I'm using a Moto G 2nd gen (XT1072), with the default launcher (Android 6.0)

The most feasible way I can think of as of yet is to do this with the NDK and C++. This will require me to first build a working analyser in C++, so it will be added to a different backlog than all Java or resource adjustments/improvements.

Interesting links to get started:

/u/Terra_corrupt's simple and portable beat detector (might get some licensing issues since it uses FMOD)
A general idea on cboard on how one would implement such a thing.
An interesting PFD that covers the logic behind analysing the BPM.
/u/beavioso suggests looking at the RMS which is also doable, but might require more than the processing power I want this to take.
This blog post talks about beat detection in Java (which I assume will be miles slower than doing it natively).
Another resource that talks about BPM detection. Love the website design too!
And lastly, this website shows some options to take into consideration regarding genre and best approaches.

Most logical way of analysing the BPM:

This will be my second attempt at a C++ thing that actually works without flooding me with segmentation faults, so I might consider just doing it with Java if faeces start hitting the ceiling mounted whirling device... Also, it's worth noting that even though it could work when compiled by my system, the Android system might want to compile it using different headers.

UPDATE:

this library promises a lot of the good stuff :D (although it does require me to sign up... wat.gif)
this library also covers a lot of the good stuff. But I can't really find any good documentation am blind

If a user hasn't visited the settings yet he might not know the level of precision the app is using. Wouln't it be better if said something to let the user know. Perhaps 'value below precision point' serves the purpose, but it's long. Or maybe at least show 0 alone without the decimal point.

The app crashes when you try to enter a number in a field if you have a phone with Dutch locale.