Suppose I have a C major scale in front of me, and I label them by scale degree.

C D E F G A B C D  E  F  G  A  B
1 2 3 4 5 6 7 8 9 10 11 12 13 14

If my understanding is correct, then

  • C Major is 1, 3, 5 (C, E, G)
  • C Major 7th is 1, 3, 5, 7 (C, E, G, B)
  • C Major 9th is 1, 3, 5, 7, 9 (C, E, G, B, D)
  • C Major 11th is 1, 3, 5, 7, 9, 11 (C, E, G, B, D, F)
  • C Major 13th is 1, 3, 5, 7, 9, 11, 13 (C, E, G, B, D, F, A)

I have all seven notes of the Major scale in 1 chord. From my understanding, the notion of calling them 9, 11, 13, instead of 1, 3, 5, 7, 2, 4, 6, is telling users that those notes should be higher in pitch than the 7th note.

But what's the reason behind this? And if I had a piano, what's the difference between pressing 7 white keys on the piano vs pressing a Major 13th chord? Thank you for reading.

  • 2
    The white keys of the piano make a G 13 chord, as long as you have G as the lowest note. – piiperi Reinstate Monica Sep 29 '20 at 9:15
  • @piiperiReinstateMonica - it does - technically. Would you play it like that? I certainly wouldn't - not even in jazz... – Tim Sep 30 '20 at 6:43
  • @Tim I was trying to point out to the OP that it's G13, not C13. – piiperi Reinstate Monica Sep 30 '20 at 9:00
  • @piiperiReinstateMonica - just found out there is a major 13th chord, as OP states. But I understand what you say - all those notes constitute G dominant 13 - generally written G13 - whilst at the same time they constitute C major 13 . Can't say I've ever knowingly played - or had to play - a major 13th chord: possibly written Cmaj13? – Tim Sep 30 '20 at 9:12
  • Never heard of a "maj13" before, but I guess it could be systematically called that, just like "maj9" has a major seventh in it. – piiperi Reinstate Monica Sep 30 '20 at 9:28

They're kind of the same thing. (But only kind of...)

The Wikipedia entry for Extended chord includes an example of exactly what you're asking: a 13-chord "collapsed" into a tone cluster (though by convention, the chordal 4th/11th is omitted).

Interpretation of 2-9 / 4-11 / 6-13 is open to debate

There have been a variety of interpretations over time of how 2 vs 9, 4 vs 11, and 6 vs 13 have been viewed, and modern practice primarily depends on which school of thought you adhere to.

One way of considering things is that 9/11/13 are considered consonant members of a seventh chord; whereas, 2/4/6 are considered dissonances that should be resolved. Put another way, 2/4/6 arise from suspensions; 9/11/13 can be used at any time without preparation.

Another view is that they're equivalent, and you name the chord according to convenience or ease of reading/interpreting.

And yet another view is that the chord name indicates voicing: 2/4/6 mean those notes should be voiced below the chordal seventh; 9/11/13 mean those notes should be voiced above the chordal seventh.

So a 13-chord differs from a heptatonic scale how?

Ultimately, the difference is that scales are interpreted by step -- i.e., sequences of seconds; chords (of the type discussed here) are interpreted as stacks of thirds.

  • oh wow thank you for this answer, it addresses most of my confusions directly. It is surprising to me that the interpretations of 2-9/4-11/5-13 are still up to debate! – mofury Sep 29 '20 at 20:42

Scale is a bit abstract concept. You can play a melody based on a scale, or you can build a chord from the scale steps. But if we say "play a scale" we really mean to "play a melody consisting of consecutive notes of a scale".

If you play several notes together it's a chord. What's the difference between C-D-E-F-G-A-B and C-E-G-B-D-F-A (all in increasing order)? Well, they sound differently, because it's a different voicing.

Speaking of nomenclature, "C13" means "major chord with flat 7 and 13", C-E-G-Bb-A. In most cases you could add 9, but 11 is considered an "avoid note" by default.

A proper chord symbol would be something like "Cmaj9 13 add11", though it's going beyond scope of functional harmony. If you want the musician to play a cluster of 7 consecutive diatonic notes, writing it in music notation would be more appropriate. Chord symbols give place for interpretation, adding or dropping notes, choosing voicing, instrumentation, while you're apparently looking for a very specific sound.

