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Re: reverse engineering of acoustic sources (Helmholtz's hollowness)
Dear Jim, Georg, Neil, Pierre, John and others,
Regarding the problem of determining the shape of a vibrating structure from its spectrum, it is of interest to revisit Helmholtz's hollow sound quality.
Hermann von Helmholtz (1877) reported that if only the odd-numbered harmonics were present, the quality of the tone was hollow. It seems that the label "hollowness" in audition reflects an association between the shape of a sounding object and its sound spectrum.
Imagine, for instance, a piece of bamboo is exposed to a grazing wind flow along its opening. Its "whistle" sounds will be predominated by odd-numbered harmonics because it is an open-closed cylindrical pipe. Such sounds may have been associated with hollow objects and labeled as "hollow" according to their shape through a learning process.
>From a physical perspective, the mechanisms of producing sounds with the predominance of lower odd-numbered harmonics can be classified into three types.
(1) Wind instruments with an open-closed cylindrical pipe – e.g., the clarinet and panpipes.
(2) Strings that are plucked at (or near) the midpoint – e.g., some tones of the harp, the guitar and others.
(3) Flute-type instruments with an open-open cylindrical pipe and blown with symmetrically vibrating jet – e.g., the recorder. Some flutists tend to produce sounds with the predominance of lower odd-numbered harmonics.
Among the three types, only the first one is relevant to the shape of the musical instrument.
Even if we focus on the first type, caution should be exercised because some hollow object such as open-closed conic pipes do not produce "hollow" sounds. Note that their sounds do not possess spectral features that can easily be extracted for object identification. Hence, the majority of hollow objects provide no distinct auditory cues worth learning for our cognitive system. On the other hand, the tones with the predominance of lower odd-numbered harmonics have a robust spectral feature for sound recognition. We may have learned to extract this spectral feature and utilize it for recognizing the shape of open-closed cylindrical pipe, especially when they are not within the field of vision.
One topic of my dissertation is the perception of sounds with the predominance of odd-numbered harmonics. After being familiar with the hollow quality, I tend to guess the plucking-point of a string on the basis of the degree of holloeness of its sound. So, acoustic cues can also be used in the recognition of performance technique. Likewise, I tend to judge if the vibration of the jet is symmetric when I hear a flute tone.
Ph.D Musicology, Humboldt University Berlin
--------- Original Message ---------
DATE: Fri, 30 Jan 2004 14:24:03
From: beauchamp james w <jwbeauch@UX1.CSO.UIUC.EDU>
>In the Februrary, 2004 issue of Scientific American, Wayne Hu and
>Martin White in their article "The Cosmic Symphony" write
> "...researchers have been able to use [temperature variations of
> the cosmic microwave background] to precisely estimate the age,
> composition and geometry of the universe. The process is analogous
> to determining the construction of a musical instrument by
> carefully listening to its notes."
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