The “state of art” of western musical scales are the bebop ones. Beautiful and fulfilled, the bebop scales represent the pinnacle of tonal music.
They consist of an heptatonic ♭7 scale, plus the leading note. Historically they are presented descending (eighth to first).
The simpler bebop scale is the bebop Mixolydian, which is grounded on the diatonic scale’s Mixolydian mode (Ⅷ, Ⅶm, ⅥM, Ⅴ, Ⅳ, ⅢM, ⅡM, Ⅰ) getting the extra leading note: Ⅷ, ⅦM, Ⅶm, ⅥM, Ⅴ, Ⅳ, ⅢM, ⅡM, Ⅰ.
Looking up close, you can see that each degree pair starts with a note from the tonic Δ chord: Ⅷ / Ⅶm / Ⅴ / ⅢM / Ⅰ. Another remarkable feature is the chromatic passing from Ⅷ through ⅥM.
The next bebop scale is a minor mode: the bebop Dorian. The Dorian mode degrees are Ⅷ, Ⅶm, ⅥM, Ⅴ, Ⅳ, Ⅲm, ⅡM, Ⅰ, so its bebop version is: Ⅷ, ⅦM, Ⅶm, ⅥM, Ⅴ, Ⅳ, Ⅲm, ⅡM, Ⅰ.
The great improvement bebop scales bring is the gravity increasing. For example, an amazing scale is the super-Locrian exotic scale. It presents itself as Ⅷ, Ⅶm, Ⅵm, Ⅴ-, Ⅳ-, Ⅲm, Ⅱm, Ⅰ. But this incredibly beautiful scale has a weakness: lack of gravity. Our western ears simply can’t accept the tonic degree as ending.
It can be fixed simply adding the leading note, so the bebop super-Locrian is: Ⅷ, ⅦM, Ⅶm, Ⅵm, Ⅴ-, Ⅳ-, Ⅲm, Ⅱm, Ⅰ, and the problem is solved!
Another problem happens to two scales: the Phrygian dominant scale (a.k.a. Freygish or hitzaz) and the minor harmonic scale.
The Phrygian dominant scale comes from the Phrygian scale, just raising the third degree: Ⅷ, Ⅶm, Ⅵm, Ⅴ, Ⅳ, ⅢM, Ⅱm, Ⅰ.
The minor harmonic scale is produced from the Aeolian mode, by raising the seventh degree: Ⅷ, ⅦM, Ⅵm, Ⅴ, Ⅳ, Ⅲm, ⅡM, Ⅰ.
If you take a look at the intervals, you may notice that they are the pretty same scale, so how to discern one from another?
Simply by making them bebop!
- The Phrygian dominant scale leads to the so-called bebop Mixolydian ♭9♭13: Ⅷ, ⅦM, Ⅶm, Ⅵm, Ⅴ, Ⅳ, ⅢM, Ⅱm, Ⅰ;
- The minor harmonic leads to the bebop Aeolian: Ⅷ, ⅦM, Ⅶm, Ⅵm, Ⅴ, Ⅳ, Ⅲm, ⅡM, Ⅰ.
Then we got two different well-ended scales.
Not even by far it would fully cover the subject, but I hope this post can be useful.