Re: Definition and Measurement of Harmonicity (Reinhart Frosch )

Subject: Re: Definition and Measurement of Harmonicity
From:    Reinhart Frosch  <reinifrosch(at)BLUEWIN.CH>
Date:    Fri, 14 Jan 2005 18:23:39 +0000

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".

Reinhart Frosch,
(r. Physics Dept., ETH Zurich.)
CH-5200 Brugg.
reinifrosch(at)bluewin.ch

>-- Original-Nachricht --
>Date:         Thu, 13 Jan 2005 14:50:20 +0000
>Reply-To: Chris Share <cshare01(at)QUB.AC.UK>
>From: Chris Share <cshare01(at)QUB.AC.UK>
>Subject:      Definition and Measurement of Harmonicity
>To: AUDITORY(at)LISTS.MCGILL.CA
>
>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