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What makes singing bowls and gongs sound so cool in the first place is that the overtones are not exact harmonics, and a single note can seem to beat with itself. At 4:23 PM -0700 10/19/00, Bret wrote: >--- Matthias Grob <matthias@grob.org> wrote: > > > > > >The spectrogram allows us to see, in a scrolling chart, over time in > > >the horizontal axis, the frequency components in the vertical axis, > > >with the amplitude of each component indicated by shading. The > > lowest > > >tone recorded was about 390 hz, approximately a G. The first > > overtone > > >was at about 1070 hz, the next at about 1950 hz. These measurements > > >are +/5.4 hz with the scale and tool used. > > > > hm,,, for me overtones are multiples... > > > > >We attempted to match the tone by ear, to a synth patch that had > > >fundamental and 2 harmonics (390hz,1170hz, 1950hz , fund, 3rd and > > 5th > > >harmonics). We compared the audibly matched synth tone to the bowls > > >tone in the spectrogram. The fundamentals matched in frequency. > > What > > >we heard as tones in the bowl, matched what we heard on a minimal > > >overtone synth oscillator. These sounds differ by the first > > overtone > > >frequency. The synth has 1170hz (3rd harmonic) and the bowl has > > about > > >1070hz which is about 2.74 times the fundamental (390hz). > > > > may this mean that 390 is not the fundamental? > > Then again, I cannot find a fundamental with overtones 390 and > > 1070... > > I can easily imagine several fundamentals, so 390 and 1070 could be > > independent vibrations (axial-radial, for esample). > > But why is the third harmonic 1170 present? Did the 1070 "eat" it? > > > > More even I wonder now how they select the bowls: Could yours be a > > good one because the 5th harmonic appears cleanly... or a cheap one > > because the 3rd does not? :-) > > > > >We found no illusion between perceived pitch, and measure pitch with > > >the 2 types of sounds. The beats in the rubbed bowl do change the > > >character of the sound dramatically, however. > > > > I am not sure I understand what the beating sounds like... > > Is it a subharmonic maybe? > > Interference between the stick movement and some fundamental? > >I used the word beating, as the effect was rather like two tones very >close in frequency to each other, but not quite (say 1hz to 8 hz >difference). We hear this as a pulsation of amplitude as they go in >and out of phase, and reinforce and cancel each others output at a rate >of 1hz to 8hz. To me it sounds like "yun yun yun yun". It is amplitude >modulation (of the tones of the bowl). > >I find it interesting that this frequency range (of the pulsing) covers >the lower end of the brain wave frequencies that are known to be very >deep relaxation, meditation, and altered states of conscienceness. >Could this entrain the brain to these frequencies like flashing light >can? > >So, what I heard and see on the spectrogram is the amplitude of the >tones pulsing, at a 1hz to 8hz rate. Somehow the stick rate influences >it, maybe as it hits nodes and antinodes of the movement (wave) on the >edge of the bell (this is wild, pure speculation). > >Lindsays' reference (http://www.mmk.ei.tum.de/persons/ter.html) to the >Ernst Terhardt has some great research topics. > >See http://www.mmk.ei.tum.de/persons/ter/top/strikenote.html for an >interesting article on the part-tone series of bells, and that they do >not fit the normal harmonic series (and what that does to human >interpretation of pitch). > >My use of the word 'overtones' seems to be confusing. I was not sure >what to call these nonharmonic part-tones. I called them overtones >because they are over (higher in freq) the lowest tone produced (what I >considered the fundamental). Typically part-tones of musical >instruments are harmonic (multiples), except in clangorous tones (like >bells) where some partials appear out of place. > >bret > >__________________________________________________ >Do You Yahoo!? >Yahoo! Messenger - Talk while you surf! It's FREE. >http://im.yahoo.com/ "The reasonable man adapts himself to the world. The unreasonable man persists in adapting the world to himself. Therefore, all progress depends on the unreasonable man." -- George Bernard Shaw Emile Tobenfeld, Ph. D. Video Producer Image Processing Specialist Video for your HEAD! Boris FX http://www.foryourhead.com http://www.borisfx.com