Toneless Sinetic Dialects/Topolects
In modern Shanghainese and some other of Wu dialects, the adherence to the five tones has basically diminished in speech (still exists when referring to single characters), and converted into three pitches(low, mid, high).
Pitches for the same character, however, do vary through speech. For example, notice how the pitch for character 大's one pronunciation &quot;da&quot; differ from word to word: first the characters, then Shanghainese and corresponding pitch, then meaning, and finally the character's Mandarin Pinyin.

High: 澳大利亚 [O-da-li-ia] {lo-hi-md-md} (Australia) Ao4-da4-li4-ya4
Low: 大世界 [Da-su-ka] {lo-hi-md} (an entertainment venue) Da4-shi4-jie4
Mid: 大饼 [da-ping] {md-hi} （large flatbread) da4－bing3

(I'm not using any established romanization system for Shanghainese, instead I just used my own way for this ad hoc purpose.)
I couldn't find the definition to &quot;pitch accent language,&quot; so I can't answer you whether Shanghainese has become one.