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Each note of a scale has a particular name called, Scale degrees. We will use them to single out notes function in chords.
First, let's have a look at what a Tetrachord is. To me, it is fundamental to understand and to feel the concept of a Tetrachord.
One can easily notice that the lower and upper Tetrachord is exactly the same, One tone, one tone and, a halftone. The halftone between the 7th degree (B) and the "upper tonic VIII, C" is called Leading Tone, since B is greatly attracted by C. The same with the IV degree F, he wants to go downwards to E. This downward and upward motion is "orchestrated" by the Tritone placed on the IV and VII degree. Also to mention that the upper tetrachord begins with G which is called Dominant. The term Dominant is associated with its position in a key. The fifth note of the scale and the chord built on that note give a perfect 5th. (P5). See the table"Type of chords"
This time one has a G7 scale with a G7 Chords called Dominant 7th chord. Although the notes, from the lower and upper Tetrachord one, are placed the same, now one has the Tritone that has moved one step down. What does that mean? We have seen that B wants to reach C and at the same time F wants to do the same but downwards, one has then the reconstitution of the C chord (Tonic) with the notes C and E adding then the fifth degree G.
Finally, we have come to the final step, to resolve the Dominant G7 chord to the Tonic C chord. Motion that is called perfect cadence. The Fifth degree resolving to the first degree by a downward and upwards motion (F to E) and (B to C). The 7th up to the 1st and the 4th down to the 3rd. Pay attention to the G scale degrees. G is, effectively, the 5th degree in C tonality. We come to the conclusion that the Function of a Dominate Chord is to resolve on its Tonic. See, the circle of fifths Scales.