user26341: I'm building a MIDI guitar, using an Arduino, sound synthesising and wood.
To properly know which note I'm pressing, I built a voltage divider with 12 equal resistors (10K). One side is connected at +5V and the other end at GND, so each of the 6 strings connects the right tap to the ADC. 
I had just calculated the expected value w/ a bit of math considering I also needed a pullDown resistor(1M) and capacitor for every analog channel to keep the readings stable when no key is pressed.

When measuring with my multimeter the readings are stable, and there are variations of less than 0.02V, and since the difference from tap to tap is about 0.4V that's quite good. 
The problem is when reading the 6 channels together: channels supposed to be pulled down to gnd read voltages caused by nearby channels, readings are shaky and similar errors.
This mess disappears on one channel when I connect the multimeter to that one.
Instead of buying 6 multimeters, I figured I could ask you if someone has an idea on why this happens, my guess is on the pulldown resistor, but I'm not sure about Arduino's ADC; I'm also worried about having 6 wires half of a meter each so close, so any other idea on finding the keys is welcome.
EDIT
@EdgarBonet was right, I used 12x220ohm resistors, and at first the results were absolute garbage, then I made it so the code would read each channel about 10 times, discard the readings, wait a millisecond and finally read and store the value. Now it is perfect.
Thanks again.

user7508: The datasheet of the ATmega328P (the main chip of the Uno) states:

The ADC is optimized for analog signals with an output impedance of
  approximately 10 kΩ or less.

The Thevenin equivalent output impedance of most taps of
your voltage ladder is higher than 10 kΩ. You 1 MΩ pulldown is
way beyond that limit. Cross talk from previously read channels is
exactly the symptom you expect from excess output impedance.
Taking each reading multiple times, until the value stabilizes, should
help. A buffer (e.g. an OP-amp set as a unit gain amplifier) is the
usual solution to this kind of impedance problems.


Actually, the whole works perfectly with R as 220 and pull downs as
  10K. The problem comes when connecting more than 3 strings at the same
  time, on any tap, as the pull down resistors become part of the
  ladder (i belive).

The pull down resistors will indeed have an effect on the potentials of
the voltage ladder, especially if you connect several strings. This
could be minimized by having the pull-downs be a lot more resistive
than the resistors along the ladder, but then you would need very low
resistances along the ladder, which is not desirable because of current
consumption and heating.
Here is an idea for an alternative solution: If you can spare 6 digital
pins, you could build for each analog input a pull-down circuit that is
switchable between a “strong pull” mode and a “weak pull” mode. Assuming
D0 is the “pull strength control” pin for A0, it would look like this:
A0 ---+--- 1 kΩ --- D0
      |
     1 MΩ
      |
     GND

Whenever you want to read A0, you:

set D0 to OUTPUT LOW, which creates a strong pull-down to ground
take a couple of analogRead()s
set D0 as INPUT, which leaves only the weak 1 MΩ pull down
take a couple of analogRead()s, keep the last one.

If A0 is not connected to the ladder, then the first reads will
discharge the internal sampling capacitor of the ADC. The final read is
done with only a weak pull-down, but this should be OK since the
capacitor has already been discharged.
The potentials along the voltage ladder will be disturbed by any string
connecting a tap to its strong pull-down, but this disturbance will
disappear when you switch to weak pull-down, so it will not affect the
readings.

26341: <p>I'm building a MIDI guitar, using an Arduino, sound synthesising and wood.</p>

<p>To properly know which note I'm pressing, I built a voltage divider with 12 equal resistors (10K). One side is connected at +5V and the other end at GND, so each of the 6 strings connects the right tap to the ADC. 
I had just calculated the expected value w/ a bit of math considering I also needed a pullDown resistor(1M) and capacitor for every analog channel to keep the readings stable when no key is pressed.</p>

<p><a href="https://i.stack.imgur.com/bZM2i.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/bZM2i.jpg" alt="circuit"></a></p>

<p>When measuring with my multimeter the readings are stable, and there are variations of less than 0.02V, and since the difference from tap to tap is about 0.4V that's quite good. </p>

<p>The problem is when reading the 6 channels together: channels supposed to be pulled down to gnd read voltages caused by nearby channels, readings are shaky and similar errors.<br>
This mess disappears on one channel when I connect the multimeter to that one.
Instead of buying 6 multimeters, I figured I could ask you if someone has an idea on why this happens, my guess is on the pulldown resistor, but I'm not sure about Arduino's ADC; I'm also worried about having 6 wires half of a meter each so close, so any other idea on finding the keys is welcome.</p>

<p>EDIT<br>
@EdgarBonet was right, I used 12x220ohm resistors, and at first the results were absolute garbage, then I made it so the code would read each channel about 10 times, discard the readings, wait a millisecond and finally read and store the value. Now it is perfect.
Thanks again.</p>
 7508: <p>The datasheet of the ATmega328P (the main chip of the Uno) states:</p>

<blockquote>
  <p>The ADC is optimized for analog signals with an output impedance of
  approximately 10&nbsp;kΩ or less.</p>
</blockquote>

<p>The <a href="https://en.wikipedia.org/wiki/Th%C3%A9venin%27s_theorem" rel="nofollow">Thevenin equivalent</a> output impedance of most taps of
your voltage ladder is higher than 10&nbsp;kΩ. You 1&nbsp;MΩ pulldown is
way beyond that limit. Cross talk from previously read channels is
exactly the symptom you expect from excess output impedance.</p>

<p>Taking each reading multiple times, until the value stabilizes, should
help. A buffer (e.g. an OP-amp set as a unit gain amplifier) is the
usual solution to this kind of impedance problems.</p>

<hr>

<blockquote>
  <p>Actually, the whole works perfectly with R as 220 and pull downs as
  10K. The problem comes when connecting more than 3 strings at the same
  time, on any tap, as the pull down resistors become part of the
  ladder (i belive).</p>
</blockquote>

<p>The pull down resistors will indeed have an effect on the potentials of
the voltage ladder, especially if you connect several strings. This
could be minimized by having the pull-downs be <em>a lot</em> more resistive
than the resistors along the ladder, but then you would need very low
resistances along the ladder, which is not desirable because of current
consumption and heating.</p>

<p>Here is an idea for an alternative solution: If you can spare 6 digital
pins, you could build for each analog input a pull-down circuit that is
switchable between a “strong pull” mode and a “weak pull” mode. Assuming
D0 is the “pull strength control” pin for A0, it would look like this:</p>

<pre><code>A0 ---+--- 1 kΩ --- D0
      |
     1 MΩ
      |
     GND
</code></pre>

<p>Whenever you want to read A0, you:</p>

<ul>
<li>set D0 to <code>OUTPUT</code> <code>LOW</code>, which creates a strong pull-down to ground</li>
<li>take a couple of analogRead()s</li>
<li>set D0 as <code>INPUT</code>, which leaves only the weak 1&nbsp;MΩ pull down</li>
<li>take a couple of analogRead()s, keep the last one.</li>
</ul>

<p>If A0 is not connected to the ladder, then the first reads will
discharge the internal sampling capacitor of the ADC. The final read is
done with only a weak pull-down, but this should be OK since the
capacitor has already been discharged.</p>

<p>The potentials along the voltage ladder will be disturbed by any string
connecting a tap to its strong pull-down, but this disturbance will
disappear when you switch to weak pull-down, so it will not affect the
readings.</p>
