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Software :: Stiffness Calculator, v.2.0.0

This is a program that calculates the stiffness and sound velocity of the material using the three resonant frequencies of the violin material. This program is a reconfiguration of Alvin Thomas King's Excel program in Python.


his program calculates the stiffness*1, which is one of the characteristics of the material (wood) for the front and back plates of a violin. The stiffness is an important factor to consider when making an instrument. This is because, depending on the stiffness, you will have to change many things such as the height of the arch, the pattern, and the thickness of the plate. However, it is a significant handicap for violin makers not to be able to know in advance the stiffness of these materials before they start working. Therefore, reducing uncertainty about stiffness would be of great benefit to manufacturers. In this program, stiffness along the grain, stiffness across the grain, and shear stiffness are calculated using the size and weight of the material and the frequency of three vibration modes (resonance). And the sound transmission speed, quality value, and response characteristics are calculated.

This program is based on Alvin Thomas King’s Excel program*2, and I re-created it in Python. Therefore, the calculation method and the result are exactly the same as his Excel program. Some of the explanations (AREA 5) on the right side of the program screen are transcribed from his explanations, and some have been added by myself. The illustration (AREA 1) on the left side of the screen and this manual were written by me. Underlined in this manual is his commentary.

The calculation of stiffness in Alvin Thomas King’s Excel program is based on Oliver Rodgers’ Fortran program[1], and calculations of other items are based on references[2][3]. For stiffness calculation, there is a slight improvement*3 in accuracy compared to Oliver Rodgers’ Fortran program.

Oliver Rodgers’ Fortran program and Alvin Thomas King’s Excel program may have very small differences in the results due to the above improvement. And, although this program and Alvin Thomas King’s Excel programalmost match the result, there may be a difference of ‘1’ in the last digit of the result in some cases. This error is caused by different rounding rules*4 in Excel and Python.

*1 The property of an object to resist deformation in shape or volume when subjected to a force.It is a different concept from strength (resistance from deformation until the material is destroyed by giving it an impact).


*3 The stiffness calculation is done by finding an approximation through iterative calculations, and the accuracy of these iterative calculations is improved.

*4 Excel:2.5→3, Python:2.5→2, Python does not round up if the number in front is even when the number to be rounded is 5.

Figure 1: Screen layout

The reference image (AREA 1), input field (AREA 2) and calculation button (AREA 3) are on the left side of the screen of this program, and the result value (AREA 4) and program description (AREA 5) are displayed on the right side. In the input field, enter the size, weight, resonance frequency, Q value, and sound (vibration) transmission speed (Lucchi Meter). In the result column on the right, the volume, density, stiffness, sound (vibration) transmission speed, quality value, and response characteristics calculated from the input values are displayed.

Formulas or methods for calculation are explained in each item of [How to use], but complicated contents are omitted, so please read the references for details.

In the program screen (AREA 2), underlined input items are mandatory, and the underlined text in this manual is a copy of Alvin Thomas King’s commentary in the Excel program.



It is used to determine how suitable the spruce and maple are for violin making or to make a making plan. In the study of Oliver Rodgers, the prototype of this program, the size of the material is specified. Therefore, if the size of the material is out of that range, the error in the result will inevitably be large. Please refer to Section 3.1 for the range of material sizes. Rodgers’ research is on violin material, so application of this program to viola or cello material is not recommended.



Since this program is a portable version, no installation work is required. After unpacking, double-click the 《Stiffness_Calculator_v.X.X.X.exe》 file in the 《Stiffness_Calculator_v.X.X.X》 folder to run the program immediately. However, it may take a long time to run depending on the specifications of your computer.

When running this program, sometimes it is impossible to run with the phrase "The file has been quarantined because it contains a virus or suspicious file". It is caused by a problem with the Python compiler, and this program does not contain any viruses. If the above warning message appears on the Windows system, please un-quarantine the file and run it again.


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