Are you tuning your 5th to A, or are you spiking it at the 7th fret for an A? That would make the difference. I just tried it on my banjo. When I’m spiked at A, the 10th (12th unfretted) fret sounds just like Ben’s video.
Discuss the Banjo lesson: Arkansas Traveler
I am tuning the 5th string to A. My Fender does not have spikes.
Yup. That’s definitely the difference. I had to get a B spike for that very reason when I was learning Dancing On My Grave. I tried spiking at C and tuning down, but it made it impossible to fret the 5th string where I needed.
I am confused, how would fitting a B spike make a difference in my case. I am tuned to A, the 12th fret (10th using a capo) sounds an E note and the 10th (8th using a capo)sounds a D note. To my ear the E note is too high for this tune but that just may be me. The TAB displays a D note.
Sorry, I didn’t mean the B spike would help in your case. You need an A spike for the same reason I needed a B spike. Your song is in A and mine was in B.
If you tune your 5th string to A, every fret will be 1 full step up from what it would be playing if you spiked at the 7th fret. Your ear isn’t deceiving you. You’re hearing an E instead of a D because your string is tuned 1 step higher than what you’re hearing in Ben’s video.
Think of it like this. If your 5th sting is tuned to G and you spike it at the 7th fret, the string itself is still tuned to G. It’s just as if you’re constantly fretting that 7th fret for an A note. Now, if you tune the string to A and you fret the 5th string at the 7th fret, you’re going to hear a B. That will be the case for every other fret as well. They’ll all be 1 full step above where you’d expect them to be.
Ok, So are you suggesting @BanjoBen 's banjo is not spike at the 7th fret? ie. not tuned to A
Whether the 5th string is tuned to A or spiked at the 7th fret the result at the 12th fret will be the same. An E note at the 12th. Am I correct ?
Archie, he is fretting the “actual” 12th fret…in tab it would be designated as the 10th fret because the capo is up to frets…the TAB matches the video…the TEF does not…
I’m saying Ben’s 5th string IS spiked at the 7th fret, giving it an A note, which is functionally different from tuning the 5th string to A without using a spike.
https://banjobenclark.com/lessons/arkansas-traveler-banjo/video/a-parts
Check out this video at 0:38.
Hi Dave, I realise that and that’s what I am doing. But the sound of my banjo fretted at the 12 fret (10th fret in this case because we are in A tuning) doesn’t sound right and I am thinking is this a typo, should I be fretting the 10th fret ( 8th fret in this case because we are in A tuning)
I agree on the video @BanjoBen is fretting the 12th fret with his thumb but what I am hearing on the video is a much lower note than I get on my banjo at that position. This is what I am seeking clarification on.
are you sure your banjo isn’t actually playing at a higher fret than your fingering?
Ok I turned my tuner on fretted the 5th string at the 12th fret it displays an E note. Fretted at 10th Fret it displays a D note.
If the string is tuned open to A…
Then I’m thinking the increased tension is causing it to fret sharp up the neck (i.e.Mark’s comments)
How does your 5th string sound tuned to A and fretted at the physical 12th fret. Maybe that comparison may answer my query.
OK. Let’s start from scratch.
5th string tuned to G:
5th fret (not fretted) - G
6th fret - G#
7th fret - A
8th fret - A#
9th fret - B
10th fret - C
11th fret - C#
12th fret - D
5th string spiked at 7th fret:
5th fret (not fretted) - Nothing
6th fret - Nothing
7th fret - A (That’s where the spike is.)
8th fret - A#
9th fret - B
10th fret - C
11th fret - C#
12th fret - D
5th string tuned to A:
5th fret (not fretted) - A
6th fret - A#
7th fret - B
8th fret - C
9th fret - C#
10th fret - D
11th fret - D#
12th fret - E
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Mark has it figured…
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Right now I follow you. So because my fifth string is tuned to A rather than spiked at the 7th I should therefore fret the 5th string at the 10th fret to get my D note. And that’s the reason my 5th string fretted at the 12th sounds out…
I guess I need to go back and revisit @BanjoBen 's lesson on the use of capo’s,
Thanks @Mark_Rocka your my hero 
Adding a wee footnote here for @BanjoBen . Might be worth reminding student’s of this little anomaly next time you do a lesson that involves fretting the fifth string. Not all banjos have spikes
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If you can, that’s the way to go. In the cases where I was retuning the 5th string, I couldn’t physically get my thumb in place in time to make the note. Your mileage may vary.
Glad I can return the favor every now and then. 
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Oh, and I don’t know what the shipping would cost, but these little guys are GREAT if you’re missing a needed spike.