I am wondering if there are any scales (that are in actual use) that also contain non-fixed pitches. By that I mean that in addition to having several fixed pitches, also have some "flexible" pitches that can be raised or lowered at will?
For example, are there any scales that can have either a raised or lowered scale-degree 3, where the descision whether to play a raised or a lowered 3rd is left at the discretion of the performer, and not prescripted by the scale itself?
Some examples of what I AM NOT after:
- In the melodic minor, scale-degrees 6 and 7 are raised on ascent and lowered on descent. Yet, in the context of either ascending or descending they DO have a fixed pitch.
- Similarly, in Indian music, the Arohana and Avarohana often contain different pitches, but those pitches are fixed in either context.
- Chromatic passing notes, which by definition are not intrinsically part of the scale.
- The use of modal mixture, that through some harmonic alteration may impact the notes of a melody.
- In the Klezmer scale Adonai malach (on C), there's an E natural when playing within the 1st octave of the scale, and an Eb when playing in the 2nd octave of the scale (see below). So the scale sometimes has E natural and sometimes Eb, but those too have very clear contexts, and in that sense those pitches are fixed as well.
Purely, to illustrate my point, I am attaching an example (below) of such scale (which I invented for the sake of explaining my question). This C scale, can make use of either E natural or Eb, as well as A natural and Ab interchangeably (at the discretion of the performer). In that sense, the scale itself contains some non-fixed pitches.
Are there such scales in wide use anywhere?
UPDATE The Hindustani Raag Pilu (or Piloo) seems to fit the bill. Any other examples?