Harmony Notes: Thirds and Sixths
The best harmony notes are 3rds and 6ths.
The most common harmonic structure, by far, is tertian harmony, which is a stack of 3rds. Therefore it would be expected that a note a 3rd below the melody or a 3rd above the melody will often be a good choice for a harmony note. A note a 3rd above the melody note is usually lowered an octave to keep the melody note the highest note. It then becomes a 6th below.
Using scale notes there are only four other possible harmony notes: 2nds, 4ths, 5ths, and 7ths. Although 2nds and 7ths are frequently used as harmony notes in certain situations, they are probably never used as consecutive harmony intervals. 5ths are very similar in tone to octaves and don’t add much texture or colour. Also consecutive 5ths are frowned upon in classical harmony.
We are left with 4ths. Quartal harmony uses a stack of 4ths. It is used in jazz and musicians who promote quartal harmony will claim that they produce a unique and modern sound. The 3,6,9 chord sometimes used as a final chord in popular music is an example of a stack of 4ths.
Using a 6th or a 3rd as a harmony note creates a pleasing and satisfying sound and one will always sound right. If one doesn’t work the other one will.