Inharmonicity

Last modified by

on

Jul 24, 2020, 6:28:07 PM

Created by

on

Nov 12, 2013, 5:59:11 AM

I_{n} = 1731 (n^{2} - 1) {S (1 + \frac{B}{8}) + 3 \frac{B}{1 + B} [{| \frac{a}{L} - \sqrt{S} |}^{3} + {| \frac{b}{L} - \sqrt{S} |}^{3}]}

$I_n = 1731 ( "n" ^2-1) { S(1 +B/8)+3B/(1+B)[| "a" / "L" -sqrt(S)|^3 + | "b" / "L" - sqrt(S)|^3]}$

Wrap Material

$"Wrap Material"$

Overal Diameter (mils)

$"Overal Diameter (mils)"$

Speaking Length

$"Speaking Length"$

Tension

$"Tension"$

Unwrapped End Length

$"Unwrapped End Length"$

Unwrapped End Length

$"Unwrapped End Length"$

Core Wire Diam

$"Core Wire Diam"$

Partial Number

$"Partial Number"$

NOTES

Acoustic factor in the unit of cents.

Note, stiffness (S) $= \frac{d^{4}}{139439 L^{2} T}$ $= d^4/(139439 L^2 T)$ .

Also note, that $B = A (\frac{D^{2}}{b^{2}} - 1)$ $B = A( D^2/b^2 -1)$ , where A is a function of the wire wrapping material (copper,iron,aluminum,none).

REFERENCE

[1] inharmonicity
Source: Wikipedia
URL: https://en.wikipedia.org/wiki/Inharmonicity
Public License: CC Attribution-ShareAlike 4.0 International

This equation, Inharmonicity, is used in 2 pages

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• Music 19s01abt037 by Winnie18

• Piano Tuner by KurtHeckman

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Inharmonicity

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REFERENCE

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