All definitions by Joe Monzo unless otherwise cited irrational A number which cannot be described as an exact ratio between two proportions.
Irrational numbers have an infinite and non-repeating string of digits after the decimal point.
Two of the most famous examples are pi and the 12-EQ Semitone . Irrational algebraic surface. Also, the irrational numbers are precisely those infinite decimals which are not repeating. For many more diagrams and explanations of historical tunings, see my book . Let me know if you don't understand something.