source file: m1420.txt Date: Tue, 19 May 1998 03:41:35 EDT Subject: RE: Tuning Digest 1412 - Integer ratio harmonics/Additive analysis From: Ascend11 The reference given by Patrick Ozzard-Low on Frequency ratios of spectral components of musical sounds is of interest to me and I plan to copy the article and read it at first opportunity (next trip to UC San Diego library). It has been over five years since I did intensive work improving a frequency tracking / additive analysis computer program system which I'd received from the Univ. of Illinois' CERL Music Lab. I used an autocorrelation technique to track frequency, using trial window sizes for paired "windows" of duration one estimated period of the fundamental - e.g. 2.27 milliseconds for a pitched sound of fundamental frequency 440 Hz. Then, using a frequency vs. time basis line, I would use a Fourier analysis algorithm to track partial amplitude and phase, window by window, over the course of the sound. I added empirically calibrated error correction modifications to the basic program and tested these using artificially constructed "sounds" having time varying amplitudes coupled with time varying frequencies. I do not recall specific numbers (these are "buried" in my not very well organized logs and notes), but I believe that in cases of "well behaved" sounds - normal pitched singing, instrument notes at moderate volume, etc. the method faithfully yielded, for a partial, the number of cycles it went through over a sound's course (from under a second to several seconds for most sounds I analyzed) accurate to .01 of a cycle. Thus I believe the method would, for example, give AVERAGE frequency results for, say, the second partial of a 440 Hz fundamental analyzed over one second to an accuracy of about one part in 88,000. If the results of my work would be of significant value to a researcher or researchers in the field, I would like to make my programs &c. available to them. Some work would be needed to make my software "user-friendly", although someone with a technical background (C programming, basic scientific mathematics) might be able to make use of it quickly. I'm currently working on another research project (preparing listener intonation response - e.g. preference, descriptive observations of contrasts, etc. - tests to be given in late June/early July for research purposes to high school/junior high school summer music campers - I'm doing another post regarding this). This limits the amount of time which I can presently give to dealing with the additive analysis material, but if there is a serious need it might meet I certainly would like to make it available to meet that need. Dave Hill