a tetrachord is a series of three smaller intervals that span the interval of a perfect fourth, a 4:3 frequency proportion.
the circle of fifth is obtained from diatonic tetrachord (this is sh!t, there are too many difficult words for beginner guitarist like me to understand!). I’ll try to explain what is in my mind and let pictures redefine all these.
let’s divide an octave into 2 parts,
1 2 3 4 5 6 7 1 into 1 2 3 4 and 5 6 7 1
put them on a paper and write down the note intervals
now we have separated and identical intervals, 1 2 3 4 = w-w-h and 5 6 7 1= w-w-h
put the alphabet notes, then we have C D E F and G A B C plus the intervals.
the rest is easy. pay attention to the fifth note and observe how each fifth note is transferred onto the first(root) note. there you can see the number of sharped notes in each transferred note. here is the complete picture.
from that picture above, we can make a circle of notes called ” the circle of fifths”
here i share picture of it from wikipedia
please, correct me if i shared the wrong information via your comments. your feedback is my teacher. thanks