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 ARCHIVED TOPIC: Just Intonation nut


Please note this is an archived topic, so it is locked and unable to be replied to. You may, however, start a new topic and refer to this topic with a link: http://www.banjohangout.org/archive/399166

banjo roo - Posted - 09/01/2024:  04:50:11


The open B string in Open G tuning has always grated on me, because when I tune to the standard tuning system of today (Equal Temperament) it is in fact 14% out of tune, and it poorly harmonises with the g note. This system (Equal Temperament) is a compromise for fretted instruments, but it bugs me.

But, I have found a simple way to solve this issue. It won't be a solution for all, and possibly I am the only one. But I thought I would share in the event someone else found interest in it.

I cut a slot in the nut for the B string so the point of contact for the string is set approximately 5mm back towards the peghead. I was worried this would create string buzz, but there is no buzz at all. Cutting the nut slot this way effectively made the distance between the nut and first fret 14% longer, which is exactly where it needs to be for pure harmony (Just Intonation).

I simply tune the B string till it harmonises most sweetly with the open G string. The B string ends up being 14% flatter, and in Just Intonation. The B string now sound so beautiful.

There is a few compromises, as there is in any tuning system (the standard tuning and fretboard system that 99.999% of people use is a compromise, although many may not realise).

The remainder if my entire fretboard is still in Equal Temperament. The only note that is in Just Intonation is the open B. But that is ok with me. The only note that I really wanted to fix was the open B. For me, this is a better compromise than every note being in Equal Temperament.

It won't work in any other tunings (eg double C, or G modal). But I solved this problem by cutting two slots in the nut for the B string, right beside each other (in the attached image the string is sitting in the second nut slot, usual slot is visible right beside it. One used when in Open G, the other for any other tuning. I can easily swap the string over to the other slot by just lifting it over, it takes about 5 extra seconds, but since I am retuning anyway, no big deal.

It won't solve any issues when using the capo, but nor does it create any. When capoed to Open A all notes will be in the exact same tuning as any other instrument (Equal Temperament).

I cut the slots by simply angling the slot back towards the peghead (angled in the complete opposite direction to how you would normally cut the slot). Diagram below. Standard nut slit is in red pen, Just Intonation nut slot in black pen. The slot angle was quite sharp to prevent string buzz.

Certainly no commercial use of this idea. But for me, it has lead me to fall back in love with Open G tuning and enjoy pure harmony.


Dan Gellert - Posted - 09/01/2024:  10:14:40


This is exactly the same idea as the split 2nd fret you see on some 19th-c. banjos-- you get a just third in the most natural home key for the standard tuning, which then was (relatively) gCGBD ("low bass").

A good idea, but there's no free lunch... make one interval sweeter, and others will become more sour. In "normal" banjo music, the only one you'll be up against regularly here is that the just 3rd is going to be way out of tune with the tempered 6th. The relative minor chord to the home key tonic is not going to sound pretty. IMO that's especially problematic in open G-- I seldom play a full e minor chord, but will often sound the B on the open 2nd string against the E fretted on the 1st.

Old Hickory - Posted - 09/01/2024:  11:52:33


Congratulations. Except for the original idea of a second slot for different tunings, you've partly reinvented the Stelling compensated nut.



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