Definition and Measurement of Harmonicity (Judy Brown )

Subject: Definition and Measurement of Harmonicity
From:    Judy Brown  <brown(at)MEDIA.MIT.EDU>
Date:    Sat, 22 Jan 2005 11:06:36 -0500

I have a paper measuring this ratio plus calculation on other instruments.

  Brown, J.C.(1994).  ``Measurement of harmonic ratios of sounds
produced by musical instruments,'' J. Acoust. Soc. Am.  95, 2889.


>At 05:23 15/01/2005, Reinhart Frosch wrote:
>>The inharmonicity of piano strings is treated in
>>section 12.3 of the book "The Physics of Musical
>>Instruments", by Fletcher and Rossing (Springer,
>>2nd ed. 1998).
>>
>>The basic equation for the frequency of the k-th
>>partial tone is:
>>
>>f[k] = f[1i] * k * (1 + k^2 * B)^0.5 ;
>>
>>here, f[1i] is the fundamental frequency of an
>>idealized string that has the same length, mass
>>and tension as the real string but is infinitely
>>flexible (i.e., has no stiffness).
>>
>>B = 0 corresponds to a string without stiffness
>>and thus to a harmonic complex tone;
>>B is an "inharmonicity coefficient".

etc



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    Judy Brown            |http://www.media.mit.edu/~brown
    jbrown (at) wellesley.edu|http://www.wellesley.edu/Physics/brown/jbrown.html
    brown (at) media.mit.edu |E15 483,   MIT, Cambridge, MA 02139
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