In all of these characters, 万 is a simplification of the traditional 萬, but I’ll ignore that for the sake of simplicity).
虿 was originally written without the 虫 radical, so it was the same character as 万. The pronunciations in Old Chinese, from approximately 500-1000 BC, are unknown, but comparative linguists have reconstructed them using the International Phonetic Alphabet (IPA) as *mlans for myriad and *m̥ʰraːds for scorpion.
IPA uses the following notation (see chart):
- * means the word is a theoretical reconstruction
- m is the consonant in em
- l is the consonant in el
- a is open vowel, felt central-back in the mouth
- n is the consonant in en
- s is the consonant in ess
- m̥ʰ is like m, but voiceless and aspirated
- r is a trill
- aː is like a, but long
- d is the consonant in Dee
The two words were closely related in Old Chinese, (I suppose because scorpions were a big problem and there seemed to be no end to them), and although they have changed quite a bit now as まん and たい, we can still see some similarities: まん still begins and ends with a nasal and has a similar vowel; たい still begins with an voiceless forward consonant and has a long vowel.
Now it’s time to explain how れい came about. The reconstruction of 励 is *m·rads, where m and r are in different syllables. That makes it easy to drop the m, just as たい drops the r. The vowel shifts slightly, but it is still long, and just like in たい, the final consonants are truncated.
That’s it, really. There are three roots involved, and they all evolve like crazy, and in different directions, so it’s hard to put it all together into one simple picture, but I think that’s all the essential points of the story.