"Beat" as proposed just now seems wrong since it would hardly do for off-beat notes.
"Note column" would be the technical term employed in the music typesetter LilyPond, but I don't really know whether it has some origin in actual music terminology, and it obviously refers to the visual arrangement primarily.
"Musical moment" might be another choice but strictly speaking those form a continuum.
music.stackexchange.com/users/8773/User8773
stem?
Are you sure you want to have 2 rectangles for the double stems split since it's held across a beat?
I'd consider the pair to be one,
ummm, "note set".
I just call them "note set"s.
But that's just a term I came up with, not something standard.
music.stackexchange.com/users/2248/Stephen Hazel
A beat is probably the best term since you are more referring to a duration then the actual notes being used.
music.stackexchange.com/users/7222/Dom
Sound is as good as any.
That's till someone writes a rest.
Then I'm in trouble...
music.stackexchange.com/users/2808/Tim
Going with the MIDI theme, that some of the comments refer to, how about "event"?
music.stackexchange.com/users/9198/Bob Broadley
For formal, technical purposes (e.g. when discussing musical audiation and other aspects of musical cognition) the terms "acoustic event" or "notated event" or "vertical event" is pretty much standard terminology within psychology of music for referring broadly to any individual single tone or simultaneosly experienced combination of tones (i.e. an individual chord) within a passage or composition.
An acoustic event can also include a silence.
Really useful all-inclusive terms, (though not yet in musicians' common parlance)!
So, I'd use the term "notated event" (or the more generalized "vertical event") to fill in the blank in the OP's question.
music.stackexchange.com/users/13338/RichT
It depends on whether you're asking for MUSIC nomenclature, or music NOTATION nomenclature.
If it's music, I might say "sound" for each thingy.
If it's notation, I might say "event" for each thingy.
i.e. a note event, a score event, etc.
music.stackexchange.com/users/21900/dwoz
Take a passage like this:   Fill in the blank: Each of these boxes denote a  ______  Is there a single general term for these that's better than  note or chord ? Or maybe there's a term for "anything that has a duration" that also encompasses rests? It seems like enough of a fundamental concept that it should have a name.
Is there a general term for a single note or a chord?
music.stackexchange.com
<terminology>
music.stackexchange.com/questions/17282
music.stackexchange.com/users/16/Trillian
Beat, sound, event, acoustic event, notated event, note column and musical moment are all suggestions for describing a single note or chord. There are range of terms that may apply in this context, including "event", "beat", "sound" or "note column".
You may wish to use the term "event". The term "beat" may be applicable in this context. "Sound" may be a perfectly acceptable term in this case. Some terms that could be used include "note column" or "musical moment".