A simple math FORMULA behind guitar improvisation in order to STAY in position!!!

We can't call this improv engineering, but is more of a method.  Take it for what it is and run with it :)

So you are improvising on a tune that called for a change of key that is a 5th up (or 4th down)...example = from C major with all natural notes you will now go to G major with one sharp note which is F# (7th degree).

Here is the formula...

If you are playing on C major and are on the 5th position soloing on the Aeolian more (thus, A on C major), you can do some math, stay in place, and keep playing...so what is the formula?

STAY WITH ME PEOPLE.....PLEASE!!!
You take the mode number you were improvising "on" "in" C major...in this case you were playing on the 6th mode...so you take 6 and add the inverted interval of the key coming up...the key coming up was up a 5th and up 5ths are the same as inverted 4ths...so you add that inverted figure to the 6th we just mentioned, and subtract 1 from the result, but keep in mind that when you reach 7 in the process of adding you must NOT keep going to 8 but rather 8 takes the place of 1...so here is the example applied: 6 (original mode) + 4 (inverted interval) is equal to 3 (6+1=7+1=not 8 but 1+1=2+1=3)....then you always subtract 1 from any result...so the mode is 2....therefore by staying in position you would play the mode of 2 in G major...the mode of 2 in G major is precisely A Dorian...and you will be safe of course playing A Dorian in the key of G major!!! 

"Buyer beware"...this works every time but you must check for "accidentals" in the coming key.  For example once you do your math, the mode number will work, but the 1st note in the mode may need to get sharpened or flatted.  An example is IF you would have gone to the key of B major the formula would have given you a mode of 7...and YES!, you could play that mode but you need to sharpen the A to A# and play the 7th mode pattern a step up.

Hope you stayed with me...sounds complicated but it WORKS EVERY TIME...this lends itself to more vertical playing and seamless shifts of key on the neck.  It gives you the ability to maximize your creativity by not having to think of the shift and simply do some math even before the tune starts (if you get the chance).

I am currently developing an effective methodology to use this formula in a notation format.