Tones in Korean language

I'm not sure but I think you're talking about old Hangul which had 3 tonal markers to help the reader pronounce words borrowed from Chinese.

Otherwise, though standard Seoul Korean is totally atonal, certain other dialects still have the features of a pitch-accent language, like Japanese where tones matter but the wrong tone won't give a word an explicitly different meaning.  Lots of languages have seemingly spontaneously gained and lost tonality.  Vietnamese is classified with Mon-Khmer but it somehow developed 6 tones while its relatives have none.  Conversely,  Vedic Sanskrit was a pitch accent language but all its descendants have lost that feature. 

It appears I was wrong.  Middle Korean did have three tones (low, high and rising) and old Hangul used small diacritical marks to distinguish between them (no dots, 1 dot, 2 dots).  Roughly speaking, modern dialects in the eastern half of the peninsula retain some tonality whereas dialects in the western half have lost them.  The loss of tonality seems to have occured in the 16th century, a hundred or so years after the invention of Hangul.  Maybe the two events are related?