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Grade Level Grades 6-12
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The use of ratios in Western music harmony is more complex, going at least as far back as Pythagoras’ experiments with a monochord, a single stringed instrument, in the 6th century B.C.E. In his experiments, Pythagoras discovered that plucking a string at certain ratios to its total length created sounds he considered pleasant. From these experiments, he derived a collection of seven notes for creating music. These notes were not based upon specific frequencies, but rather derived from specific ratios in relation to a root pitch. In other words, it was the ratios between the notes that created the Pythagorean tuning system – it was only much later that the notes in the Western musical system were set to specific frequencies, and expanded into twelve total notes. Even today, Pythagoras’ seven-note based system is regularly used, and referred to as a scale. 

In this lesson, students simplify ratios and find equivalent ratios using proportions as they investigate rhythm and harmony in Western music, recreate the 7-note Pythagorean scale, and calculate ratios between musical intervals.

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Musical Ratios.pdf

Lesson Plan
June 22, 2022
0.9 MB
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