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I was learning about extension chords where I stumbled upon a question: if we play Cmajor11(sharp 13), wouldn't that have the note B flat which is supposed to be there in dominant chord? Shouldn't that make the Cmajor11 into a Cdominant11 or something like that?

I tried experimenting around and even thought that it could be both, but then I also had the question, if sharp 13 in a major 7 chord can be considered an avoid note or not.

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    @Aaron’ answer sums up things clearly, +1. I would like to offer a few comments. First, in several decades of being a musician I have never encountered a #13 chord so this chord is more theoretical than practical. Secondly, 11th chords with a major 3rd are also extremely rare because for example, in a C chord the E and F in the chord create a very dissonant b9 interval. It is much more common to use a sus4, replacing the 3rd with the 4th. Major chords, either maj7 or dominant 7 much more commonly will use a #11 instead of an 11 for more of a Lydian sound. – John Belzaguy Jan 19 at 7:29
  • @JohnBelzaguy - interesting (maybe) that a dom 13 chord already contains that A# (Bb) note, and often sounds better without the 11th - for the reasons you quote. Like you, never had the misfortune to meet a maj 11#13 chord in real life. But just by spelling, they're not the same. – Tim Jan 19 at 8:54
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A complete CMaj11(#13) chord is spelled C E G B D F A#, and a C11 (that is, Cdominant11) is spelled C E G Bb D F.

So these are not equivalent, because one contains B natural and the other does not.

However, it's true that both chords contain the enharmonically equivalent (i.e., they represent the same pitch) A# and Bb. The difference in spelling relates to technical/theoretical differences in how those pitches are used in context.

In jazz/pop contexts, chord spelling is often more a matter of convenience as ease of reading/understanding, but the underlying theory suggests that a #13 (A#) should move upwards; whereas a b7 (Bb) should move downwards.

As to whether the #13 would be an avoid note against a major7 chord -- more likely than not. It would be highly dissonant against the major seventh (A# against B), but could be quite useful in an appropriate musical context.

@JohnBelzaguy's comment on the OP is recommended reading. It explains how these chords are used (or not used, as the case may be) in practice.

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