Subject: Re: [Fwd: technical notes on data used by Martin Braun] From: "Alain de Cheveigne'" <Alain.de.Cheveigne(at)IRCAM.FR> Date: Wed, 13 Jun 2001 18:15:30 +0200Paul Boersma wrote: >Is it likely that the measured F0 values had a spacing of 1/4 semitone? >It seems more likely that they were expressed as an entire number >of samples per period. I don't know about GIPOS, but it is true that many F0 estimation methods measure 1/F0 with a resolution of one sample. I made an experiment inspired by Paul's praat script (translated to matlab). Specifically I did the following: - Generate 500000 random frequency values uniformly distributed on a log scale between A2 (110 Hz) and A4 (440 Hz), which is roughly the extent of the data in Braun's paper. - Convert frequency to period. - Quantize based on a sampling rate of 16000 Hz. - Convert to an octave scale relative to a reference value (440 Hz). - Make a histogram with 1/4 semitone bin size. As Paul found, the histogram has a very pronunced structure. Some bins are actually 0. Folding the histogram into 4 bins representing counts modulo one semitone also gives a clear structure. If consecutive bins are paired and averaged, the ratio between largest and smallest is about 1.11, not too far from the ratio 480:416 (about 1.15) found by Braun. If the statistics are limited to ACDEFG, the ratio is about 1.25, not too far from the ratio 248:182 (about 1.36) found by Braun. The exact values vary strongly with the reference value that defines the boundaries of the 1/4-semitone-wide bins (which according to Bob Ladd were not aligned exactly on 440 Hz). They also depend on the overall shape of the F0 distribution, and of course they fluctuate from trial to trial. Interactions between successive quantization operations (a sort of moire' effect) can produce a very salient pattern even if the underlying distribution is smooth. Of course this does not imply that such was the case for the original study. The surest way to verify would be to look at the original data. Alain -------------------------------------------------------------- Alain de Cheveigne' CNRS/IRCAM, 1 place Stravinsky, 75004, Paris. phone: +33 1 44784846, fax: 44781540, email: cheveign(at)ircam.fr http://www.ircam.fr/equipes/pcm/cheveign --------------------------------------------------------------