Perfect fourth is dissonant when there's no note below it?

Question

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?

Answer 1

There are two definitions to the term dissonance.

On the one hand, "sounds bad" is a common take.

However, in the realm of theory, the term dissonance means "needs to resolve".

Here Piston is referring to the second definition.

All music works on tension which needs resolution, or restlessness moving towards restfulness, or anticipation towards satisfaction.

Consequently, an interval or chord may "sound good" or "not sound bad", but since it needs to move to a resolution is considered dissonant.

Answer 2

Well, it feels consonant to you because it feels consonant to you. Does the perfect 4th by itself sound dissonant to you? Add to it the thirds in the second inversion triad, and it does sound entirely consonant.

Few would think a perfect 4th is a "dissonance" in the same class as a minor 9th. But we are talking about "common practice" here, which is a set of conventions that arose over time, without any attempt to legitimize them scientifically. In the common practice era the second inversion chord, aka the 6/4 chord, is treated as a dissonance that requires resolution. Unless the bass is approached by step and left by step. In which case it is treated as a "passing" dissonance. Hope that helps. Ask more if you like.