According to Walter Piston's Harmony book, a perfect fourth is dissonant if there's no tone below its lower tone, while it's consonant if there's a third or a perfect fifth below the interval. In that case, why does a second inversion triad with no third or fifth below the interval feel consonant?
At the risk of inviting flames, I would say that dissonance is subjective. There seems to be a historical convention about what intervals are considered dissonant, but it depends on context. If that fourth is in the bass and low horns, the dissonance will be much more obvious. For higher pitches, less so.– S. ImpSep 21, 2018 at 0:26
Possible duplicate of Perfect 4th is dissonant?– user53472Jun 22, 2019 at 9:31
A first inversion triad DOES have a note a third below the perfect 4th. A second inversion triad doesn't. Hence the slight instability of a second inversion.
(edit: I should explain that the original question, before correction, asked about a FIRST inversion triad.)
Piston is talking about stability, not the sort of dissonance we get from minor 2nd intervals. A second inversion triad has the feeling of being a double suspension - hence the classic '6/4' cadence sequence.
(Actually, post-Common Practice, we've rather lost sight of the 'crunchy minor 2nd' concept of dissonance. A major 7th is hardly noticed as dissonant now.)
I notice the dissonance of the major seventh right when I hear it, the interval or the chord. And I hear a strong sense of a need to resolve to the root, a strong leading tone, despite function theory dismissing the major seventh as a dominant. So if I somehow land on a major seventh chord, I treat it just as I would a dominant seventh or a diminished seventh and I resolve it. If any seventh chord is stable enough to have tonic function, it is the minor seventh, not the major seventh.– CatersOct 19, 2019 at 1:58