And a few other ideas to file away for the practical work:
The STIX folks have been keeping up with developments to Unicode, and are maintaining tables of recommended Type 1 character names. Look into that.
Structured documents can have a tough time dealing with the level of granularity that might be required for complex font changes, unlike TeX documents that seem to thrive on it. What can be done to anticipate fitting and usage problems in when it's not easy to change back and forth between fonts? For instance, can OpenType contextual alternates be used to insert terms like "sine" and "cosine" that wouldn't be set italic like other characters in math?
Also, spacing would have to be very different for characters that get used for equations, so a different font that spaces the glyphs differently may be needed: probably not monospaced, but certainly set wider, and with no italics that kern or overset their bounding boxes.
Should the type be optimized for screen display, publication, or some happy medium?
Italics should be fairly upright, but definitely italic in style rather than staying too close in form to the roman. They will need to be very distinct from one another.
Not too much contrast, or any details that are too delicate. However, not too blocky and informal, either.
The equation might may also benefit from having short ascenders and descenders to minimize trouble with spacing of overbars, stacked combining symbols, and divisions.
In addition to standard text and numerical glyphs, a good family for dealing with math would need a pretty robust set of agate glyphs for superiors, inferiors, dense tables, etc.
Mitja's "Reflection on Practice" essay talks about some good qualities that would be relevant to what I’d like to do, especially the notion of case-sensitive punctuation and operators.
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