overtones,
It sounds like a spectrogram would be very valuable to you. You can take a look at our Mac software for sample
spectrogram displays.
For now, with SignalScope on iPhone, your best bet may be to work with a linear frequency scale and a dB magnitude scale. Increasing the number of spectral lines will improve the frequency resolution, but it will slow down the responsiveness of the spectrum display. A little trial and error can help you find a setting that you like best.
The harmonic cursors may also be helpful.
Enjoy!
Ben