Relating Spectrum and Tuning of the Classical Thai Renat Ek

This paper discusses the relationship between the frequency spectrum of a Thai metallophone called the Renat Ek and its traditional tuning. A spectral analysis of the instrument produces a dissonance curve with consonance minima at ratios very close to the 7-tone equal-temperament scale often used in Thai classical music, as well as the tuning of one specific Renat Ek, suggesting a strong correlation between spectrum and tuning. Analysis of several musical performances shows the 1st, 5th and 6th scale degrees to be the most consonant (and the 2nd and 7th the most dissonant), a fact that is also supported by the relative consonance implied in the dissonance curve. BACKGROUND The discussion of consonance and dissonance and the relationship between timbre and tuning seems to begin with Hermann von Helmholtz characterizing dissonance in terms of the rapid beating between sine waves in close frequency proximity; an interval would be dissonant if some of the sine waves involved were close enough in frequency to produce a fast beating. After Helmholtz, others began to explore the idea of tuning in