Equal temperament is the system that has been use for the last two hundred years or so.   The two tuning systems above are based on the harmonic series to one degree or another and need to be re-calibrated or re-tuned for each key because the relationships of each note to the other is dependant on the beginning pitch.   The above systems are best used for melodic or modal type playing (or harmony by a large group or orchestra), whereas as equal temperament will be shown to reduce these problems (or solve).   As mentioned earlier the measurement of intervals generally used is called the cent. In equal temperament all ½ steps are equidistant.   Look at the chart below.

Pitch	Measurement in Cents	Interval	Ratio
C	0	Fundamental	1/1
C#	100	m2	7893/7450
D	200	M2	5252/4679
D#	300	m3	10754/9043
E	400	M3	6064/4813
F	500	P4	6793/5089
F#	600	A4	11482/8119
G	700	P5	10178/6793
Ab	800	m6	4813/3032
A	900	M6	9043/5377
Bb	1000	m7	17189/9647
B	1100	M7	17843/9452
C	1200	Octave	2/1

 

As you can see above all the minor and major seconds are the same distance away from the previous note.   Now we will look at a comparison of the three above systems.