Bass String Scale

[Ron Overs]

Hi List

Newton Hunt said,
(regarding bass string scale design)

>Designing a decent scale is not hard as long as you have some minor
>understanding of tension, power, inharmonicity, computers, math and
>general engineering principles.  The main problem is measuring and
>data entry, the rest is just patience and asking, "what if?"

Well said Newton!

The following extract outlines the procedure we use for setting the cover 
length terminations of a redesigned bass scale.

Manufacturers rarely take care to ensure that the copper wrap terminates 
at a uniform and close distance from the agraffes and bridge pins. During 
the late 1980s, we started marking adjusted winding termination points 
(with masking tape) on the original bass strings prior to destringing. 
The tape was placed as a guide for the string maker. When the original 
string scale is retained, this works very well. However, when a bass 
section is rescaled. the wrap terminations will shift in response to any 
change in the percentage of breaking strain of the core wire. For some 
years now, whenever rescaling basses, we mark the original strings with a 
corrected cover termination point. The adjusted termination points are 
calculated by entering the original and revised scales onto a 
spreadsheet. The spreadsheet, which uses the modulus of elasticity of 
piano wire, calculates the core wire stretch of the new and old scales. 
The difference is used to adjust the tape-mark for wrap termination 
adjustment. Using this method, the cover ends of the new strings will 
line up at the intended distance from the agraffes. Our preferred wrap 
termination points are achieved when they terminate 10mm from the 
agraffes and the bridges pins.

I notice that there was some debate on the PTG list, regarding the actual 
modulus of elasticity of plain wire, ie. earlier this year.

The formula we use is;

Wire stretch in mm =([string length in mm]*[string tension in 
Kg])/((((([string diameter in mm])/2)^2)*PI())*21500)

* If the above formula is copied to an excel spreadsheet in the form;

=(A3*B3)/(((((C3)/2)^2)*PI())*21500)
[copy into cell D3 - include the equal sign] 
To avoid errors when translating the formula to excel, select the formula 
in this email, then copy it across to the excel spreadsheet.
Insert the variables into line 3 as follows
cell A3 - the string length in mm
cell B3 - the string tension in Kg
cellC3 - the string diameter in mm

The core wire stretch will now appear in cell D3 in millimetres, with the 
string at pitch.

The above formula applies to Roslau wire only. I have heard that the US 
manufactured piano wire is softer than Roslau, so it is possible that the 
modulus of elasticity might be somewhat lower for the US wire. However, I 
would be very interested to recieve an email on the modulus of elasticity 
of piano wire from US maunfacturers. The figures we use for Roslau wire 
(21.5 Kg applied to a metre length of wire with a sectional area of 1 sq. 
mm will stretch it 1mm) results in accurate terminations for the copper 
wrap on our rebuilt instruments.

Ron E Overs
Overs Pianos
Sydney Australia

Email: ron@overspianos.com.au
Web site: www.overspianos.com.au