In music theory, we have names for intervals involving quarter tones. These terms are most commonly used in microtonal music, but can be profitably applied to blues playing (which is, after all, a kind of microtonal music).
Some examples: An interval halfway between a minor third and a major third is a neutral third (n3). An interval halfway between a minor seventh and a major seventh is a neutral seventh (n7). An interval halfway between a perfect fourth and an augmented fourth is a major fourth (M4). And an interval halfway between a diminished fifth and a perfect fifth is a minor fifth (m5).
Here are those intervals again in ascending width:
- m3 < n3 < M3
- m7 < n7 < M7
- P4 < M4 < a4
- d5 < m5 < P5
We can invert these like any other interval. Neutral intervals are like perfect intervals, and do not change quality when inverted. So a neutral third (n3) inverts to a neutral sixth (n6), and a neutral seventh (n7) inverts to a neutral second (n2). A major fourth (M4) inverts to a minor fifth (m5), and vice versa.