Re: OT:Singing bowl measurements

["Emile Tobenfeld (a.k.a Dr. T)" <emile@foryourhead.com>]

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
>
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"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."

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                Emile Tobenfeld, Ph. D.
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