Why do music key signatures work? Is there science behind why music scales sound good only with the correct notes?

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Answer 1

In western music, an octave is divided into 12 equal intervals called semitones. Key signatures sound good because of the way that tones resonate and interact with each other; it works because ratios of the sound frequencies between the pitches on the scale are equal, so it’s easy to find those notes that harmonise.

Visually if you were to show each semitone as a soundwave, the higher the frequency/ pitch, the tighter the sound wave becomes. The peaks and troughs of these sound waves are related, and can either clash or harmonise.