…. Music Theory opened it doors for me. They also have modulation concept, and it so close to mathematics even in "reduction" as principle.
The composition became an interesting topic for me. Rhythm (Variation), Melody (Scales), Harmony (Chords).
It's a mathematical framework of sound over time. Imagine a Rhythm, it will lead you to a Melody, which eventually you will sweet it with Harmony.
Each of them, come with something I called it "Co-Structure" (Like Co-Set in Group Theory). When you algebraize the Rhythms, and manipulate it variables after. you will get a different variation. They are topologically equivalence, however, their "shape" could be different.
The same for the Melody. A Rhythm leads to Melody, which in it heart, the basic element unit of the musical composition. It is the abstract language of your composition, the message. The Co-Structure of it, is the scales. Which are the language alphabet. Scales like the dialect. Starting from the Major Scale with predefined intervals, then pick different start point, and that's another scale. Imagine the mathematical possibility of represent one a music piece with different scales & variations.
Finally, the harmony & chords, are like an extra structure you add it to make it good. Feel Good.
There is a circle, called, Circle of Fifths:
Can you see how beautiful it is? Look clockwise & counter clock. For example, Mozart k466 is written in d-minor scale, which is also called the F Major scale. A scale where only the B(Aka. Si) being Flattened, and the rest in natural mode.
The great thing here is, by the key signature, you can figure out the scale immediately. A good perspective of the scale, as the product of the reduction process, where the composer eliminate the redundant notes.
Then, transpose it! do a mathematical transformation, from the space of F Major to the space of C Major! and so on, with minor scales.
Nevertheless, this is only the western music! The Arabic music & scales (Maqams) are much rich, and fruitful.
© Random Thoughts, by Fares AlHarbi.