Of fundamental importance here is the establishment of the Pythagorean scale
founded on string ratios (2:1 = octave, 3:2 = fifth, 4:3 = fourth, etc.
But this number is also the limma, or leimma, (also called a minor semitone) from the Pythagorean scale
in music theory, which expresses the difference between the minor third and the tone.
Apples leader Robert Schneider claims he has invented a new musical scale, which he has called the Non- Pythagorean Scale
A story, well-formed, must comply with certain rules of structure, just as (most) music complies with the Pythagorean scale
Part I provides a comprehensive account of the history of scales, modes and tuning systems: the Pythagorean scale
, the tetrachords of ancient Greece, the church modes, the Guidonian hexa-chord system, mean-tone temperament, major and minor modes, chromaticism, and twentieth-century modes and scales.