In the Western music tradition we would call this method 'detuning' or 'microtonal shift'
In the western music tradition there are scales which follow the pattern
Whole Whole Half, Whole Whole Whole Half
This means that from one note to its octave higher we can play a "scale" that sounds like beautiful travel up the notes to the next tonic (like from D up to D, or C to C)
If you look at the staff with the word "common line" to the left and you start on the higher D, you can see the scale wrap around in the fashion
1 1 .5, 1 1 1 .5 (whole whole half...)
Now look at the staff below this one and start on D again and wrap around
1 .75 .75, 1 1 .75 .75
This means that the Ds will sound the same as in the western piano tuning, as well as G and A.
The remaining notes of this scale ([d] E F [g] [a] B C) ... E, F, B, and C are all slightly different than in the western tuning. How are they different?
The X means to detune the "western traditional note" by 25 cents or 1/4 tone.
Detuning C, E, and F by 25 cents should make everything work because the total number of steps in the octave will still be the same as a "western" scale.