People use to say that JRs are a mid term between flats and rounds. I disagree. Jazz rounds are ROUND strings, but have a softer fret noise (probably due to the silk inside them) than usual rounds. Not metallic, more like a nylon guitar fret noise (kind of

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The string tone is also warmer than usual strings. They sound less hi-fi than usual rounds, with less overtones. Maybe like... mmm ... a mid term between flats and rounds...
Bottom end: warmer rounds.