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Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?

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All about Ratios

Age 16 to 18 Challenge Level:

Finding several methods can often help us to a better understanding of the mathematics involved, giving us a richer experience than gained from simply finding the answer. Although these ratios can be found using coordinates and finding intersections of lines and distances, this is not the most efficient method.