The Tyranny of the Diatonic Scale by Robert Morse

We look at the evolution of musical scales and discuss the limitations and tyrannical aspects, as noted by the composer Bela Bartok, of the "just" diatonic scale, and the devastating aspects of the equal-tempered (E-T) scale on harmony in its attempt to minimize the dreaded "Pythagorean-comma" and lesser temperament diseases.

As physicists, we will propose, like the musicians before us, a "least-squares" fit to minimize the angst and drama and decide along with most musicians that the present 12 tone octave E-T scale is probably the best we can ever do, realizing that the next improvement comes with the added expense of having separate black notes for G-sharp and A-flat, when we introduce the 53-semitone octave, a scheme actually proposed by Isaac Newton and others!

Details on other tuning schemes such as the half-dozen or so "mean-tone" temperaments, all of which try to fix the "just" scale when we modulate to different distant keys and how the individual color and nuances of each key which resulted from these tunings fall victim to E-T will also be discussed. We will demonstrate with some characteristic examples.

Event Sponsor
Physics and Astronomy, Mānoa Campus

More Information
Xerxes Tata, (808) 956-7690, xerxes@hawaii.edu

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