Use of odd or even numbers to name extensions

[alez]

Hi guys,

I think you are supposed to use odd or even to correctly reflect the function of the note in question, but in practice I'm confused about it, probably because I don't know enough theory to tell those functions.

Could you please explain why A is called major 6th in the context of the chord C, but major 13th in the context of C7 (say V in the key of F or Fm)?

Also, in the context of C7, I think I've seen the note F# be called the raised 4th, but also the raised 11.

As for the note D, I think I've seen it as the major 9th in the context of pretty much every C chord, with the exception of Csus2.

Is there any easy rule that would help me name those notes correctly?

Thanks.

[JonR]

Originally Posted by alez

Hi guys,

I think you are supposed to use odd or even to correctly reflect the function of the note in question, but in practice I'm confused about it, probably because I don't know enough theory to tell those functions.

Could you please explain why A is called major 6th in the context of the chord C, but major 13th in the context of C7 (say V in the key of F or Fm)?

"13" implies the inclusion of the 7th, and reflects the practice of building chords in 3rds: ie, alternate steps, or "tertian" harmony: 1-3-5-7-9-11-13.
"13" just indicates the addition of the last 3rd in the stack (but not necessarily the 9 and 11 too).

"6" implies no 7th, and can be voiced anywhere - ie right above the 5th, or the octave higher. (But not generally below the root, which would turn C6 into Am7 - although if a bass is playing C you'd still have a C6 chord.)

Originally Posted by alez

Also, in the context of C7, I think I've seen the note F# be called the raised 4th, but also the raised 11.

Yes, convention varies there.
Most often it's labelled "#11", implying the next extension above 9, and including 7th, although the symbol will probably include the figure "7" too.

But sometimes you'll see it labelled "C7#4", presumably by someone who thinks (reasonably) it doesn't need labelling as "11" because the number "7" is shown. ("11" on its own meaning "7 + 4", just as "13" means "7 + 6".)

Originally Posted by alez

As for the note D, I think I've seen it as the major 9th in the context of pretty much every C chord, with the exception of Csus2.

Yes.

"C9" and "Cmaj9" both imply the inclusion of the 7th (b7 or maj7 respectively), following the above stacked-3rds ("tertian") rule.
"Cadd9" is a variation meaning "omit the 7th" (C-E-G-D).

"Csus2", meanwhile, derives from the idea that "sus4" means "replace the 3rd with the 4th". So if you replace the 3rd with the 2nd instead, then you'd call it "sus2". Csus2 wouldn't have to be voiced C-D-G, it could be C-G-D: like Cadd9 without the E.

In jazz (as opposed to rock), sus2 chords are rare, because 3rds are important in jazz; and while adding a 4th makes a dissonant interval with the 3rd (so the latter is omitted), the 2nd doesn't - not even with a minor 3rd. Or rather, the half-step dissonance between 2-m3 is (apparently) less objectionable than the one between M3-4. So a chord can have a 2nd added without needing to lose the 3rd.
A "Csus2" voicing therefore (C-D-G) is likely to be regarded as an inversion of Gsus4.

[alez]

I don't think the matter could possibly be explained more clearly than that. Thanks very much, Jon.

[engelbach]

I agree. Well done, Jon.