In Western music, the notes are based on ratios of pitch frequencies. If you take two frequencies, and one is exactly double the other one, we call those frequencies one octave apart. So it makes them the same note.
We then divide the octave into 12 evenly-sized intervals. Since the ratio of 1 octave is a factor of 2, that means the ratio of each interval is 2^1/12
This gives us certain very pleasing ratios, like the perfect fifth, 2^7/12 – which is very nearly 1.5. A 3:2 ratio of frequencies just “sounds right” to the human ear.
Really, it’s all mathematics. We’ve been using these same ratios since the ancient Greeks.
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