Voltage divider, adding voltages back?

I am working on detecting fingers being placed on guitar frets. My idea is to run a small voltage through each of the strings, a different voltage for each string. The player touches the string and makes the string touch the fret. On the end of the fret I detect the voltage with an Arduino (analog input). Since each string has a different voltage, the system can detect which string is touching the fret. So far, so good. But when two strings touch the same fret, I don't get the addition of the two voltages. The voltage goes down. How would I go about to solve this? How do I add voltages or detect multiple strings touching a fret?

I am using a 5V input and then using resistors as voltage dividers to get the different voltages for each string. See schematics attached.

But when two strings touch the same fret, I don't get the addition of the two voltages.

Correct, you simply short together two voltage sources.
Sorry but basically this is a flawed idea, and it will not work.

You are not the first to think of this away of detecting a string’s contact with a fret, but I haven’t seen such a question for about six years.

The only solution I think is to split each fret into six separate sections and wire that up, but that is a lot of wires. The wires from each sub fret would go into a conventional voltage summing circuit using an op-amp.

You might, possibly, maybe be able to get something to work if you put different values of resistors in series with each string then measure the resistance in contact with the fret. You would need to choose resistors so as to give unique values for every possible combination of strings. Do a search for R 2R resistor ladder.

I am suggesting this as a highly speculative idea, I've not thought it through properly and I certainly have not tried it.

I think a MIDI guitar (or MIDI guitar adapter) works by detecting the frequency being played by each string (essentially a separate pick-up for each string). But, it seems like a lot of people have had trouble making a guitar tuner from an Arduino so detecting the fundamental frequency (or note) from a guitar string is not as easy as it might seem...

Remember that when a string is against say the fourth fret, then it is also in contact with the first, second and third frets. This then shorts out any such system for another string to be on say the second fret.

Keep it simple initially.

Start with 1 string electrically isolated at the tensioner end.

You could apply a voltage to it at the fixed end, then detect when it touches a fret.

Then activate each string seperately in turn, from its own digital output, with diodes to prevent reverse conduction.

Surely when a string is played it should only touch the frets above & 1 below the finger?

(my melodeon doesnt have strings as you may have guessed)

It seems to me it would make much more sense to detect the frequency of the sound and displace the note (whole, flat etc) on an LCD. Audio Spectrum analyzer and FFT would nail it but , unfortunately, is not a practical solution for
a beginning hobbyist. Maybe someone knows a simpler way to detect the frequency. Music stores sell a pocket tuner but I think that just generates notes and doesn't detect them. Not a musician so I don't know. Obviously, more
than one string will result in harmonics so that would make it even harder to detect (I would think).