source file: m1412.txt Date: Mon, 11 May 1998 18:36:58 +0000 Subject: Integer ratio harmonics etc From: "Patrick Ozzard-Low" The following may be helpful in the 'integer ratio harmonics' for acoustic sustaining instruments dscussion (sorry if some of it reduplicates stuff already discussed, but confirmation/contrast can't be a bad thing). Judith C. Brown, 'Frequency ratios of spectral components of musical sounds', Journal of the Acoustical Society of America, Vol. 99, No. 2, 1996, pp. 1210-19. The article places considerable emphasis on methodology and accuracy of measurement. Some quotes and comments: "A recently developed high resolution frequency tracker. has made it possible to measure the ratios of the frequencies of the upper harmonics of a sound with respect to its fundamental frequency with high accuracy. Calculations were carried out on digitised sounds produced by a clarinet, alto flute, voice, piano, violin, viola and cello." (p. 1210). For the sustained instruments in this group the frequency ratios of spectral components (in this study the number of harmonics considered (or at least, included in the graphs provided) for each instrumental sound varied from 5 to 25) were in what Brown calls 'exact' integer relationship - that is, as exact as the accuracy which the measuring process itself allowed. As I understand this, it was shown that spectral components will normally deviate from an ideal harmonic series by no more than about 2-3 cents, but that relative to the accuracy of the calculation smaller deviations could not be detected. "Continuously driven instruments such as the bowed strings, winds, and voice have phase-locked frequency components with frequencies in the ratio of integers to within the currently achievable measurement accuracy of about 0.2%. Since frequency fluctuations greater than the measurement accuracy are inherent in any sound produced by a human performer [on such an instrument], improvement of the measurements is unnecessary.' (ibid., p. 1218). I can't pretend to understand the detail of the methodology to explain it to you. But would be particularly interested to hear Dave Hill's and other's reactions to the methodology, should they be familiar with the article. Also, more important, - Dave, have you published your own results? Sorry if I missed this somehow. Thanks. Patrick O-L