Pianist Vijay Iyer is one of the most original jazz musicians of his generation. He also has a Ph.D. in music cognition and the rare ability to describe the interplay between music and the brain.

PermalinkSubmitted by Robert Thomas (not verified) on Tue, 07/16/2013 - 6:22pm

"Fascinating"? Yes indeed but not surprising. People have been using math to explore music, in the Western tradition, for millennia.

The "Golden Ratio" (or nearly this number) appears a lot in organic structures because it's an algebraic number related to the square root of five.

If you draw two squares (with sides of length equal to one) side-by-side, so that the squares share one side and then draw a line diagonally from the lower left corner of the square on the left to the upper right corner of the square on the right, "phi" (the Greek letter referring to this ratio) is the sum of: [one half] plus [one half the length of this diagonal line]. In a math expression this is

(1 / 2) + (sqrt 5 / 2)

You can see that this number is closely related to the geometry of two living cells of roughly the same size, packed next to each other (you can also easily construct a line segment of this length using two adjacent same-sized circles that touch each other at one point). As cells or other compartments grow in an organism, it shouldn't be surprising that this number shows up in their structures. You can also see that a sequence of numbers each of which depends on the value of the two (adjacent) immediately preceding neighbors might also appear in this geometry.

Whether art works that incorporate phi as a value of proportionality (width of face : height of face etc.) are more "pleasing" or whether they really aren't special in this way is a separate question.

There's no question that the talented Mr. Iyer's accomplishments are impressive, either way.

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## Fascenating Fibonacci

"Fascinating"? Yes indeed but not surprising. People have been using math to explore music, in the Western tradition, for millennia.

The "Golden Ratio" (or nearly this number) appears a lot in organic structures because it's an algebraic number related to the square root of five.

If you draw two squares (with sides of length equal to one) side-by-side, so that the squares share one side and then draw a line diagonally from the lower left corner of the square on the left to the upper right corner of the square on the right, "phi" (the Greek letter referring to this ratio) is the sum of: [one half] plus [one half the length of this diagonal line]. In a math expression this is

(1 / 2) + (sqrt 5 / 2)

You can see that this number is closely related to the geometry of two living cells of roughly the same size, packed next to each other (you can also easily construct a line segment of this length using two adjacent same-sized circles that touch each other at one point). As cells or other compartments grow in an organism, it shouldn't be surprising that this number shows up in their structures. You can also see that a sequence of numbers each of which depends on the value of the two (adjacent) immediately preceding neighbors might also appear in this geometry.

Whether art works that incorporate phi as a value of proportionality (width of face : height of face etc.) are more "pleasing" or whether they really aren't special in this way is a separate question.

There's no question that the talented Mr. Iyer's accomplishments are impressive, either way.

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