As you can see, most of the notes of the scale are harmonized as the root of a triad, the exceptions being that the scale degrees that are members of the tonic triad (1, 3, and 5) or the dominant triad (5, 7, and 2) tend to be harmonized as either a tonic or dominant chord, even when the result is an inverted chord.
We can also create a chromatic “rule of the octave progression, in which each of the twelve chromatic pitches is harmonized in a way that makes the most functional sense in terms of C major:
The idea here is that, if you wanted to have a functional-sounding chord progression combined with the melodic pull of a stepwise or chromatic bass line, the “Rule of the Octave” progressions above could provide you with a possible solution—something relatively easy to remember that you knew would work at least reasonably well.
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Below is an example of a circle of fifths progression in C major and C