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why does a C7(b13/#9) use numbers higher than seven?

the notes (from a recent Adam Neely video) are, (I think, from watching the video "a few" times) from bottom to top C G | E bA bB #D ... Thanks

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    why isn't the first line of your question the title? I'll edit it. Dec 19, 2019 at 21:40

3 Answers 3

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A bit of terminology...

The numbers are intervals above the chord root.

Chords build by stacking up third are called tertian chords.

The complete tertian "stack" is: root, 3rd, 5th, 7th, 9th, 11th, 13th.

Intervals an octave or smaller are called simple and those larger are called compound.

From the tertian stack the 9th, 11th, and 13th are compound intervals.

Sometimes simple intervals and their compound octaves are considered as practically the same. Ex, a simple third and a compound tenth (third plus an octave) are sometimes considered practically the same.

In tertian harmony the compound intervals 9th, 11th, and 13th are NOT considered practically the same as their simple interval forms of 2nd, 4th, and 6th.

When the 9th, 11th, and 13th are added to seventh chords they are called chord extensions and the resulting chords are extended chords.

The important point is this: when compound intervals are given in chord symbols the complete tertian stack under the interval is considered to be theoretically present. So when a C13 is used the complete stack under it is considered present: C E G Bb D F A. However, in practice the root, 3rd, 7th, and the optional extensions are the actual tones played.

If the simple form of a compound extension were used for a chord, the implication is the extended tertian stack isn't present. So, a compound 13th could be simplified to a 6th. But if we use that for a chord name like C6 then the extended stack is not implied and the meaning is a C major triad with a sixth added, sometimes written more literally as Cadd6. The chord would contain only the tones C E G A very different from the set of tones for the C13 above!

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Because there's a convention that chords are built and named as a 'pile of thirds'.

There's a certain amount of justification for this. A triad, the basic chord in tonal harmony, is certainly a small pile of thirds. C, E and G. D, F and A. etc. Then there are a lot of 7th chords in functional harmony, particularly the minor 7th on top of a major triad that we call a 'dominant 7th'.

Beyond that, it's largely convention. We build up in thirds, C, C7, C9, C11 (but keep a bit quiet about that one) and C13. The stack of thirds looks pretty in a harmony textbook. C9 'includes' all the notes in C7, C13 'includes' all the notes in C9 (remember, keep quiet about C11 :-) ) But, in practice, C13 very often DOESN'T include the 9th, and it sounds quite different when it does and when it doesn't.

Yes, beyond the 7th chords, naming is largely conventional.

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  • that first sentence explains almost everything.....I never knew that. Thanks for the responses
    – LILarry
    Dec 20, 2019 at 1:57
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A couple of practical reasons, although the two existing answers cover well.

When writing out chords such as this, it's neat to keep using the next line up from root, and so on, meaning each note has its own line, moving upwards. That makes it easier to read, rather than trying to squash all the notes on lines and spaces next to each other. But it's a minimal reason.

Playing notes that are a tone or semitone apart creates discordant sounds. So spreading out the notes involved makes a chord sound better. In the quoted, there's C E G B♭ D♯ and A♭. Playing G and A♭, or E and D♯ next to each other rarely sounds as good as playing them nearly an octave apart.

The main reason, though, as already stated, is that convention says we stack notes of more complex chords in thirds, so here, root=C, 1st third = E, next =G (although that is often omitted), making next third =B♭, then there's the next third - officially a ♯9 =D♯, jumping over the 11 (which has many good reasons not to join the party) and on to the last third jump =A♭.

I'd expect it to be better called C7(♯9♭13).

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