A scale is a collection of pitches that follows a set pattern of ascending or descending intervals. A major scale, for example, may start on any note, as long as the subsequent notes follow the appropriate pattern of whole steps and half steps. The same is true of minor scales—but with a different pattern of steps, of course.
Since there are so many major and minor scales, all with differing pitches, it can be useful to refer to the steps of the scale by numbers rather than notes. These numbers are called “scale degrees” and are assigned in ascending order, beginning with the lowest pitch as 1. You may also hear scale degrees referred to by more technical names, as shown below. (Scale degree 7 has two names, depending on whether you are in major or minor.)
A note’s scale degree gives you an idea of how the note will function in a piece of music written in the scale’s key. Music is all about creation and release of tension—so the function of a scale degree has to do with the amount of tension it creates and where it “wants” to move next in order to resolve the tension. The most important functions to understand are those of scale degree 1 (tonic), scale degree 5 (dominant) and scale degree 7 (leading tone or subtonic, depending on whether you are in major or minor, respectively).
The tonic is the tonal center of a key; it is like home base, where all harmonic tension is released. You will notice that nearly every piece of music ends on the tonic, or a chord built on the tonic.
The dominant is the second most important scale degree in establishing the key in your ear. It is harmonically strong, so it often has the effect of creating an uplifting mood. The dominant is further strengthened by moving to the tonic—but of course, just because it wants to move there doesn’t mean it always does. Often, a songwriter or composer will continue to draw out tension in order to make the final resolution more meaningful.
Scale degree 7—the leading tone or subtonic—creates more tension than any other. In a major key, 7 is called the leading tone because it so strongly wants to lead up the half step to the tonic. In a minor key, it wants to drop down a half step to 6. Unlike the dominant, this scale degree and the chords built on it are harmonically weak, and sound somewhat unstable.
While these three scale degrees have the most firmly defined functions, the rest have unique roles and qualities, too. Scale degrees 2 and 6 gravitate toward and strengthen the dominant; the harmonically weak 3 gravitates toward 4 or 6; and 4 often leads to the tonic, especially for the purpose of creating a gentle resolution rather than a strong one.
Who wrote this ignorant post? (sorry to be blunt)
“The most important functions to understand are those of scale degree 1 (tonic), scale degree 5 (dominant) and scale degree 7”
What about the third? Isn’t it important?
The harmonic series suggests consonance and strength, and in further depth, it hints at the gravity between different functions as mentioned.
Consider the order and ratios(strength) of the first six intervals of the harmonic series:
1:1 fundamental/unison, 2:1 octave, 3:2 perfect 5th, 4:3 perfect 4th, 5:4 major 3rd, & 6:5 minor third.
Then consider the pitch-class repetition in the first 16 harmonics:
root 5x, perfect fifth 3x, major third 2x, minor seventh 2x.
Some instruments favor either even or odd harmonics – strings favor even, so, of this set:
root is even 4x, fifth is even 2x, the rest are even once.
But of course, your third is going to define the color, even if it’s substituted(/sus’d) with a second or fourth.
Still, there’s nothing incorrect with the information provided.
src: sengpielaudio(dot)com(slash)calculator(dash)harmonics(dot)htm