Melodic lines are diatonic, harmony doesn't seem to be

Question

Okay so this is something that I came across as I was writing my canons and analyzing the harmony to try to figure out which canon is best for my symphony. There is a section in one of my canons where the harmony seems to be outside of the key. Now I did get this sort of thing in another canon where I had a C power chord and then the rest of it was dissonant. But here, I seem to be getting something which is not only out of key but not all that related to the key. The key I am doing these canons in is Bb major.

Here is the section I am referring to:

My first instinct was that it was an F major chord in second inversion but without the root because of the key being Bb major. This though did not make sense. So then I decided on it being A minor. But then I started questioning myself because there is no E natural to make it clear that it is A minor and the C and the A are a sixth apart. So then I thought maybe it is A diminished without the tritone since it lands on Bb major 1.5 measures after the last statement of the chord in that section but once again it did not make sense. The tritone is what makes it sound diminished. Without the tritone, it seems wrong to call that chord A diminished.

So is the harmony in that section that I circled A minor or is it F major? And yes, the second line is a second up from the first line and delayed by 1.5 measures. If the harmony in the section I circled is indeed A minor, why did I get non-diatonic harmony out of a completely diatonic melody?

Answer 1

Trained musical ears tend to do two things when identifying what they hear:

1. Make a determination that is most in line with prevailing musical practice.
2. Make a determination that makes the least unnecessary assumptions (in short, Occam's Razor).

This is why, when we hear a harmonic intervals 4 half steps wide, we'll typically hear it as a major third instead of a diminished fourth: because prevailing musical practice results in major thirds being more common than diminished fourths, and because a diminished fourth academically requires some type of extra accidentals.

So when I see your excerpt, I view this as an incomplete A-diminished triad. Hearing it as A minor breaks both of the above rules, because:

1. A minor is less common than A diminished in a piece that begins on a B♭.
2. A minor makes the assumption that either a) that opening B♭ is not tonic or b) the A minor is a chromatic chord.

From the standpoint of common-practice music theory, triads can be incomplete by omitting their chordal fifth; that's all that you've done here. But our ears will tend to assume the chordal fifth is E♭, not a chromatic E♮. (Our ears also probably won't assume a missing root, especially one that results in a non-standard second-inversion F-major chord.)

But you're right, not having the E♭ (and thus not having the tritone) definitely softens the sound. I would shy away from calling it A minor (for the reasons listed above), but you also might just choose to call it an A/C dyad.