Musical scales before tempering Natural musical scales The musical scales of human cultures developed naturally, i.e. without any conscious mathematical considerations whatsoever, in the course of millennia. The fact that there is a great deal of mathematics behind them nonetheless has something to do with the resonances between the scale tones and the fundamental tone. These resonances strike us as attractive, and music that is based on such resonances is capable of uniting human communities. Mathematically, resonances can be traced back to fractions with as low numbers as possible, and we were able to deduce mathematically which nine intervals have