i think the trills in blues serve an interesting function. they sort of act as filler in between the almost continuous runs and licks that players slide around the blues scale with. trills sort of act as space between the traveling runs, they fill up the dead spots between the ideas. blues players like to trill the 3rd and 5th or the 5th and 7th (also 6th and 8th) and not much else. playing trills helps keep a continuous right hand sound going at all times rather than putting in open spaces. of course trills also function as a way to sustain a note sound to make a note wail sort of like a harmonica trill.

here is somebody, it's not me, playing blues piano trills on youtube:
There are 8 comments, leave a comment.
in his books, dr. john talks about how players going back to jelly roll morton (when he would sing a blues) would use trills underneath a vocal.
of course i neglected the other trill intervals, i was only thinking about the trilling intervals in 3rds. there are also other intervals to be trilled,  such as octaves, 6ths, the 5th with the 8th, chords, etc.

i am not a fan of trilling eb and g on a c7 although i like it when the chord changes to f7.
i've always understood that that technique you describe above was called "piano tremelo" (ie rapidly alternating between the 3rd and 5th), aka "shake".

i was under the impressions that a trill only refers to seconds, so that in standard music notation the "trill" indication is "tr" or a horizontal wavy line, whereas "piano tremelo" (with notes spanning more than a second) is indicated by a set of diagonal lines in between the two notes that are being "shaken".
sp: tremolo
in tim richards' best seller "improvising blues" he calls them trills whether they are 3rds, 6ths or octaves, never shakes.
that being the case, how does he notate them?
he writes tr over the interval.
tr could mean tremolo
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