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Do you have a computer as well as the tablet? If not, I would start by downloading an RTA app. I like being able to see resolution that's better than 1/3 octave, but only because I'm a control freak human hearing is sensitive to the level of 1/3 octave but that won't show deep troughs in the response that are very narrow, so I use REW when I have my laptop and mic, JL AUdio's RTA app when I only have my iPhone.
Did you try using Audyssey and have bad results? I have found that starting with the best speaker position helps, whether Audyssey is used, or not.
Google Room EQ Wizard and you'll see several links. They have a tutorial and they show suppliers- the mics I have seen mentioned most often are the Behringer ECM8000 and the Dayton version- the difference is that the Dayton comes with a calibration curve that's specific to each mic and the Behringer is a general one, so the variations aren't known. I have one and it seems to work well, but the Dayton hadn't become available when I bought it. The mic input on most sound cards is good enough for this and the brand/model of the sound card will be determined by the software- you would need to provide the mic's info. If the computer doesn't have a mic input, you'll need some kind of USB interface- I use a Tascam US122L, but many brands and models are available. If you want to keep the price down, look on ebay or Craig's List in Musical Instruments.
The mic in a computer may be good enough for this- mine isn't- when I use that, the response curve dumps at about 3.5KHz and doesn't show much until around 16.5KHz, which I know is wrong because I can hear it and this was confirmed when I connected my ECM8000/US122L.
However, the computer's mic is good enough to show the nulls in the low end and mid-bass, which is what you're really concerned with. Run REW and use the RTA and you'll be able to watch the response change as you move the mic. I used it when I positioned the acoustic panels in my living room and watched as the response trough gradually disappeared. Moving main speakers and subs will show the problems to the extent that's possible in your room.