: Unaccented Appoggiatura I'm looking to categorize a non-chord note that occurs before a chord note. The non-chord note occurs on the offbeat and the chord note can occur offbeat or on beat, it doesn't really matter. I've

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From Kostka/Payne, Tonal Harmony...

...One way of classifying NCTs is according to the ways in which they are approached and left .
...Other terms used in the description of NCTs include accented/unaccented, diatonic/chromatic, ascending/descending, and upper/lower. These terms will be brought up in connection with the appropriate NCTs
...As a very general rule, appoggiaturas (also called incomplete neighbors) are accented, approached by ascending leap, and left by descending step.

Kostka/Payne's real world example:

You can find various NCT cheat sheets online. This one from Toby Rush shows an un-accented appoggiatura:

...I suppose that is an artificial and unusual example, but it is un-accented.

I found another one that seems like a more realistic harmonic case...

...but I don't know the original source.

It seems that contemporary theory at least provides the terminology for an un-accented appoggiatura, and you can unambiguously write such a thing distinct from other NCTs, but it is not the norm.

FWIW, sometimes appoggiatura refers to a kind of grace note which involves a separate discussion about how to interpret the grace note. That's different that a written appoggiatura like in the Kostka example.

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It might be simpler to refer to 'long' and 'short' appoggiaturas.

From Grove's Dictionary of Music, 1880 (emphasis mine):

With regard to its length, the appoggiatura is of two kinds, long and short; the long appoggiatura bears a fixed relation to the length of the principal note, ... but the short one is performed so quickly that the abbreviation of the note is scarcely perceptible. There is also a difference between the two kinds in the matter of accent; the long appoggiatura is always made stronger than the principal note, while in the case of the short one the accent falls on the principal note itself.

You can interpret this as saying that short appoggiaturas are 'unaccented' and long appoggiaturas are 'accented'. It then goes on to say that there has always been confusion and that some theorists (incorrectly) used the term acciaccatura to describe short (or 'unaccented') appoggiaturas, when acciaccatura is strictly a keyboard term.

So 'short' and 'long' seem to be less contentious than 'unaccented' and 'accented'.

For a discussion on the appoggiatura see this page from Rick Wilson's historical flutes (which is where the Grove picture was taken from).