# Why there is a single-flat key signature for a F major triad?

I am reading a book for beginner about building the chords, basically on triads so far. It is said that the major triads is formed by a root, third and a fifth. From that instruction, it is easily to setup a C major triad by making the root as C; to get the third, I add 4 half steps to C so to get E; to get the fifth, I add 7 half steps to C so to get G. The C major triad is shown on the left of the following stave

Similarly, I am getting the F major triad by using a F note as the root, A as the third and C as the fifth, so F-A-C be the F major triad, correct?

In the book, the author introduces anohter way to construct major triads by taking the first, major third and fifth notes from a major scale. It then gives me F major triad as shown in the right side of above stave. The book does not tell why there is a single-flat key signature added. I am trying to reason it by listing the C major scale, C-D-E-F-G-A-B, from that, the first, major third and fifth notes is just C-E-G but this does not give me F-A-C. However, I find that if I lower the F by half step, I get the E, which may get E-A-C by adding one-flat signature on F. This still does not show me why the RHS staff is connected to the F major triad.

Also, is it any noticeable difference between the F major triads with and without the flat key signature? I tried to repeat the following pattern in a virtual keyboard and listen very carefully, I can't tell the difference honestly

(I am trying to search the related questions on generating F mjaor triad but it comes up with few threads with some terms I don't understand yet).

• Wait, minor triads and major triads sound the same to you? Can you repeat the test pattern with C major and C minor chords, for instance, and do you also find you cannot distinguish between those by ear? Commented Sep 18, 2019 at 10:01
• Did you intend the flats and naturals in your last example to be on A rather than B as in the first example? In the first example, the flat will have no effect as there is no B in the chord. In the second, changing the A from flat to natural should have a very noticeable effect. Commented Sep 18, 2019 at 13:55
• Hi Dekadeci and badjohn, to reply both comments here. Yes, my bad to place the flat on the wrong position, it should be placed on the line of "B" on the sheet and the chord actually doesn't have B, I think that is why I can't tell the difference between them (in actualy play, I do place flat on B line and no effect to the chord). Commented Sep 19, 2019 at 5:19

The key signature shown there doesn't affect the notes in the triad, as you've correctly worked out. It's just there because it's the signature for the key of F major. The author has just chosen to show the one flat of F major because that's the key they're talking about: it might be confusing to see the F major triad in a C major key signature. It doesn't affect the way you play the triad at all.

It would make more difference for B♭ major. The key signature for that has two flats, on B and E. Obviously the root is on B♭. So if you write a B♭ major triad, you have to either write out the key signature or use an accidental.

About the connection between the triad and the key signature: each major scale has the same sequence of steps and half-steps: TTSTTTS (where T is a whole tone and S is a semi-tone). This is what links the root note of a major scale to its key signature, and it's probably described in more detail later in your book. In C major, this sequence lines up with the pattern of "white notes" and "black notes", so there are no sharps or flats. The F major scale contains a B♭ (as its fourth), so the key signature has a B♭. It just so happens that in this case, the notes of the triad (F, A, and C) don't have any sharps or flats. In some scales (such as B♭ major or D major), the notes of the triad do contain some that are sharp or flat.

• Thanks Dan. By reading the context of your reply carefully, I think I may find out the reason confusing me: I thought chords is isolated from key and scale since it states in the book that a chord is nothing but a stack or "vertical" combination or 3 or more notes. But as in your explanation, can I say major chord is always related to the key and a major scale? The major scale constrains what notes could be used and arrange in what order and key tell which note should be flatted, sharped or natural, is that right? Commented Sep 18, 2019 at 9:57
• @user1285419 That's pretty much right. A chord is just a stack of notes but you don't just choose random notes, you choose them from a particular scale (the scale of a particular key). That's the starting point, but obviously you aren't limited to the chord of the key the piece is in: if your piece is in C major, you'll tend to use chords whose notes are in C major, such as F and G; but you might also use chords containing accidentals. It's more of a guide than a constraint. Commented Sep 18, 2019 at 10:37

Triads are indeed formed from 1, 3 and 5 of a key, or the scale from that key. So in key C, 1 3 and 5 are C E and G, as you state.

On to the F triad. Exactly the same idea - but now we count from F. 1 3 5 is F A C.

Do the same for G, if you like - G B D. It all works as simply as that.

However (there's often a however!) sharps and flats in certain keys can affect which notes are actually played. Take A major triad. Count up A C E. Wrong! Because there's the key signature of 3♯ to consider, making that C into C♯.

On to your example. In key F, there's the key signature of one flat - B♭. That goes at the start of each line of music. Another however - that B♭ isn't played in an F triad, so is a red herring. I guess it's put in that music to show it's in key F. Confusing! But some would say it's technically correct. I wouldn't as we get an F chord in key C, so don't necessarily need to show that key sig. of one flat.

EDIT: noticing the last para. - don't know why the B♭ has changed to A♭, but now you have F minor and F major triads. They sound very different to most people, and ought to to you. If not, there's a serious problem with your discerning the difference!

• Hi Tim, thanks for the explanation. I sort of understand how to figure out the triad by counting now. But I think I need more time to digest what I learnt so far. Based on your first statement "triads are indeed formed from 1,3 and 5 of a key, or the scale from that key". Can I conclude that the key will be always the lowest tone of a scale? C major scale: CDEFGAB, F major scale: FGAB(flat)CDE, that is why when we say to sing a song in certain "key", we are saying from what starting pitch we sing the "Do" as? Commented Sep 18, 2019 at 10:06
• @user1285419 - got me there! As there are two distinct 'do' meanings. If it's fixed do, as used in France for one, then do is always C, regardless of any key. If, as I guess you mean, it's movable do, then yes, as do is the root of any key we happen to be in at the time. But don't get confused by the fact that we can have an F triad in key C. And that then is produced from 4,6 and 8 of the C scale.
– Tim
Commented Sep 18, 2019 at 10:46
• Hi Tim. Yes, my mistake in typing. The flat should be on B line, thanks for pointing that out. Commented Sep 19, 2019 at 5:21