The decision to divide an octave into 12 equidistant sound points and assign 7 of them as natural notes and 5 as sharps or flats is based on the Western music system, specifically the 12-tone equal temperament system. This system has been developed over centuries and has become the standard tuning system in Western music.
The concept of dividing an octave into 12 equal parts can be traced back to the ancient Greeks, but it was not widely adopted until much later. In the 16th and 17th centuries, various tuning systems were explored, including systems with more or fewer divisions of the octave. However, it was the 12-tone equal temperament system that gained widespread acceptance.
The 12-tone equal temperament system divides the octave into 12 equal intervals called semitones. Each semitone represents the smallest perceptible pitch difference in Western music. The seven natural notes (A, B, C, D, E, F, and G) are placed at specific positions within these 12 semitones. The remaining five points are assigned to the sharp or flat versions of these natural notes.
The decision to have seven natural notes and five sharps/flats within an octave is rooted in the diatonic scale, which is the basis for much of Western music. The diatonic scale is a sequence of seven notes that follows a specific pattern of whole steps and half steps. By incorporating the sharps and flats, the 12-tone equal temperament system allows for the flexibility to play music in various keys and tonalities.
It's important to note that this system is not the only way to divide an octave or represent musical pitches. Different cultures and musical traditions around the world have their own tuning systems and scales, some of which use different divisions of the octave and have different numbers of natural notes and accidentals (sharps or flats). The choice of 12-tone equal temperament in Western music is largely a historical and cultural convention that has endured over time.