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Math Meets Music

The Golden Ratio is not only aesthetically pleasing in art and architecture, it is found throughout nature in sunflowers, conch shells and spiral galaxies. Now a composer has put it to music.

New Scientist just posted an unusual article, "What the Golden Ratio Sounds Like." It includes a music video by composer Michael Blake, who wrote a tune based on the Golden Ratio phi. This irrational number (1.6180339887...) represents a condition where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. It's related to the Fibonacci Series, in which each integer is the sum of the two prior integers. The ratio of two adjacent numbers approaches the Golden Ratio as one proceeds down the series.

You may recall our recent entry that shared a stunning animation of how the Golden Ratio is tied to the Fibonacci Series and shows up throughout nature in surprising ways.

As Blake had previously done with pi (3.1416...), he assigned note values to the first 15 digits in the irrational number phi (1.61803398874989...) and composed a tune based on it. Then he expanded his melody into an instrumental composition rising in intensity and complexity. On the bottom of the screen, you can watch the digits of the series as they are played.

This is only one possible way to use the Golden Ratio in music, since variables such as timing, instrumentation and number of digits selected is subject, just as in nature, to the composer's intelligent design. There might also be ways to compose a piece based on the geometry of the Golden Ratio rather than its numerical representation.

But it's interesting to ponder the question of whether the ubiquitous number has the same pleasing effect on the ear as it does on the eye. Next, let's try the tongue and nose -- we hereby volunteer as tasters for the Golden Ratio pizza!