VSL Breakpoint Angles, Radiuses, and Excess String Lengths
Instruments- discuss specific features, luthiers, instrument problems & questions
This might end up being a controversial topic, since I cant seem to find a lot of agreement on it elsewhere, but I'd like to know what y'all know and have observed about how much the headstock angle, length of the headstock, radius of the nut, and bridge breakpoint angle, radius of the bridge, and excess of string between the bridge and tailpins affect tone, volume, and sustain.
My research has indicated to me that people just dont agree for the most part on these questions. The highly credible @Ken-Hulme said in a forum post *"Position of bridge relative to the string pins or break over the end (how much string is aft of the bridge) affects sustain"* Lutes have an extremely sharp headstock angle, apparently due to the desire to ensure that the strings have a rigid boundary to their VSL. Brian May's Red Special has such a subtle headstock angle it almost appears that the string is not bent over the nut at all. One local luthier has personally told me that a 10 degree headstock angle is necessary to ensure that the string is held in place and anything past that is just builders preference. Gibson has some guitars with infamously sharp headstock angles, which their website claims improves tone. My friend Allen took a board and stretched several strings across it at different angles, and told me that a 6 degree angle was the lowest he could avoid buzzing at. (interestingly I looked at my acoustic guitars and noticed both of them have a <10 degree angle that they stretch over the bridge at) He is much stronger than me at physics, so I'm inclined to believe his explanation that you need enough downward force on the VSL boundary to be greater than any upward force from the string's vibration, and any additional force past that is redundant. Makes sense to me since that's the case with fretting; you only need just enough pressure to keep the string in contact with the fret, adding more pressure past that does not give extra sustain, tone, or volume, so why would the bridge and nut be different?
One key difference that has come up in my own experiments is that in the past I often cut my nut and bridge at a straight angle (whereas frets are obviously rounded on their tops) and noticed buzzes, and abnormally quiet sound. It was explained to me that I should not expect a steel string to bend at an angle, rather at a radius. When I went back and cut new bridges with a radius past the break point the difference was night and day in terms of increased volume and resolving buzzing issues. In the attached image the black objects represent 'bridges' the red lines represent 'strings'. The first diagram shows a 'bridge' with very minimal contact, which I believe puts tremendous amounts of extra stress on the bridge and the string. The second shows better contact but still a sharp angle at the breakpoint, which i believe can cause intonation issues and buzzing since the string might not actually be able to bend all the way to match the angle of the bridge without over-applying string tension, and therefore the breakpoint may be further back on the bridge than intended. The third diagram is what I currently do more or less, which is round off the side of the bridge and nut that is outside the VSL so that the string has a lot of contact and no sharp angles. I have never paid attention to the length of string outside the VSL, I have always assumed that if you have adequate downward force on the bridge and nut, that anything past them is irrelevant. A lot to think about but I'm sure plenty of you have thought about these things before! I'd love some more perspective
updated by @natebuildstoys: 05/10/20 02:34:31PM