Though people say ‘octave’, there are only 7 different notes in the major scale. This is annoying if you’re trying to play scales in melodies with, say, 8 beats per measure. The scale keeps drifting out of synch.
One solution is to add an extra note to your scale! In this video, jazz cat Adam Maness explains the virtues of the ‘bebop major scale’, where you add a minor 6th to the major scale:
1 2 3 4 5 ♭6 6 7
Just playing this scale up and down, 8 beats per measure, already suggests some melodies. Even more so if you play it with both hands in ‘contrary motion’—up with one hand, down with the other. Listen to the video and you’ll see what I mean! This is just the start of the interesting things you can do with the bebop major scale.
Why do they call this the ‘major sixth diminished scale’? The jazz pianist and educator Barry Harris introduced this term: he said this scale is derived from a major 6th chord (1 3 5 6) and a diminished 7th chord starting at the 2 (that is, 2 4 ♭6 7).
You can get other bebop scales by putting the extra note somewhere else:
• Wikipedia, Bebop scale.
Sometimes the extra note in the bebop major scale is described as a ♯5 rather than a ♭6:
Azimuth 
It’s for guitar but ‘The Barry Harris Harmonic Method’ by Alan Kingstone is nice and condensed (the theory part is instrument independent).
Thanks—it sounds interesting! I am gearing up to buy some serious jazz harmony books. So far I’m keeping myself pretty busy watching YouTube and seeing if I can incorporate the ideas in my piano playing (despite my massive technical deficiencies).
In my case learning common practice period functional harmony, condensed to a few simple patterns, as i. e. secondary dominants, gave a windfall of dividend. And an important part of the harmonic analysis of say Jazz standards uses that language. There are quite good people in YT narrating that principles, so one can soon start writing his own chord progressions, but not by trial and error, but in a principled way, and that makes all the difference. And writing the progression in a backing track generating software and playing along is extra fun.