The Piagui scales and the eq.tempered intonation

As I said before, two equal triads given by different scales (Gmajor Piagui and G major eq. tempered forexample)can be classified according to their chord wave peak responses which practically are their harmony photos. Equal tempered and Piagui triads where their corresponding tone frequencies show rather small discrepancies present aesthetic Piagui responses while highly discordant eq. tempered chord wave peaks. Both graphs correspond to the same triad, like Gmajor.

What about chord wave peaks?--- First the sum of the three pure sinusoids whose frequencies are the ones of the triad tone frequencies that work in scale A should be added in the computer in such a way that the three origins coincide at t = 0 sec. It gives a dark response of course. The same for scale B. In both combined waves a great number of peaks appears and part of them can be detected at first sight. Since chord waves A and B differ due to the small tone frequency discrepacies, the peaks on graphs A and B are detected and printed to get their chord wave response. An special procedure let de conversion of peaks to marks or points and this transformed information (peaks to marks) depicts the chord wave peak graphs, a sensible response even for extremely low discrepancies.

This information will be extended to morrow.

Mario Pizarro

piagui@...
May 29, 2009