What is the theory behind cord and harmony relationship? For the bars at the top of the page?
My copy of the music has 3 sections divided by double bars. The measure numbering is 1-16, 17-25, 26-33. That's 16 + (8+1) + 8 bars for the section lengths. I'm not sure why you ask only about the end of the middle section. I'll include the whole middle section along with the ending.
|B7 |Em |B7 |Em | |A7 |D |Am7 |D7 |G D7 || |G G7 |C C#dim7|D6 Em7|A7 D7 | |G G7 |C C#dim7|D6 Em7|A7 D7 G||
A few structural notes, because they are important to understand what's going on...
- B7 to Em, two bar phrase is repeated to make 4 bars, B7 is outside the key G major, but it is the secondary dominant of Em
- the bar I list as Em sort of looks like an odd scale, because it has a lot of step-wise movement, but it really just adds a bunch of non-chord tones to decorate a broken chord
- the next 4 bars are a harmonic sequence meaning the B7 to Em idea is dropped down a step to A7 to D, there are two small modifications in that the D is a major chord instead of minor like the Em, and when the A7 to D is repeated (following the pattern of the original B7 to Em idea) the A7 become a minor Am7, these changes in chord quality major/minor are common in harmonic sequences, the repetitions that happen in harmonic sequences can be chromatic or diatonic the choice is a matter of style and preference
- the change of A7 to Am7 above also reflects a pretty common thing in jazz which is a change from major quality to minor quality, sometimes it happens directly from one chord to the next, in this case there is a D chord in between
- the third section is a 4 bar phrase repeated with alternate endings, this kind of phrase structure is called a period, the harmony G G7 C involves the G7 which is technically outside the key of G major, this is another example of a secondary dominant, this time of the C chord, it is a very common move that emphasizes the subdominant tonal region, there are more secondary dominants but I won't list them all
I imagine your initial question was about all the various sharps and flats found in the score which don't belong to the key G major. That could make a person wonder if some strange scales from other keys were being used. As you can see those chromatic tones come from the harmony and all the chromatic chords are explained as secondary dominants.
I can't help but point out how this exercise from Peterson reflects so clearly a classical music convention. In a short work like this it is very typical of classical music to place the periodic phrases at the opening and closing sections, and put the sequential harmony passages in a middle section as a kind of bridge. Obviously Peterson is showing a classical sensibility. He even titled the other pieces in this collection 'minuets' and 'etudes.'
I didn't explain every concept in detail, but I emphasized in italics several topics which you can look up for further study. A good theory textbook will explain all of them.
Just adding my written notes, 'cause they're there...
You can see some chords are anticipated being struck just before the barline or the next strong downbeat.