There are some simple rules of thumb to help you think your way through.
On E9, open strings 3, 4, 5, 6, 8, 9 and 10 are an E7 chord with strings 4 and 8 as roots.
All the other strings, 1, 2, 5, and 7, are a B chord, with string 5 as the root.
On any chord, roots, 4ths and 5ths are approximately straight up to each other.
Major 3rds and 7ths are 14 cents (3.5 Hz) flat of the root. I round this to 12 cents (3 HZ).
Minor 3rds and 7ths are 16 cents (4Hz) sharp of the roots. Accordingly, the 6th of a major scale, which is the root of the relative minor that uses the same scale notes, is 16 cents flat of the major scale root. A 6th tuned that way works as either the 6th of the major scale I6 chord, or the root of the relative minor chord.
So you really only need to know 3 numbers: straight up (Hi, Eric
), -12 cents, +16 cents; or 440, 437, 456. In a pinch, you can forget about that extra 4 cents (1 Hz) for the 6th and minor 3rds and 7ths. If you tune everything either straight up, or 12 cents (3 Hz) one direction or the other according to the above rules, you will have very acceptable intonation in playing. So that's really only one number other than straight up.
So basically I tune everything striaght up to begin with. I know string 2 is the 3rd of the B chord, so I tune that to 437; and I know strings 3 and 6 are the 3rds of the E chord, so I also tune them 437. String 9 is the minor 7th of the E chord, so I tune that to 456. I'm done. I've only used two numbers other than straight up.
For Just Intonation there is no conflict between the E and B chords, because B is the V chord of the key of E, and so both chords are taken from the same E scale. Also, when tuning the A and B pedal stops, A is the IV chord of E, and so likewise is taken from the same E scale with no conflicts. This is one of the simplifying concepts that makes the E9 tuning work out so well with Just Intonation charts such as the Newman charts. The Newman charts differ from the above rules on some strings or stops by 1.0 - 0.5 Hz; but you would be very hard pressed to hear those increments outside of tuning alone in a very quiet room.
There are other refinements that can be added to the above. To compensate for about 8 cents (2 Hz) cabinet drop, I add 4 cents (1 Hz) to all the open strings; and I subtract the same amount from pedal or lever raise stops. So basically, my reference pitch for unpedalled open stings is 441, and for raise stops it is 439. This is very similar to what happens in the Newman chart that references the Es to 441. Lowers that release multiple or heavy gauge strings can actually cause cabinet rise. So I tune those stops 4 cents (1 Hz) sharp to match the rise that occurs in all the other strings. All these compensations are added to (or subtracted from) the above simple rules.
Another refinement is that I know on my 12-string uni, or on 10-string C6, bar pressure adequate to keep the strings from rattling causes the two lowest strings to go sharp. So tuning at the nut, I tune those two a little flat, and they sound right when I use my bar up the neck.
Also, one should know that the F# on strings 1 and 7 as tuned above will not work well as the root of the F#m chord with the B and C pedals. Some people split the difference. I tune as above, and get the F#m root by raising string 8 on my C pedal from E to F#. As the root of that minor chord, that stop is tuned 16 cents (4 Hz) flat of the A stops on pedal B, so that those As will be minor 3rds appropriatly 16 cents (4 Hz) sharp of the root of that minor chord.
When you put all those refinements together, you have a fairly complicated chart, something like the Newman charts, if you were going to memorize it from scratch. But if you know the simple rules above, and the two chords involved, you can easily think your way through tuning the open strings. And, with a few more chords and a little more thinking, you can tune stops if needed.
Of course it is way easier to take a single reference pitch and tune those chords by ear to what sounds good open at the nut. Then put the bar at the C fret (8th) and do some fine tuning. By doing that, I automatically do everything above.