Easy music theory question

When I hear a major sixth interval (also called a “diminished seventh”) – for example. middle C and the A above it played simultaneously, with no other context – my brain “fills in” a note to “create” a major triad whose root (in this case, F) had been “missing.”

But it should be just as likely for my brain to “fill in” a note to “create” a minor triad, right? (In this case, A minor, by “inserting” an E).

Why do I “hear” the former spontaneously, yet have to force my brain to hear the latter? Is it just because my post-Medieval Western ears have been conditioned to look for major chords as a first option?

Or is it that it’s easier to “fill in” a 1 than a 5? (Maybe because what the brain is really looking for is a third interval – either major of minor – and we tend to hear the top note of an interval as the “melody,” so my brain is saying, "I hear an A…that’s the top of what third? How about F major? Perfect – you’ve already got a C down there, to complete the triad!)

Or is my particular brain just weird?

I’ve just played those notes on the piano and I have the same thing. So you’re not weird (or we both are) but I don’t know why.

It has to do with how the frequencies match up. C and A are the 5th and 6th harmonics of a fundamental F, so when you are playing these notes (even one that’s an octave up, as in your case) the sine waves exactly line up (momentarily) at the fundamental frequency. This is what your ear, and brain, are hearing.

Don’t know for sure, but I suspect it’s a matter of psychoacoustics. Have you tried the inversion – instead of C and the A above it, C and the A below it (= A and the C above it)?

I’ve studied music theory but I’m going with a non-theory response:

How much NBC do you watch?

Maybe I’ve studied music too much, but I don’t automatically “fill in” an F when I hear a C and A, unless there are other tones or instruments involved, or preceeding harmony that might establish a tonal center.

This exercise reminds me of a demo I often do for beginning music theory students. I play, as fast and as loud as possible, with the piano sustain pedal down, all the Cs and Gs on the keyboard, and let them ring. Ask the class: “Does this sound major or minor?” The correct answer would be “neither,” since the defining note (E or Eb) is not present.

Then I do it again, and shortly after all tones have loudly sounded, I press very softly, one single E somewhere in the middle range. Students note that a single, soft tone is sufficient to define what they hear as major. Then I repeat the exercise with the single tone as E flat, and the overall sound is minor.

However, it does seem like your exercise produces the opposite result in your head, so I can’t explain the reversal. Gyrate’s answer is the best so far.

GaryT, I tried that, and I now REALLY hear that same F Major triad. So strongly, I can’t override it with an A minor. I even tried playing a full A minor triad, and THEN the A-C interval, and I STILL “hear” an F Major chord, although not as strongly (I can easily “override” it now).

Musicat, perhaps I was unclear, but that interesting exercise you do with your students didn’t contradict my experience as I had expressed in in the OP…but it DOES sort of run against the experience I just described now. Well, the overall fact is valid in all cases: musical context matters. As you implied, even “no context” situations have some ambient tones in the background (refrigerator motors, etc.), plus dim memories of songs or sounds that have been jangling inside your brain for the past few hours.

So, maybe my brain (probably through conditioning) is more apt to focus on ambient sounds and/or remembered tones which happen to help newly heard sounds resolve into major chords.

And then there’s **engineer_comp_geek’s **suggestion. I understand how some harmonics coincide with some intervals we hear as “correct” or at least as consonant – you mentioned the 5th and 6th harmonics correspond to the major third and open fifth intervals (which with the root make up a major triad.) So, does the MINOR third interval correspond to some harmonic or other? If not, or if it’s a very “weak” one (let’s say 7th or higher), then really what you’re saying is that there’s something fundamentally “better” about the major chord as compared to the minor one. You might be right, but that wasn’t what I had been led to believe – I was under the impression that the Western post-1400 AD mild preference for major chords was just a random cultural thing.

I have no definite answer, but I’m guessing this. When I hear A-C played together as a minor third or C-A as a major sixth, without context I don’t really get a sense of tonality. I just tried it on the piano, and, if forced, I’d probably call the former minor and the latter major, but that’s only if forced, and I think I’m cueing in on the interval names. C-A without context really does sound to me like it could just as easily be minor, but I do noodle around a lot in A minor (moreso than F major), and that voicing is no uncommon for me, so that could be my own biases creeping in.

Thanks, all! Any more thoughts on this are welcome.

You have just confirmed why one is called minor and the other major, even though they are only inversions.

OK, so play C->A (major 6th), which you say sounds minor, followed by C->A flat (minor 6th). What does that sound like?

If you’re addressing me specifically instead of the general “you,” well, of course. But the act of playing those one after another gives me context. (I can just as easily say to you, play E->A and then C->A…what chord do you hear?) Without context, C-A> to me sounds just as likely to be minor as major. I would call it a “major 6th,” because that’s what the interval is called, but it can go either way. Since my own ear tends to be a bit more geared towards minor, contextless, it’s more likely to sound minor to me. In the OP’s case, it’s more likely to sound major.

Actually, now I’m wondering if we’re agreeing. It’s all about context. C->A major sixth might sound minor to me (because I’m used to hearing it as such in my playing), but C->Ab to me recontextualizes the original C-A to establish C as the tonality (rightly or wrongly, but I don’t have anything else to go by) and now the original interval sounds major, while the new interval sounds minor, without a context. Alone, I couldn’t tell you one way or another without some sense of key. C-Ab played together first would probably conjure up major tonality, as that’s the opening notes for the way I play “Linus & Lucy,” so whenever I hear that or play it on the piano, I think major.

pulykamell, it seems, in both of your examples (E->A, then C->A; Linus & Lucy opening notes) you are retaining memory of previous tones, mixing them (in your mind) with the new ones, then analyzing the combined results.

That may be a common human trait, but I don’t seem to have that problem unless I deliberately force it. I have no idea if your experience or mine is more prevalent, but it does seem like personal experience is a big factor here.

Exactly…I think. Without context, either is as likely to me. For me, without some indication of a tonal center “minor” or “major” just means “small” or “big.” Depends on what day you catch me. “C-A” is a called a “major sixth,” but it doesn’t imply a major chord to me. It might be C major. It might be A minor. It could be something yet completely different with a different root. My contention is that if you always hear it as a major, you are, as you say, “retaining memory of previous tones, mixing them (in your mind) with the new ones, then analyzing the combined results.” There is nothing implicit in a two-note interval that suggests major or minor tonality (as defined by whether the two notes are implying a major or minor triad) without any further context.

^ Of course, that should say “F major,” not C major. But I was thinking in terms of a Cmaj6, which is another common context of C-A, at least in my style of playing (which tends to be bluesy/New Orleans or country-tinged piano which uses maj6 fairly regularly.)

Is there some reason you don’t call this C6?

Some notation schemes prefer C add 6, but I don’t know what a C Maj 6 would be or how it would be different from CEGA. Standard notation assumes that a single letter refers to a major triad unless modified (minor, diminished, augmented, flat 5).

No, it’s the same. C6 would be the usual way to refer to it.