DESCRIPTION:
This music file and comments have been part of the demonstration of Dr. Demetrios Lekkas during his lectures at Columbia university, Princeton and other international conferences. They are complementary examples and comments to his dissertation "The mathematical Theory of Music" Athens,Greece 1998

The author addresses some common misconception among western musicians about the just intonation system.
For instance: they use to raise the 3rd of a major 3rd when it functions as a leading tone while they should do the opposite, wrongly assuming that raising the leading tone when it goes to the tonic, contributes to the clarification of the melodic intend and the new raised note is also instantly supported by the slightly modified chord. The truth, though, is that the raised leading tone creates a "out of tune" chord which consists of irrational and thus non periodical and non harmonic ratios (pitches). The result is a chord which is muddy, and its harmonic properties ( tension and direction ) have been slightly distorted and obscured. Also the chords difference notes are out of tune which further contributes to its cloudiness. Our brain, of course, makes the necessary adjustments and the distortions caused by this practice are corrected: so even if we hear an out of tune leading tone our brain corrects the error and we perceive it as an acceptable deviation from the the prototype ; slowly our ears and minds are trained to disregard this acoustic phenomenon and to consider out of tune chords as correct.

Listen for

1. The sharply dissonant quality of the augmented sixth chord and the relaxation resulting from resolution, a fact typically pointed in harmony theory but inaudible in orchestral interpretations, as modern symphony orchestras do not play in just intonation, as they did in Mozart' s time. This is an authentic reconstruction of orchestral playing in early 19th century. ( Using midi).

2. The dark and "evil" quality of the justly intone minor tonality.