To resolve it the solution found and accepted has been to reduce all the intra-octaval ‘consonances’, fifths, fourths, major and minor thirds, etc., to what fits within the limits of an equally divided octave, which, of course, distorts the purity of the intra-octaval consonances. This solution has been called ‘twelve-tone equal temperament’. Without it, modern classical music, which requires modulation over a plurality of octaves, would not be possible. With it, the duration of modern classical music was limited by the persistent ability to hear pure (pythagorean) intra-octaval consonances.
