On this page we look at chord formulas and chord compositions and their inversions, using the notes of the (chromatic) scale of the key.
Harmony singing is all about singing chords. Even though it's possible to sing perfect harmony without knowing anything about chords, a bit of basic understanding of chords doesn't hurt. In fact, chords are quite fascinating...
Basic chords relevant to harmony singing
Now, below are the formulas for basic chords. A chord formula is simply the breakdown of the notes relative to 1 that constitute the chord. So, the first formula on the list below tells us that every major chord or triad consists of the first, third, and fifth note of the major scale of its key, equalling to do-mi-so.
| Chord name | Formula |  |
| major chord | 1-3-5 | |
| 6th chord | 1-3-5-6 | |
| 7th chord | 1-3-5-7b | |
| major7th chord | 1-3-5-7 | |
| minor chord | 1-3b-5 | |
| minor6th chord | 1-3b-5-6 | |
| minor7th chord | 1-3b-5-7b | |
| minor-major7th chord | 1-3b-5-7 | |
| diminished chord | 1-3b-5b | |
| diminished7th chord | 1-3b-5b-6 | |
| half-diminished7th chord | 1-3b-5b-7b | |
| augmented chord | 1-3-5# |
b (flat) and # (sharp) signs are there to tell us that the respective scale note has been flattened/decreased in pitch or sharpened/increased in pitch by a half step.
Getting chords out of the scale
Let us now go through the scale to see how chords are composed of notes of the key (1) scale. So, in contrast to the formulas above, we will not set the first chord note to 1, but instead use each scale note, one by one, as the basis for a chord.First, here is the most important group of chords. These are the ones that are entirely made up of notes of the key (1) major scale. The first column lists the chord names, then the first, second, and third inversion. For better reading, primes and sub-primes have been omitted.
| Chord name | 1st inv. | 2nd inv. | 3rd inv. |  |
| 1major | 1-3-5 | 3-5-1 | 5-1-3 | |
| 2minor | 2-4-6 | 4-6-2 | 6-2-4 | |
| 3minor | 3-5-7 | 5-7-3 | 7-3-5 | |
| 4major | 4-6-1 | 6-1-4 | 1-4-6 | |
| 5major | 5-7-2 | 7-2-5 | 2-5-7 | |
| 6minor | 6-1-3 | 1-3-6 | 3-6-1 | |
| 7half-dim7th | 7-2-4-6 | 2-4-6-7 | 4-6-7-2 |
Have you noticed that the first inversion of each of these chords consists of notes found by skipping every other note of the scale? Example: 2minor = 2-(3)-4-(5)-6
The chords below contain flat (b) or sharp (#) scale notes.
| Chord name | 1st inv. | 2nd inv. | 3rd inv. |  |
| 1minor | 1-3b-5 | 3b-5-1 | 5-1-3b | |
| 2major | 2-5b-6 | 5b-6-2 | 6-2-5b | |
| 3major | 3-5#-7 | 5#-7-3 | 7-3-5# | |
| 4minor | 4-5#-1 | 5#-1-4 | 1-4-5# | |
| 5minor | 5-7b-2 | 7b-2-5 | 2-5-7b | |
| 6major | 6-2b-3 | 2b-3-6 | 3-6-2b | |
| 7bmajor | 7b-2-4 | 2-4-7b | 4-7b-2 | |
| 7bminor | 7b-2b-4 | 2b-4-7b | 4-7b-2b | |