A major eleventh chord is composed using a root/1st, major 3rd, perfect 5th, major 7th, major 9th and perfect 11th (or R/1-3-5-7-9-11) intervals played simultaneously. Generally written as CMA11, Cmaj11 or CΔ11, it is good practice to simply use an uppercase C with the uppercase letters MA followed by a super scripted 11 to represent it in writing (ie: CMA11).
Major, Minor & Dominant Eleventh Chords
Although it is uncommon to see a major eleventh or dominant eleventh chords in manuscript, they are none-the-less chords in their own right. Theoretically, the major third interval and the perfect eleventh (equivalent to a perfect fourth) clash and cause dissonance, which is why most voicings omit the third degree, this however changes the chord into a MA9sus4 or a 9sus4 depending on quality. Another common solution is to simply raise the eleventh degree turning the chord into a MA7(♯11) or 7(♯11). There are many musicians (myself included) who like the dissonance created between the third and eleventh (fourth) intervals when the chord is voiced correctly however, if you happen to come across a major eleventh or dominant eleventh chord(s) in manuscript or while gigging, it is more likely the composer wants the third omitted to form a MA9sus4 or a 9sus4.
Among the chord voicings below there a some that contain a major third and some that do not, the choice is yours as to which voicings you play but as a general rule: (1) when reading manuscript and/or gigging, play the voicings without the major third and (2) in any other situation (ie: practicing, composing) use either chord voicing to your liking but keep in mind when adding other instruments on top of the guitar, the dissonant major third/perfect eleventh (perfect fourth) combination can get mucky, be sure the other instruments stay away from the major third and perfect eleventh (perfect fourth). If you are composing and specifically want the musician to play a chord voicing with the major third, be sure to include a chord diagram showing the voicing and notation, otherwise he/she will likely play a MA9sus4 or a 9sus4. If you wish the voicing not to contain the major third interval, then please notate it as a MA9sus4 or a 9sus4.
Major eleventh chord profile
|Intervals||root/1st, major 3rd, perfect 5th, major 7th, major 9th, perfect 11th or R/1-3-5-7-9-11|
|Stability||Somewhat dissonant, resolved|
|Common names (examples in C)||CMA11, Cmaj11, CMAJ11, Cma11, CΔ11, CMA9sus4, CMA9sus|
|C Major eleventh chord voicing #2|