Pythagoras And The Amazing 12 Note Scale

Pythagoras believed that pleasant sounding frequency ratios are fractions of small numbers such as 3 / 2, 4 / 3, 5 / 3, 5 / 4 and 6 / 5. The just scales contain these ratios as well as unpleasant sounding intervals. The equal tempered scales have equal intervals between adjacent notes. The 12 note equal tempered scale is the only equal tempered scale containing good approximations for all the aforementioned small number ratios, and, more consonant intervals than dissonant intervals!