Perhaps the concept of modality, which prioritizes sound of a scale over functional harmony, would be interesting to you.

  • To be fair, in some contexts a "sharp 11th" is considered more suitable than the "natural 11th". I suspect this is in part due to equal temperament issues (for piano), but I do not have the numbers at hand. – paul garrett Sep 29 '20 at 19:31
  • @paulgarrett yeah, #11 is used to avoid natural 11. Natural 11 sounds "bad" not really due to temperament issues (in fact it is a consonant), but because it undermines the harmonic function of the chord. – user1079505 Sep 29 '20 at 19:49

These chord-names evolved to describe what musicians were actually playing. Your major 11th and major 13th chords would rarely if ever have been played: they don't sound good. Gm7 over C is common and it was named G11 as a kind of shorthand description. But the third (E) is left out. It does of course contain the 11th (F).

You said, From my understanding, the notion of calling them 9, 11, 13, instead of 1, 3, 5, 7, 2, 4, 6, is telling users that those notes should be higher in pitch than the 7th note.

That is probably a good way to think of them when you're learning, but the order is usually changed. For example, on a piano G13 is often voiced (from the bottom up): G F B E (G). The 7th is where you might expect it, but the 3rd (B) is above it. And there's no 5th (D), though there could easily be, or 9th (A), though there could possibly be, or 11th (C), and there never is!

It's what sounds good. Pressing seven consecutive keys on the piano is unusual in jazz or pop, though many composers have used it. Henry Cowell springs to mind.]

  • Indeed, ... and, I feel compelled to add, as in another comment of mine for this, that (outside of suspensions...) a sharp 11th often seems fine, both for major 7th and "minor 7th" (=dominant...) chords. – paul garrett Sep 29 '20 at 19:35

Several answers already point out the importance of voicing and common omissions with 13th chords so I won't repeat those points.

...From my understanding, the notion of calling them 9, 11, 13, instead of 1, 3, 5, 7, 2, 4, 6, is telling users that those notes should be higher in pitch than the 7th note.

A few additional things you might want to know about, mostly terminology:

The second, fourth, and sixth being an octave or less in size are called simple intervals while the ninth, eleventh, and thirteenth are like the simple intervals plus an octave and are called compound intervals.

Listing compound intervals like a thirteenth does signal the chord is assumed to also have a seventh, and those chord with intervals above the seventh are called extended chords, but the extensions aren't necessarily above the seventh. However, the extensions will normally be above the root. Also, regarding inversions the extension are not normally in the bass, for practical purposes third inversion with the seventh in the bass is the limit.

But what's the reason behind this?

To make the root clear.

Think about it. If all seven tones are played simultaneously and six inversions and all voicings were used, there wouldn't be a way to determine the root! Actual practice is more circumscribed. It's more like four part harmony with seventh chords with extensions added in the upper voices.


What's the difference between a 13th chord and a full heptatonic scale?

You mean "a theoretical 13th chord". In practice, when someone writes a chord symbol like G13, they don't mean a full theoretical 13th chord, they mean "9 add13". A commonly used guitar chord fingering for G13 is 3x3455, which doesn't have an 11th anywhere. Or even 3x345x, which doesn't even have the 9th either, but has the 13th as the topmost note, which is often wanted.

what's the difference between pressing 7 white keys on the piano vs pressing a Major 13th chord

Assuming you mean "a theoretical G 13 chord", then pressing down 7 consecutive white keys G A B C D E F is a very dense voicing for it. But if you ask someone to play a G13 chord, they most probably won't play it like that, they'll play a more open voicing and omit the 11th, maybe even the 9th.


Simply expained: the scale is an ascending and descending set of notes - the diatonic scale meaning each neighbouring note is either one semitone of one tone away from each other. And - eacch played as a separate sound. Chords are played with all the notes sounding simultaneously. So even that negates the two being the same.

A 13th chord - which actually rarely uses all the seven notes, is, by definition, made up from notes which are rarely less than a third apart. Usually, the fifth and eleventh are omitted - I generally play a 13th chord with R, 3, 7 and 6. But I doubt if anyone would agree that playing seven consecutive keys on a piano constitutes a 13th chord. On guitar that would be impossible anyway.

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