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In my training, I've always learned (and I still teach) that 11th chords don't have the chordal third; the dissonance between the 3rd and 11th (an octave-displaced fourth) seems to weaken the chord, and composers of the late-19th and early-20th centuries didn't typically use 11th chords with 3rds.

Yet the answers to What makes a chord a sus chord? paint a different picture. To quote from three of the current four answers:

An 11th chord, for example, theoretically comprises 1,3,5,7,9 and 11.

an 11 could (should?) contain both the third and the fourth

An 11th or 13th or 9th chord by definition will contain the third

I spend most of my time in the Classical realm, where these chords typically do not have thirds. Is this just a difference of style/genre? Is jazz different from rock, etc.?

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    In the classical realm, what is the difference between an 11th and a 4th? I wrote what I wrote because I never encountered the concept of an 11th chord in my classical training. Why call it an 11th if you can call it a 4th? – phoog Feb 15 at 18:46
  • "I spend most of my time in the Classical realm, where these chords typically do not have thirds." Are you referring to 6/4 chords and harmonic delays? – musicamante Feb 15 at 18:52
  • @phoog In my experience, it's one of register; an eleventh is very clearly over an octave above the bass, whereas a fourth can be within that octave or beyond it. – Richard Feb 15 at 19:36
  • @musicamante No, I'm mainly thinking of 11th chords. There are examples with thirds, but most of them, in my experience, don't have thirds. Perhaps it's an outgrowth of training with four-part voice leading, where we have to omit thirds just to get all the chord tones in? – Richard Feb 15 at 19:37
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    The distinction that Aldwell and Schachter make -- in a classical context -- is that 4ths and 6ths are suspensions that delay the arrival of the 3rd or 5th; whereas 11ths and 13ths replace the 3rd and 5th altogether. (See "Harmony and Voice Leading", 2nd ed, 449–453.) Also, it should probably be clarified that it's major thirds where there's a class with the 11th. In minor seventh chords, for example, the 4th/11th is a common part of quartal jazz voicings. – Aaron Mar 22 at 2:29
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From a jazz perspective, whenever a chord symbol contains an upper extension like 9, 11, or 13, the 3rd and 7th are implied. Moreover, in jazz, the chord C7 has many well-known voicings, including Bb-D-E-A and Bb-D-E-G. So if a lead sheet goes to the trouble of writing C13 when C7 would suffice, then this usually implies that the 13th carries special significance: the 13th should be included in the voicing or should be used for voice leading--or maybe the 13th appears in the melody. But C13 still contains an E and Bb, and it can also contain the 9th.

So a voicing like C11 implies use of E, Bb, and F--though not necessarily in that order, of course. But jazz songs don't often contain chords like C11 or CMaj11, because the E and F conflict, just as you describe. And if a pianist does see C11 on a lead sheet, then her eyebrows will raise and she will try to figure out what's intended. Perhaps the melody in that measure contains both an F and E, and C11 is supposed to convey this, and the pianist should follow the melody when voicing the chord. Or perhaps she is actually supposed to play a bona fide C11 voicing like Bb-E-F-A, which can work really nicely. (That particular voicing creates a cool opportunity to emphasize either the E or the F, which can change the sound.) Another good voicing for C11 is F-Bb-D-E.

In jazz, C7sus implies a range of voicings--as does virtually every chord symbol. C7sus could be played as F-A-Bb-D, G-Bb-D-F, Bb-C-D-F-A, D-F-Bb-C, C-F-G, C-D-G, Bb-D-F, etc. The main idea behind C7sus is that it does not contain the 3rd. One might wonder if this is sufficient to qualify as a "sustained" chord. But even if C7sus never resolves to C7 (with the 3rd), the ear still wants/expects to hear that resolution. In jazz, that implied/desired resolution--which is achieved by omitting the 3rd--is sufficient to qualify as a 'sus' chord.

Overall, C11 implies that the third is included, whereas C7sus implies that the third is omitted. However--and this might be where it gets weird--it is not required for every single C11 voicing to include the 3rd (or even the 11th for that matter). In a single jazz song, the band might cycle through the form 10-20 times. We cannot possibly constrain each voicing to the same 4 or 5 notes on every pass through the form, because the music will quickly begin to sound repetitive and stale. Improvised melodies often develop harmonically, starting with melodic lines that emphasize/end on the 1st, 3rd, or 5th and evolving toward melodic lines that more heavily emphasize alterations/upper extensions. The chordal instruments often do something similar. That sort of flexibility in the voicing is often essential to jazz--especially post-swing era jazz / bebop and beyond.

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My school harmony textbook said 'The 3rd is always omitted'. So G11 was Dm7/G. Which may go some way towards explaining (if not excusing) the modern tendency to write F/G (which is perfectly clear and unambiguous) as G11 (which isn't).

'Jazz theory' allows the 3rd and 11th to co-exist, but admits 'the 11th is generally sharpened'.

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