X noteheads, also referred to as “cross” or “crossed” noteheads have a number of functions in modern music notation.
In percussion writing, they are the go-to for non-pitched metallophone instruments such as cymbals or tamtam or gong. For drum set, particularly in jazz or rock charts, cymbals are typically the most active part, and X noteheads help these stand out from the other parts on a 5 line staff.
In vocal music, x noteheads are often used tor spoken text, or for unvoiced sounds / vocal effects. In both instrumental and vocal writing, they can be used to indicate notes of indefinite pitch. And in jazz charts, X noteheads can be used to indicate “ghost” notes in a melodic line.
(for drum set writing, there is an actual “ghost” notehead, which is a regular notehead in parenthesis.)
Cross (x) noteheads can also be used as a special effect to indicate hand / finger damping of instruments such as guitar, or tuned percussion such as vibraphone.
The shape of the “cross” for smaller durations closely resembles a lower case “x”, with two overlapping diagonal lines:
For longer durations such as half (minim) or whole (semibreve) notes, there are two conventions. Either is acceptable, but it is important not to mix these symbols, particularly within the same staff or part, as they mean the same thing.
The first is a circle cross – the “x” appears inside a circle:
An equally acceptable alternative is to use diamond noteheads for the “white” notes:
(While you may have seen X noteheads for rim shots in percussion writing, the symbol recommended by the Percussive Arts Society (PAS) is preferable. This is a notehead with a diagonal line through it. )
A more ornate, bold version of the x and circle x noteheads is also in common use:
This is an effective presentation for non-pitched percussion, however, you may want to opt for a less ornate option for pitched instrument and vocal staves, due to the similarity to the double sharp symbol.
It’s worth noting that noteheads can, and should be, a part of a comprehensive and evolving music notation language. The half note and whole note x noteheads found in the Bravura font are a good example.
All that to say, there is nothing wrong with new variations, per se. The main thing to keep in mind is that the goal of any music notation should be readability, and particularly as it pertains to the symbols themselves; clarity with a healthy respect for convention. Use your best judgement about what looks right to you, and how easily whatever symbols you pick will be read and interpreted.