@jake as a side note, unfortunately the cheap rigging tension gauge market ends at 10 mm. Larger yachts (44ft +) with 12 mm rigging or above have only the ruler method available. Second side note: the accuracy of the ruler method highly depends on the thermal stability of the ruler. Metal and plastic are bad, wood is good, however suspect to moisture.
As for acoustic analysis of the rig - it is a very sound idea and I have tuned my chainplate tie rods with a smartphone app (mast off). However these rods are very short, rather tight, and they create a relatively high pitch which also is amplified by the ships hull. Above deck, "string" lengths are way longer, as mentioned above.
If you're serious about measuring the rig tension acoustically, then a piezoceramic transducer clamped physically to the wire will have the resolution to measure the frequency. Quoting from Seldens tuning manual, a 19/20 rig cap shrouds should be tuned to 25% of the breaking load. For a 12 mm wire this is is 0.25*126 kN = 31.5 kN. Say for a 5.5 m distance on a 18m mast, to the first shrouds, the first natural resonant frequency is around 35 Hz. You will need an amplifier for amplifying the weak low frequency signal. You could then record it with Audacity and run a Fast Fourier transform on it.
Sounds pretty straightforward, but in reality probably will be way more complicated than the wooden ruler method
Noise will be your likely enemy, plus the X factor.
