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As the document of Math Time Profession 2 said,

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So the look of sub-script and super-script text in mtpro2, has a wider(fatter) appearance. How did mtpro2 achieve this? Did they literally design another font for scripts? Or did they use some package that simply scale the alphabets and numbers in sub-script and super-script? I checked the source file of mtpro2.sty, but it is too complicated that I can't figure out.

Sometimes I want to write a special character in script, suck like $a^{\somespecialchar}$, but it is reasonalbe that since mtpro2 don't have this character, so this wouldn't suit the other script style.

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    as in computer modern, it is a separate font. Commented Feb 28, 2017 at 9:46

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Like the standard Computer Modern fonts, mathtime does not simply scale a single font but has fonts designed for a range of sizes.

Perhaps the easiest place to see this is in the latex fd file which specifies what font file to use for each latex font specification.

CTAN/fonts/mtp2lite/texmf/tex/latex/mtpro2/umt2ms.fd

has lines such as

\DeclareFontShape{U}{mt2ms}{m}{n}{<-7>mt2mcf<7-9>mt2mcs<9->mt2mct}{}%

which says that in the mt2ms family medium weight normal shape, that at sizes up to 7pt, the font mt2mcf should be used, that between 7 and 9pt use the font mt2mcs and above 9pt use mt2mct.

Typically when comparing a font designed for 10pt scaled down to 5pt with a font designed for 5pt, the scaled font will have thinner strokes and thinner overall width as the designed 5pt font can be made to have the smaller height without making the strokes thinner by the same amount.

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