Divisions

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.

Certain numbers of divisions per octave such as 19, 31 ,53 or 99 produce intervals and chords that are more pure. This is because the frequency relationships between the notes are closer to exact simple ratios.
For example, in the conventional tuning system the interval between D and F (a minor 3rd) is inaccurate by about 1/7 of a semitone. This is certainly detectable by the human ear. In 53 tone equal temperament the minor 3rd is accurate to 1/895 of a semitone.
With Schismata these extraordinarily pure harmonies are possible.