A fifth pulsates 1.5 times faster than its base tone. If you put another fifth to the first fifth and repeat putting further fifths, after 12 fifths you will get a tone which is very similar to the base tone: It is its 7th octave. ( 1st octave pulsates 2 times faster as its base, 2nd oktave 4 times,...,7th octave 128 times faster.) If you only put 7 fifths instead of 12, you get octaves of all tones in a Major or minor scale. These facts prove:
=> 12-Tone Scale in Music is a universal law of nature!
7-Tone-Major- and minor-Scales are harmonical laws of nature as well!
12 fifths make up 7 octaves of a piano and these 85 tones are all in the range of a human ear.
But there is a very little pitch: After 12 fifths you would not get exactly the 7th octave, meaning a tone that pulsates 128 times faster but a tone that pulsates 129.74 times faster.
But if we change the fifth factor slightly from 1.5 down to 1,4983 then we get exactly the 7th octave! That is why since about 400 years a piano gets tuned using this factor instead of the pure fifth factor 1.5, to get this closed 12 tone system of a well tempered piano. (see also: "Pythagorean comma", "Well temperament").
This little difference from factor 1,4983 to 1,5 cannot weaken the Harmonical 12-Tone Law of Nature, because it doesn't produce a dissonance, but a comfortable vibration instead.
To prove the quality of this tuning J.S.Bach composed fugues in each of the 12 scales in this system.
In contrast to 12-tone scale, the 13-tone scale of Bohlen-Pierce (BP) ist not useful according to harmony, because the most important overtone, the octave, doesn't exist in BP. This absence affects BP Melody like a genetic defect affects human lives. Further disadvantages of BP are: It has much less tones in the range that can be heard by humans, it doesn't sound good together with 12-tone scale, and for dissonances you also don't need BP . => BP can be seen as a kind of "Anti-Music", just to demonstrate the great quality of 12-Tone-Scale by the inferiority of BP.*)