hi,
I realise that you are intending to use a 555 and pot, but I am trying to help you explain why all your Arduino frequencies are giving a doubled count value on the tacho.
I am trying to give you an idea for a simple reference frequency so that you can test the tacho for 'level or edge counting'
Ok, I don t have that 4u7 capacitor, I have 22u and 47u capacitors
Second thing, where should be output on your schematic?
Btw - I did schematic attached (rpm2.pdf) and is working but is not like I would. In the schematic attached I connected a 10k potentiometer between potm1 and potm2 and out to the device. I am not sure if this is answer your question
Update - I changed multiplier values in pwm library and I am close of what I want. So for the moment I will try make this work since is much easier to use only arduino timer
Will post some results after I have a conclusions
If there is a stable frequency available in the arduino OS, then you can use a count-down counter to generate precise time intervals for high and low time periods of your square wave signal. But in addition, it is not that complex to use a binary counter IC to generate frequencies dividing down from a stable known crystal oscillator frequency. Probably faster to design than some program to run on that little arduino board, and far easier to understand exactly what is happening.