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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Definition and Measurement of Harmonicity*From*: beaucham <beaucham@xxxxxxxxxxxxxxxxxxxxxx>*Date*: Thu, 13 Jan 2005 11:08:58 -0600*Comments*: To: cshare01@QUB.AC.UK*Delivery-date*: Thu Jan 13 12:28:53 2005*Reply-to*: beaucham <beaucham@xxxxxxxxxxxxxxxxxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Hi Chris, This is a subject that I'm interested in. However, I'm not quite sure what you mean by "harmonicity". Are you thinking of chords or are you thinking about "the degree to which single sounds contain only harmonics"? In the latter case, an inharmonicity coefficient can be defined as B[k] = 2*(f[k] - k*f[1])/((k^2 - 1)*k*f[1]), where k = partial number and f[k] = partial frequency. If B[k] follows a certain law which is approximately true for string tones, it will be independent of k. However, it real life you have to average it over k to get a single value. (For details, see, for instance, Rossing's The Science of Sound.) Typical B values for the piano are .0001 to .01. Physically, it depends on tension, mass-per-unit-length, and Young's modulus (stiffness). I don't know that it gives reasonable answers for instruments other than free-vibrating string instruments, but the idea is to compute an average deviation from a strictly harmonic relationship and normalize it according to frequency somehow. Best, Jim Beauchamp University of Illinois at Urbana-Champaign jwbeauch@xxxxxxxx ************************************************************************* Original message: >From: Chris Share <cshare01@xxxxxxxxx> >Date: Thu, 13 Jan 2005 14:50:20 +0000 >To: AUDITORY@xxxxxxxxxxxxxxx >Subject: Definition and Measurement of Harmonicity > >Hi, > >I'm interested in analysing musical signals in terms of their harmonicity. > >There are numerous references to harmonicity in the literature however I >can't find a precise definition of it. Is there an agreed definition for >this term? > >If someone could point me to some relevant literature it would be very >much appreciated. > >Cheers, > >Chris Share

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