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 and crosses the bridge. This length determines the intonation of the instrument, where the notes are found based on the divisible length of the string. This may vary slightly depending on where it was made and what measurements were used; German and French/Italian measurements are usually within a nominal difference.
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, as a rule. Either the “6th rule” is employed, the 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.
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 calculation because it is the basis from which the violin was created in the first place.
There is a more specific result that can be employed as well. In the case of instruments that struggle with wolf tones one can use a tail piece that has a further added ratio of the golden section. In this case the tail piece will not have the strings spaced in a straight line; instead the strings will be distributed along the length of the tail piece in increments of the golden section. To make this clearer, using a violin, if the stop length is 325mm then 325 x 0.1618 = 52.585 would be the back stop 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. This does cause a slight problem in that the G string may be too short to reach the peg without the wrapping of the string being on the finger board. For this there are, of course, some string types and suppliers who sell extra length strings to be able to use such a setup. To get this right either custom made tail pieces are used of specialised ones are bought from select manufacturers.