Since the time of Johann Sebastian Bach when 12 tone equal temperament became
popular there has been an awareness amongst musicians that it is not perfect.
Indeed, piano tuners deliberately make the relationship between notes slightly
out of tune.
The word "schismata" comes from Greek meaning divisions. Many mathematicians have explored alternative numbers of divisions, finding that some are better tuned than the conventional system.
Instruments have been built with alternative numbers of notes. In 1872-3 a 53 note harmonium was built based on a design by English scientist Robert Bosanquet.