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If I play the chord: GBDA, then this is considered a Gadd9. But if I play the 3rd above the 5th (GDB), it is not called a 10th.

Why don't we refer to all notes by 1-7, and is there a system to picking higher numbers (11) vs lower ones (4)?

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up vote 6 down vote accepted

The distinction is between interval distances (2nd -> ∞) and chord tones (root, 3rd, 5th, 7th, 9th, 11th, 13th).

When you play Gadd9, you are adding the chord tone that is a 9th above the root. If we just played a G9 chord, the dominant 7th would actually be implied (G-B-D-F-A).

Playing the interval of a 10th above the root (like G-D-B) doesn't change the chord. All that does is displace the chord tone (in this case, the 3rd) up one octave, so it's still called a G major triad.

So, a note would be described as a fourth if we were talking about interval distances, and an 11th if it was a chord tone (typically preceded by the root, 3rd, 5th, 7th, and 9th).

The exceptions are sus chords and 6 chords. A sus chord would typically have a 2nd or 4th above the root suspended in the middle of a triad voicing, often substituting for the third (like C-D-G or C-F-G). A 6 chord substitutes the 5th of the chord with a 6th, but maintains the same function of the original chord.

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"A sus chord would typically have a 2nd or 4th suspended in the middle of a triad voicing, often substituting for the root (like C-D-G or C-F-G)." I assume you mean "often substituting for the third" ? –  user393 Aug 17 '11 at 16:24
    
@user393 Correct; my typo. Edited. –  NReilingh Aug 17 '11 at 18:52
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Also, isn't what you referred to as a 6 chord (1,3,6 or CEA) just an inverted minor (ACE)? I guess it would sound more major than an Am (focus on C) but more minor than a C. (I can post this as a separate question, if that would be better) –  user393 Aug 17 '11 at 19:06
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That particular voicing would be identical in sound, but not in function. You're still using the chord as though it is rooted in C, and the fifth isn't necessarily missing. If you want to know more about 6 chords, you should post a different question. –  NReilingh Aug 17 '11 at 21:01
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Don't agree with NReilingh's definition of a 6 chord. Generally a 6 chord is spelled 1, 3, 5, 6.Thus GBDE is G6.The 11 chord is usually made from 1, 3, 5, b7,11. So using a '4' and a b7 makes 11.Just like a '2' and a b7 makes a 9. G11 will be GBDFand C - a sort of dominant 7 sus 4.

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I agree on your definition of a 6 chord (includes the 5th). I do not agree with an 11 chord being a 7 sus 4. A sus chord may include the third, but then usually at an octave or more above the 4th. –  Gauthier Sep 4 '12 at 14:23
    
You're right - an 11 chord should contain 1,3,5,b7 and 4.However, "a sus chord may include the third" can't be right - sus means the 3rd has been substituted, usually by 2nd or 4th.Maybe 11th is called dominant7 add 4 ? –  Tim Oct 4 '12 at 17:24
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11th is called 11th, no need to call it dominant7 add4. Sus stands for suspended rather than substituted (gives that feeling of being suspended before landing on the third). I reacted as you did when I first heard of it, but my source is trustworthy. Mark Levine in his well-known "The jazz piano book": "A persistent myth about sus chords is that the fourth takes the place of the third. Jazz pianists, however, often voice the third with a sus chord, as you can see in the examples in figure 4-5. Note that in each example the third is voiced above the fourth." –  Gauthier Oct 6 '12 at 12:15
    
He also names in "the jazz theory book" that 3rd above 4th in sus chords appeared in the 60's, and gives the start of "Someday my prince will come" (Miles, 1961) as an example. –  Gauthier Oct 6 '12 at 12:16
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These numbers come from the figured bass system of composition and performance, wherein roman numeral symbols (I-ii6-V7-I) are written under a bass line indicating to the performer what inversions to use in the chords. The roman numerals refer to the chords built on each of the diatonic scale degrees (in C major I= C-E-G, ii= D-F-A, iii= E-G-B).

When you see something that says Gadd9 its asking you to play the 9th scale degree above the root of the chord. If G is the root, A would be the 9th diatonic note above it. This indicates that the A is supposed to be played above the 5th (D). If you played A in the lower octave the chord would be a G 2nd chord (G-A-B-D).

Essentially the number is there to let you know what octave to play the dissonant note (7th, 9th, 11th). In a G major chord, 4 would most likely be referring to playing a C above the B but below the D, while 11 would suggest playing C above the D.

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