It incorporates elements of biology, mathematics, and physics.
When you play a tone at 440Hz, you produce an A note. Doubling the frequency to 880Hz changes the note to an A one octave higher.
To our ears, this sounds very similar, just at a higher pitch. Certain ratios within this range sound more harmonious, such as the “perfect fifth” (3:2) and the “major third” (5:4).
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Dividing the octave into 12 is not the only system (many folk music uses a 5-note octave), but since 12 is neatly divisible by 2, 3, 4, and 6, it creates a harmonious combination of notes. The corresponding ratios can be constructed easily.
This article addresses the question “Why are there 12 notes in an octave?” (asked by Noel Gibson of Bath).
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