Harmonising the Major Scale

Description: How to use chords - a printer friendly explanation of harmonising the major scale to triads.
We have already studied  diatonic chord theory
Taking the C major scale as an example:

The Roman numerals and generic names of each degree of the scale are constant for all keys. These are used, somewhat confusingly, to refer both to the notes on a major scale and to the chords built on those notes:

Here is the scale of D major harmonised. Notice that the key signature ensures the sequence of chord types remains the same, ie. I = major, II = minor, III = minor, IV = major, V = major, VI = minor, VII = diminished, VIII = major. This is true in all keys.