Why is the fourth against the bass considered a dissonance? [duplicate]

Question

The consonance or dissonance of an interval is determined by the simplicity of the ratio between their frequencies. An octave(most consonant interval), has a ratio of 2/1, the perfect fifth has a ratio of 3/2. By contrast, the dissonant diminished fifth has a very ugly ratio of 1024/729, and the minor second's ratio is 1:243/128.

The perfect fourth's ratio between frequencies is 4:3, the third simplest ratio behind the octave and the perfect fifth. It's even more simple than the thirds, which it usually resolves to.

If the perfect fourth has such a simple ratio between frequencies, why is it considered a dissonance when formed against the lowest note?

Answer 1

"Why" is a bit tough. I can give a modern interpretation but it seems circular to me. Second inversion chords usually act as dissonances; bare fourths seem to imply second inversion chords, etc. The problem is that the fourth was something of a dissonance before the second inversion was common.

I have two references that should help. "The Evolution of the Six-Four Chord" by Glen Haydon. He tracks various uses of second inversion chords from the 1100s on. "A History of 'Consonance' and 'Dissonance' by James Tenny.

In the latter, the first chapter has some pre-1100s stuff with a fourth as a consonance. The second chapter has some discussion with the fourth being ambivalent by at least 1300.

Somewhere between simple organum at the fourth (C-F-C type) and organum with scale-like beginnings (C-C-C, C-D-C, C-E-C, C-F-C)...and three-part counterpoint, the bare fourth or fourth against the bass was treated as a dissonance.

These books (and other sources) do point out that physics "rules" do have a fourth as a consonance by looking at its sine wave overtones (Helmholz inter alia). Likewise, auditory tests show similar things. However, composers continue to treat bare fourths and six-four chords as dissonance.

A big point is that dissonance is "what composers treat as requiring harmonic movement" and consonance is "what composers treat as not requiring movement." It seems to work but It also seems to be mostly a cultural convention.

Answer 2

I don't recall reading an explanation other than those saying the P4 is a dissonance in certain styles.

Some speculation on my part is, and I don't mean to be flippant, a fourth against the bass is considered dissonant, because it isn't a third, and so doesn't fit into the ideal consonance of the chord of nature, which is a root position major triad.

Of course that isn't completely logical, because you could have a 6/3 chord, with no fourth against the bass, but it isn't the chord of nature.

My suggestion makes more sense if you consider just two part harmony, in which case the only way to get the chord of nature is an incomplete chord of root and third. In two parts the P4 then sounds like a dissonance, a P4 that needs to resolve down to M3 to make an implied chord of nature.

The is my own personal take on the conventions of old counterpoint and the dissonant P4 and trying to make sense of it, because to my ears, born in the 20th century, listening to rock music, the P4 is absolutely a perfect consonance.