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Issues with a custom Bass VI

Hey guys! Finally got my custom Bass VI from a local luthier from Peru. But, sadly, it does have some work left to do. Regarding this particular situation I have some questions:

1. The string tree is absolutely necessary? I do not have any problem with tuning or intonation as it is now but I see that most of the bass vi around the internet do have string trees so that got me a little worried.

2. I am not sure but it seems the nut was made poorly and with the wrong dimensions. The low E and the A are like too close to be comfortable to play continuously on the first frets. So, is there any schematics for the specific measures of the nut (mostly about string spacing)? Still, I am not sure if this is a real problem because I'm using a Stringjoy 25-95 set, so I also suspect that this issue happened because of the really thick low E (?). The total length of the nut is 40 mm.

Here is a photo of the nut and headstock

Thanks in advance!
WhatsApp Image 2023-05-05 at 12.10.53 PM.jpeg
 
Make sure to set the witness points on the strings at the tuning posts as well as the nut and bridge. I am observing the A string in your picture. As far as the question at hand, if the strings don't rattle or buzz, then no, you don't need string trees. But if even one string rattles or buzzes, the rest of the upper strings might, and then string trees are indicated.
 
The spacing doesn't look even, but that could be the string gauge - make sure by measuring. They do feel a bit tight.

I just built a bass VI type, I had to add string retainers and file the nut slots to keep the strings from jumping out when I played hard - but I have a reverse headstock, with the longest stretch to the tuner on the lowest strings (opposite of usual):

Winter Build Off 2023 - Lieutenant Cushing
 
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There are two common ways of spacing the strings at the nut , equally or proportionally. In equal spacing the stings are separated from each other by a fixed amount measured from the centre of the string. The other way is to space the strings so that the space between each pair is constant, thus compensating for the thickness of the strings. A variation on this is a compromise between the two. Yours seems to be the first kind. Mostly players prefer the proportional spacing.
 
Make sure to set the witness points on the strings at the tuning posts as well as the nut and bridge. I am observing the A string in your picture. As far as the question at hand, if the strings don't rattle or buzz, then no, you don't need string trees. But if even one string rattles or buzzes, the rest of the upper strings might, and then string trees are indicated.

I don't understand well about your first point, sorry my english is not that good sometimes :( Did you mean I should take photos from the tuning posts and the bridge angle? If so, I'm attaching two pictures.

WhatsAddddpp Image 2023-05-05 at 3.12.00 PM.jpeg

WhatsApp Issssmage 2023-05-05 at 3.11.01 PM.jpeg


But the second point got me really interested. There is buzzing, from the third to the sixth fret in all strings. I thought the frets would be kinda above they should be, but what you said may imply that getting a string tree might solve it?
 
The spacing doesn't look even, but that could be the string gauge - make sure by measuring. They do feel a bit tight.

I just built a bass VI type, I had to add string retainers and file the nut slots to keep the strings from jumping out when I played hard - but I have a reverse headstock, with the longest stretch to the tuner on the lowest strings (opposite of usual):

Winter Build Off 2023 - Lieutenant Cushing

Looks amazing! And yeah, the spacing seemed odd to me at first glance, too. I'll try measuring with a measuring tape later.
 
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There are two common ways of spacing the strings at the nut , equally or proportionally. In equal spacing the stings are separated from each other by a fixed amount measured from the centre of the string. The other way is to space the strings so that the space between each pair is constant, thus compensating for the thickness of the strings. A variation on this is a compromise between the two. Yours seems to be the first kind. Mostly players prefer the proportional spacing.

Man, wow, I literally had no idea about this. That would make perfect sense!
But to this specific case, how much would be the string spacing to each string? Or how do I calculate the proportions?
 
Looking at the neck picture, the break angle is plenty enough to not need trees. That headstock is much lower than I would have expected.

I think the low E and A at the nut are not spaced evenly, the others seemed much more reasonably spaced. And it's the A that doesn't seem right.

If it were me, I'd just redo the nut with more equal spacing as others have mentioned.
Just lay it out before you start cutting anything, you can draw it out to scale on paper to experiment.
 
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Looking at the neck picture, the break angle is plenty enough to not need trees. That headstock is much lower than I would have expected.

I think the low E and A at the nut are not spaced evenly, the others seemed much more reasonably spaced. And it's the A that doesn't seem right.

If it were me, I'd just redo the nut with more equal spacing as others have mentioned.
Just lay it out before you start cutting anything, you can draw it out to scale on paper to experiment.

Using a measure tape I noticed that the strings from the A to the high E are 0.5-1 mm moved to the low E, making all this problem, I guess.