Abstract. It is possible to make a simple flute-like instrument using a straw. I used an electronic tuner to determine reference tones, and then located the required positions to create finger holes to form a diatonic scale. Pythagoras created Pythagorean tuning as part of his research into the relationship between scales and the length of strings. The oscillations that represent a scale and the length of the strings creating it can be represented by a geometric series, showing us the close association between music and mathematics.

Received: November 29, 2010

AMS Subject Classification: 00A65, 11A02, 97A20

Key Words and Phrases: reference tones, scales, Pythagorean tuning, geometric series, modular arithmetic

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