Tonal music theory (Baroque/Classical eras) is based on chord progressions; Romantic theory uses "borrowed chords"; twentieth century theory was set on pitches in patterns, where equality of pitches was deemed. It would be beneficial for you to research chord progressions to view how chords maintain common pitches, or use "leading tones" to resolve to other pitches, in successive chords. Music students and composers study compositions by master composers. Analyzing a Bach composition may help you see which chords and progressions Bach used when moving from one idea to the next.
What exactly should I have to learn to understand why certain combination of chords are harmonic when played in a sequence?
I am an intuitive music composer trying to move to a technical music composer. As a dummy, I see music as a composition of 'pieces' (my word). Each piece is a set of notes that are melodical when played in a particular sequence and in particular intervals. As the music would be very boring if it was composed of a single piece repeating over and over, you are required to compose several pieces and glue them together to produce a pleasant song.
As an intuitive composer I do manage to arrange several melodic pieces, but I lack the ability to compose other pieces that are melodical/harmonic with the first so that the whole forms a song.
I'm pretty sure that there's a lot of theory in finding combinations that are melodical/harmonical. There must be a way to say that 3 different chords are likely to form music. That given 2 chords, the third must be X and so forth.
The question is: What do I have to learn?
I'm pretty sure it has something to do with harmony, but I'd really be happy to know what exactly in harmony would answer my questions.
Thank you
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