How do you properly define diminished 9th, 11th and 13th chords?

Question

I understand that a diminished 7th chord is defined by the intervals 1-b3-b5-bb7 and a half-diminished 7th chord is 1-b3-b5-b7, but how do you determine what intervals diminished (and half-diminished) 9th, 11th, and 13th chords have?

Answer 1

Hi! Good question...

1. According to classical and traditional theory, you should incluye all 4 notes of the tetrad (4-note chord) before adding tensions (9, 11, #11, b13, 13).

For example, if you need to use the 9 tension in a C major chord, you should include:

All 4 notes of the tetrad: C (Root), E (Major 3rd), G (Perfect Fifth) and B (Major Seventh)... then D (9th)

... and the chord would be spelled as Cmaj7(9)

But...

1. In contemporary harmony/songwriting, you can add tensions to the TRIADS (3-note chords) without adding the 7th.

For example, you can have a chord consisting in just C (Root), E (Major 3rd), G (Perfect Fifth) ... then D (9th)... NO SEVENTH NEEDED!

... and the chord would be spelled as C(add9)

Have you heard The Police? Most of their chords are TRIADS with tension notes (no sevenths).

I hope this is useful for you!

Have a great week

Carlos

Answer 2

You are correct in that a diminished chord is 1-b3-b5-bb7 and a half-diminished (or min7b5) chord is 1-b3-b5-b7. Added notes, such as a 9th, 11th, 13th, etc., are called "tensions". Tensions are added on top of the other notes in the chord, after the bb7 or b7 in this case. So a dim9 chord would just be 1-b3-b5-bb7-9. A dim11 chord would be 1-b3-b5-bb7-11. A dim13 chord would be 1-b2-b5-bb7-13.

Multiple tensions can also be added. So you could also have a dim9/11/13 which would be:

1-b3-b5-bb7-9-11-13.

Hope that helps! Let me know if you have any other questions.