Music theory teaches us that a chord is made by stacking thirds. So far we have spoken of chords as complete units, however, there’s often times when you’ll need to omit notes from a chord for various reasons including voice leading, aesthetics, and not having enough voices to play every note.
The root and third are the most important notes in a major or minor triad.
That’s because the root determines where the chord belongs in the scale and the third determines its quality.
The root third and fifth are equally important in diminished and augmented triads.
Like major and minor triads, the root determines the chord’s placement in the scale and the third helps to determine its quality. Unlike those triads, in diminished and augmented triads the 5th also helps to determine the quality.
The root, third, seventh and highest/altered extension(s) are most important in 7th-13th chords. The other extensions and altered fifth are of secondary importance.
This may seem odd if you’re unfamiliar with jazz harmony so let’s take some time to break this down. If you keep stacking thirds past the fifth you get the seventh, ninth, eleventh, and thirteenth. The “fifteenth” is the same as the root two octaves higher. Jazz theory teaches us that the root, third, seventh, highest extension, and altered extensions are requited to name a chord. In other words, a chord with a C, E, Bb, and A would be identified as a C13 since A is the 13th of C. Likewise, a chord with a C, E, Bb, D, and A would still be called a C13 chord; however, if the D was lowered a half step to a Db then it would be labeled C13(b9) since the 9th has been altered.