I'm trying to find the correct notation/name for a chord, where the third is omitted and the sixth is added.
Would "Eb5add6" be a valid option?
Context: The context of this chord is a 2-chord-song, where the other chord is Bbsus4.
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It could be called Cm7(no5), depending on voicing and context. It's not unusual to leave out the 5 from a chord, as it's actually sounding in a harmonic of the root anyway. It's omitted in a lot of jazz playing.
If it's necessary to call it Eb something, then Eb6(no 3) is the best I can come up with!
Context is everything when it comes to chord labeling. We can't say exactly what this chord is without knowing where it came from and where it's going.
With that said, it's less common for a third to be omitted in a chord than it is for the fifth to be omitted. Thus, we can think of this chord as having an omitted fifth, resulting in a
Cm7 in first inversion. It's just missing the
G from its
C Eb G Bb collection.
Perhaps Eb6sus might be a less awkward way of expressing the chord (since its functionally same as @Tim's answer above).
(edit: as asker @Seb3736 mentioned, http://www.scales-chords.com/guitar-chord-chart/Eb6sus is the source)