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Does MusicXML support roman numerals and/or functions (such as T for tonic)? I know this can be done via a workaround, namely using lyrics and a special font. But I am talking about dedicated support.

Related: Software support for roman numerals and functions

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Yes for roman numerals. Maybe for functions (such as T for tonic). Look into the element Harmony in direction.mod.

The harmony elements are based on Humdrum's **harm
encoding, extended to support chord symbols in popular
music as well as functional harmony analysis in classical
music.
...

The harmony object may be used for analysis or for
chord symbols. 

A root is a pitch name like C, D, E, where a function
is an indication like I, II, III. Root is generally
used with pop chord symbols, function with classical
functional harmony. It is an either/or choice to avoid
data inconsistency. Function requires that the key be
specified in the encoding. 

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