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After a year of intensive Music Theory classes every weekday at 9 AM, hopefully I can explain it to you with the extent of my knowledge.
This is how it works fractally.
The piano is an accurate diatonic and chromatic representation of tones, so I will use it as an example in my next sentence. Music is a series of chords being followed by other chords with common tones. If you look at a piano and play a C Major triad for example (CEG), then the next chord sounds better if it either contains both common tones of C major triad C and E (making an A minor triad ACE); and E and G (making an E minor triad EBG), or contains at least 1 common tone - like the F major chord FAC and the G major chord GBD. As a result, there are always 4 possibilities for which chords to move to next from tonic in your key (that is the fractal part).
To elaborate, let me explain how this relates to roman numeral analysis. You use roman numerals to label scale degrees (basically do, re, mi) if you want to stay in key (which is an important part of how chords are supposed to work). The point is to divide the triads into scale degrees using roman numerals (I know its confusing, bear with me). Let my example explain it for you. Firstly, remember that a capital roman numeral means that it is a major triad and that a lower case roman numeral means it's minor. (LOOK AT A PIANO ONLINE FOR THIS PART) In the key of C Major (looking at ONLY white keys) roman numeral I would be the triad CEG, ii would be DFA, iii EBG, IV FAC, V GBD, and so on.
And that's only the tip of the ice berg!
Feel free to ask any questions.
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