live's piano roll has extensive functionality but the understandable consequence of a clean gui is some of these features remain hidden. you tend to learn a lot of these as you use the program, but it's easy to see how some might slip by. here's my take on some of the best piano roll features you should definitely know about~
extending midi clips & loops
I spent a long time fiddling with the loop button & loop brackets before realizing the cmd + l loop shortcut works in the piano roll as in arrangement view. just select the section you want to loop (check the teal bar above the note editor to confirm the selection is actually the length you want - it's easy to get this a grid length or two off), press cmd + l, & your midi clip is ready for you to extend as far as you please.
this is really helpful in making variations - you can loop out a smaller segment & use cmd + j on the resulting extended clip to make a larger loop. change a few things & you've got a more dynamic loop, wham!
another way to do this when you just want your smaller loop extended is with the "dupl. loop" button to the left of your midi. this has less steps than the above method, of course, but presumes you want your full clip looped as a starting point, which isn't always the case. as always, the most appropriate method will vary between situations.
if you're farther into your project & have a long loop running through the track, it's sometimes compositionally desirable to add some variation - like a drum fill - to indicate a change. it's very easy to extract the portion of the loop you want to make a change to using cmd + e. you can edit the new clip in whatever ways you wish without affecting the rest of the loop.
when you "extract" some midi out of an existing clip (especially a longer one), it's good to know you can use the "crop clip" feature to clean it up & make the whole roll less confusing by removing the greyed out zone.
time variation & adjustment
the time clipboard is one of the most useful features in arrangement mode. the same functionality exists inside the piano roll & this can be a life-saver in session view. you can quickly create derivatives from pieces of your melodies or drums & make variations. as discussed earlier, just watch the teal bar at the top to see what's selected.
a small change can make a huge difference in humanizing your midi. by holding cmd & dragging, you can nudge notes off the grid. combine with this with some of the above methods to make slight changes to small loops to make them feel less static.
quantize by selection
in the reverse scenario, sometimes you want to tighten up notes that weren't clicked in. if you recorded your midi, it will naturally be a little off time & this can be great. for important hits like kicks & snares, however, you'll likely find you want them to be more perfect. you can select those by clicking their note on the left-side piano & as quantize will only affect the notes in your selection, you can leave the others as they are.
pitch variation & adjustment
a simple & common control but an important one nonetheless. it's so quick for adding an octave to your piano's chords or expanding a melody's range.
the transform controls can help you make discoveries in your melodies by finding parts you never would have written. rev will of course reverse the notes in the selection & inv will flip them within the highest & lowest notes. note that if you engage "fold" before inverse you can make sure the resulting sequence only utilizes the notes you have already used, effectively keeping it in key without adjustment.