This tool is designed to help calculate and visualize various design aspects of the Tagelharpa. It is an attempt to try and create a level of standardisation to help amatuer builders avoid
analysis paralysis. When I started looking at how to build a bowed lyre, I was overwhelmed by how much conflicting information was available about every little aspect.
With no disrespect to all the DIY builers out there, this is predominantly being caused by a lack of knowledge, and a necessity to to have to "wing it" until a nice sound is found then that builder
will continue to build using those dimensions.
I have looked over too mamny photos of instruments that I have heard and subjectively think sound the nicest, scaled dimensions from the photos, found the ratios and low-and-behold, there is
a pattern. These patterns are what I have used in my calculator.
NOTE: These dimensions are by no means perfect. A skilled luthier will most likely be able to blow away anything made with this calculator (and I am certain to get some complaints that I am doing something wrong from them on this haha - I know it's not perfect!). However, it does
provide a strong starting point and will produce a reasonable sounding instrument. It should drastically reduce the effort that is required to start building from scratch. If it helps at least one other person, I will be happy!
Thank you, and enjoy!
Wilbur
The Tagelharpa’s design is based on a set of proportional relationships that scale the instrument’s dimensions according to the chosen scale length and number of strings. Below is an explanation of each critical dimension using traditional mathematical formulas.
The distance from the nut (or peg) to the bridge is defined as the string scale.
A = scaleMm, where
scaleMm = scaleCm × 10.
The overall length is calculated piecewise from the scale length (in cm):
For scaleCm ≤ 40:
B = scaleCm × 1.66 × 10
For scaleCm ≥ 56:
B = scaleCm × 1.43 × 10
For 40 < scaleCm < 56, let
f = (scaleCm – 40) / 16, then:
B = scaleCm × [1.66 – 0.23 × f] × 10
The window (soundboard opening) is designed for a full octave:
C = 0.5 × scaleMm + 20
The window width is based on the number of strings and a fixed peg spacing:
D = pegSpacing × numStrings,
where pegSpacing = 36 mm.
The spacing between pegs is fixed:
E = 36 mm
The headstock width is determined by the window width plus an additional 50 mm:
F = D + 50
The bridge width is defined piecewise:
If scaleCm ≤ 30: G = 60 mm;
If scaleCm ≥ 56: G = 70 mm;
For 30 < scaleCm < 56, let
f = (scaleCm – 30) / 26, then:
G = 60 + 10 × f
After subtracting 12 mm from each side of the bridge width, the usable span is:
Usable Span = G – 24
If more than one string is used, the gap between string centers is:
H = Usable Span / (numStrings – 1)
The body’s minimum width is determined from empirical data. For example:
- For scaleCm ≤ 32: I = 160 mm
- For 32 < scaleCm ≤ 37: I is interpolated from 160 to 190 mm.
- For 37 < scaleCm < 56: I is interpolated from 190 to 210 mm.
- For scaleCm ≥ 56: I = 210 mm
The body’s depth is given by:
J = clamp(scaleMm × 0.12, 45, 70),
meaning the calculated value is limited between 45 mm and 70 mm.
The tailpiece’s top width is defined as:
K = H × numStrings
(where H is the gap between strings.)
The tailpiece’s bottom width is a fraction of the top width:
L = K × 0.7
The tailpiece length is given by:
M = 0.4 × (B – scaleMm),
where B is the overall instrument length.
The headstock thickness is fixed:
N = 35 mm
The centre of the soundhole is calculated by:
O = ((scaleMm – C – (cutOutTop/2)) / 1.85) + C + cutOutTop
where C = windowLength and cutOutTop is the vertical offset for the window.
The neck start position is determined by the distance between the bottom of the window and the top of the soundhole. With:
bottomOfWindow = windowLength + cutOutTop
the neck start is:
P = ((O – bottomOfWindow) / 3) + bottomOfWindow
This sets the vertical point where the neck begins.
Neck thickness is set based on scale; for instance:
Q = { 35 mm if scaleMm > 450; otherwise 25 mm }
This parameter accounts for the need for a thicker neck in larger instruments.
The width of the instrument at the neck level is found by linear interpolation between the top width and the bottom width of the instrument. Let:
r = P / B, where P is the Neck Start and B is the Overall Length.
Then the width at the neck is:
Widthneck = F + (I – F) × r
Here, F is the headstock width (top width) and I is the body minimum width.