Re: A simple trick for getting your intervals closer to 'purity'..
detuning your notes to fit in closer with harmonic series of overtones is something which will give you the purity you want.
Making the lowest common tone the highest frequency it can be will give you consonance in the chord. Thats what it is all about.
The simple Euclid algorythm of minusing the difference of the frequencies until the integers become the same.