Adding chords and building triads-I would like to add some harmony to my little melody

Each note of a scale is the root of a triad.  For example;






             E                     F#                    G#                  A                    B                   C#                    D                                                                           
             C#                    D                    E                    F#                   G#                 A                      B                     
             A                    B                    C#                    D                    E                    F#                    G#



tonic I                supertonic ii     mediant iii      subdominant IV   dominant V   submediant vi  leading
                                                                                                                                                           tone
                                                                                                                                                           vii*


In place of moving the triads into different positions eg. root, 3rd, 5th or 7th and playing around with the sound of the different arrangements of notes that way, I think that I will draw a contouring line in opposition to the melody line before I start writing in the notes.  I don't believe that I want to make a choral (4 voices)  Something more relaxed.