Why does this melody tend to be in the key of F Major rather than in the key of C Major

Question

When composing, I generally start with C Major to be simple, but very often, I can hear that in the melody another key is suggested.

Here is such an example :

1. The melody starts by leaping to the VI degree of C Major (III of F Major)
2. The melody does not use a B Flat which is one particularity of F Major
3. The II & III degree of C Major are not used either.

Why is this melody in the key of F & not the key of C ?

Answer 1

Even though your accepted answer says they hear it more as 3/4, writing or hearing it in 3/4 is irrelevant to why this sounds like the key of F. Not only that, they actually changed your original rhythm to adapt it to 3/4. Two half note A’s were changed to quarter notes.

It legitimately sounds like 4/4 as written. Even in 4/4 the reason your piece sounds like F is because it is in F. The entire melody gravitates to and resolves to the note F on several downbeats. It also implies harmony in the key of F. Your first 2 notes are C A, outlining an F triad with no root. The leap leading from A to F going into bar 2 and the fact that that melodic phrase ultimately ends on an F, not to mention that the entire example ends on an F note preceded by an E, the leading tone of F, is enough to say that this heavily implies F. There is no hint of the key of C here at all.

If you were to leave this as is or put it in the key signature of F it wouldn’t matter because there are neither B’s or Bb’s in this melody.

EDIT: In reference to the answer provided by @Mixnik and the comment by @KarlKnechtel I decided to write a 4/4 version with more traditional melodic flow and stresses for consideration. Please excuse my poor penmanship, I drew this on a tablet screen with my finger.[

EDIT #2: Here is the same example with an anacrusis for the C melody notes:

Answer 2

I think you main problem with this music is that, although written in 4/4, the piece itself sounds to have a more 3/4 feel. This 3/4 effect makes it so the first beats of each measure mostly land on F or one of the notes of its major triad (F A or C), thus giving you a sense of F major even though a B flat is never played.
Notice that B flat itself is not a defining factor of F major, as we see here, but instead this F major sense implies the existence of B flat. Also notice that after every C the melody lands on one of the notes of F's major triad, so although the C may be played frequently, it is used to imply F major even further, especially in the C to A intervals since the C sounds like it is played on the last beat of the measure.
I have written below what the piece sounds to me which should clarify my points a little:

Answer 3

The most important thing to consider is not whether the piece includes Bb or not, but which note is serving as the tonic, or home tone.. This is the note that, simply put, sounds like the end of the song. It has a very stable sound, and it gives us a feeling of rest or conclusion. Wouldn't you agree that your last note, F, gives us that feeling that the melody is done?

Now, try a little experiment. Replace your last note with a C. Does that note give you a feeling of rest and conclusion, or does it give you a feeling that the song is unfinished? Were you to play it for 100 listeners, 99 would likely say that the note F sounds final and the note C does not. For this reason -- our perception of finality -- F is the tonic for this song.

To be correct, we should add the B-flat to the key signature to show that F is in fact the tonic (even if there are no B's in the song).

Why is F the tonic? Why can't it be C? There are two reasons that stick out. First, we are very used to the interval of the perfect fourth (here, C to F) working as 5^ 1^, or sol do for solfege readers. C-F tends to happen a lot in F major as 5-1, and much less frequently in C major as 1-4. Another reason suggested by Mixnik is that the notes of the F major triad appear on many strong beats, and this tends to set up F as the tonic, too.

If you wanted to write this in the key of C major, slide every note up 5 steps. Your opening sixth would be G-E, and all those parts that used to outline the F triad would now outline the C major triad. Your final note would be C, and it would really and truly sound like the tonic.

Answer 4

Mainly agreeing with other answers but I would like to mention one further point.

The tonality is determined by the note which gives a feeling of "finality". To me this is definitely F in your example, because

• the piece finishes on F, with a (possible) implied dominant harmony just before;
• there are many F major arpeggios (4 in 8 bars, if you count upwards and downwards arpeggios separately);
• additionally, the piece begins with two notes of an F major triad.

Others have basically said all this. But I would like to point out that (at least to my ears and brain) the feeling of F major is SO strong here that you could even have a B natural without greatly upsetting it. Suppose you take the minim (half note) A in bar 5 and replace it by two crotchets (quarter notes) A and B natural. To me, the tune would still be in F major, with a momentary hint of a possible (but unfulfilled) modulation to C major in the middle.

If you made this change (and if you agree with me that the piece is still in F major) then the "academically correct" way to write it would be with B flat in the key signature, and an accidental natural on the B I have just referred to.