In 11th chords we're adding an 11th (which is a 4th above the octave) to a given chord:
Cmin7: 1 b3 5 b7 Cmin11: 1 b3 5 b7 11
Cmin7b5: 1 b3 b5 b7 Cmin7b5/11: 1 b3 b5 b7 11
I've learned that I should alter the 11th if there is a IIIma interval in the chord, because the minnor 9th interval between the 3th and the 11th:
C7: 1 3 5 b7 C11: 1 3 5 b7 #11
Cmaj7: 1 3 5 7 Cmaj11: 1 3 5 7 #11
But in the web, everywhere I look, a C11 and Cmaj11 have a natural 11th interval.
My question is, what should I play if I come across a C11 chord? Should I alter the 11th interval, or should I do so only if specified explicitly by (C(#11), C13(#11))?