The stop length of stringed instruments refers to the length of the string from where it leaves the nut at the top of the finger board to where it crosses the bridge. This length determines the intonation of the instrument, where the notes are found based on the divisible length of the string – the space between notes.
The stop or string length, will vary slightly depending on where it was made and what measurements were used; German and Italian/ French measurements are usually within a nominal difference of roughly 5mm. Where German, for violins, will be often measure 330mm and Italian/ French 325mm. This will translate to a slightly wider intonation distance between notes when playing.
The back stop refers to the distance of the string behind the bridge to the tail piece. This length is determined in one of two ways. Either the “6th rule” is employed, a simpler calculation, where the Stop length is divided by 6 giving the distance from bridge to the tail piece spine or the Golden Ratio may be used which is, again, the Stop length multiplied by 0.1618.
eg. 325 / 6 = 54.166mm or 325 x 0.1618 = 52.585
The difference between these two measurements seems insignificant. However, small the measurements, there will be a sonic influence. That said, this is also subject to how the instrument responds to frequencies and how Regulated Irregularities help the instrument sound its best.
Both work to regulate the harmonic of the instrument within a tolerance that we use based on the difference between the two calculable results. At Svencino we choose to work with the Golden section as our starting point. From there we regulate according to how the instrument sounds and responds.
There are other experimental things that can help instruments sound and respond at their best. In the case of instruments that struggle with wolf tones or poor sound, one can use a tail piece that distributes the back stop in golden sectional increments. In this case the tail piece will not have the strings spaced in a straight line from left to right behind the bridge; instead the strings will be distributed along the length of the tail piece in increments of the golden section.
To clarify, using a violin, if the stop length is 325mm then 325 x 0.1618 = 52.585 would be the first back stop measurement for the E string. Then using the E strings back stop length the A’s back stop would be (52.585 x 0.1618) + 52.585 = 61.093 and the D would be (61.093 x 0.1618) + 61.093 and so on. What this intends to achieve is to create a clean harmonically phased crossing between the oscillation lengths of the stop to the back stop. Meaning that the length of the sine wave of either side crosses in phase, thus preventing wolf tone bumps when out of phase.
See our Harmonic tailpieces here.
This does cause a slight problem with the G string being too short to reach the peg without the wrapping of the string being over the nut and finger board. This does not cause a sonic problem but is not ideal. We do have some suppliers who sell some of their string ranges with extra length G’s for violin and C’s for cello to be able to use such a tailpiece. Violas usually do not pose this problem because the strings are often long to accommodate for their varied sizes.
Note. The science behind string length, tension, materials used, methods of construction and then only the final distributions on an instrument are so complicated and vast that a large part of it ultimately comes down to experience (trial and error) and the luthier’s regulative dexterity.