But all joking aside, the "blues scale" is rarely used by experienced improvisors except as an occasional spice in an improvisation. The idea of just slathering it all over everything without regard to the underlying harmony is something that's used to get kids started doint SOMETHING that at least doesn't sound awful. It's better to understand the harmony in the tune, the note collections that fit well with the chords, and then use the chords and their note collections to create melodies.
If we analyze the scales of song itself ( in Bb major), then the first 4 bars are built on the scale BbCDFG+Ab , synthesizing major pentatonic with tonic seventh chord characteristic for blues. The fifth bar is actually built on scale EbGBbCD , and in the 6th bar, G changes to Gb. In bars 7-10, Bb major pentatonic returns. Bars 21-26 in bridge are built on Gm and Dm chord notes , bars 27-28 - on fragment F major pentatonic scale.
The saxophonist on the record (in G major) in Part A improvises mostly on the G major pentatonic scale.
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