Fig. 1: The F Major Scale
Fig. 2: Triads Built From The F Major Scale
1.) F Major
2.) G minor
3.) A minor
4.) B Flat Major
5.) C Major
6.) D minor
7.) E dim.
The 1st, 4th and 5th chords are the most important chords in any key signature. They are often referred to by roman numerals, or the I, IV, V chords. In the key of F they are F major (I), B flat major (IV), and C major (V).
Fig. 3: Example
Here is a sample progression built from the F major scale/chord system on this page.
A#/Bb – C – F – A#/Bb – C – F – Am – Dm – Am – Dm – A#/Bb – C – F