including modulo forms, primality testing, and float-to-fraction conversion.
Units were added at the eager insistence of Mass Sivilotti. Later,
-Ulrich MΓΌller at CERN and Przemek Klosowski at NIST provided invaluable
+Ulrich M@"{u}ller at CERN and Przemek Klosowski at NIST provided invaluable
expert assistance with the units table. As far as I can remember, the
idea of using algebraic formulas and variables to represent units dates
back to an ancient article in Byte magazine about muMath, an early
the octave numbered 0 was chosen to correspond to the lowest
audible frequency. Using this system, middle C (about 261.625 Hz)
corresponds to the note @slanted{C} in octave 4 and is denoted
-@slanted{C4}. Any frequency can be described by giving a note plus an
+@iftex
+@slanted{C@sub{4}}.
+@end iftex
+@ifnottex
+@slanted{C} with subscript @slanted{4}.
+@end ifnottex
+Any frequency can be described by giving a note plus an
offset in cents (where a cent is a ratio of frequencies so that a
semitone consists of 100 cents).
The midi note number system assigns numbers to notes so that
-@slanted{C-1} corresponds to the midi note number 0 and @slanted{G9}
+@iftex
+@slanted{C@sub{-1}} corresponds to the midi note number 0, and
+@slanted{G@sub{9}}
+@end iftex
+@ifnottex
+@slanted{C} with subscript @slanted{-1} corresponds to the midi note
+number 0, and @slanted{G} with subscript @slanted{9}
+@end ifnottex
corresponds to the midi note number 127. A midi controller can have
up to 128 keys and each midi note number from 0 to 127 corresponds to
a possible key.