Acomparison of the musical scales of the ancient Chinese bronze bell ensemble and the modern bamboo flute

We compare over a two-octave range the tonal, interval, and scale relationships of an ancient Chinese bell ensemble of the Zhou Dynasty and a modern bamboo flute. By using subjective pitches, a tonal system with simple harmonic partials (the flute) could be compared with a tonal system with complex inharmonic partials (the bell). We argue that the underlying musical scales of the bell ensemble and the flute are closely related and lie between an unequal-interval pure-system scale and the just-intonation scale. There is some evidence that a least interval of 60 or 66 cents figures in the flute scale, that both flute and bell scales include a 90-cent interval and a true (1,200-cent) octave, and that neither scale includes a 100-cent interval. Since there is a true octave, the scales cannot be cycles of fifths, and since there is no equal-temperament half-tone (100 cents), the scales cannot be equal in temperament. We conclude that the flute and Zhou bell scales are very similar if not the same. Apparently, strong cultural traditions and human perceptual constancies united to sustain a common flexible musical scale during 2,400 years.