Three note voicings of seventh chords where the perfect fifth above the root has been omitted are common in jazz piano because the ear does a good job interpreting the function of the chord with or without it. In Paul Hindemith's 'Craft of Musical Composition' he expresses that because it is limiting to think of chords as being constructed in stacks of thirds, the root may not be determined by doing so and simply seeing what tone ends up on the bottom. Instead we look at the root of whatever the "best interval" within the chord is.
If there is a fifth in the chord, then the lower tone of the fifth is the root of the chord. Similarly, the lower tone of a third or aseventh (in the absence of any better interval) is the root of the chord. Conversely, if a fourth, or a sixth, or a second is the best interval of a chord, then its upper tone is the root of the chord. Doubled tones count only once; we use the lowest one for our reckoning. If the chord contains two or more equal intervals, and these are the best intervals, the root of the lower one is the root of the chord (Hindemith 97).
In a (major or minor) 7th chord with an omitted fifth, the "best interval" would be the perfect fifth between the 3rd and the 7th, the 3rd being the lower tone, then, would be the actual root of the chord. Why then would the ear hear the root of a CΔ7, for example, as C and not E? This book has been extremely illuminating so far & I'm sure there is an explanation for this inconsistency that I'm missing.