Friday 6

# Friday 6 - Friday 6 Intervals, overtones, and axis. The...

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Friday 6 Intervals, overtones, and axis . The overtone series for one-dimensional standing waves on a medium of length L and wave speed v is: 2 n nv f L = Here n is an integer: 1,2,3,4,… Each of these overtones corresponds to a "mode of vibration" of the system. Thus the sequence of mode frequencies is linearly spaced. It turns out that the lowest modes tend to sound good together so there are various musical chords that result when you add together vibrations at the various mode frequencies. For example if you play modes 4, 5, and 6 together you have what is called a major triad . If you change the length L , these modes 4, 5, and 6 will still form a major triad, but one that starts on a different pitch. This means that the musical properties depend on ratios of the frequencies. The major triad involves the ratios 5/4, 6/5, and 6/4. Here is a list of some musically relevant ratios (called "intervals"). Frequency Ratio Name Equal Temperament approx. 2:1 Octave 2 5:3 Major sixth 1.6818 3:2 Perfect fifth 1.4983 4:3 Perfect fourth 1.3348 5:4 Major third 1.2599 6:5 Minor third 1.1892 A sequence of notes separated by constant intervals

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## This note was uploaded on 03/30/2008 for the course 029 044 taught by Professor Skiff during the Spring '08 term at University of Iowa.

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Friday 6 - Friday 6 Intervals, overtones, and axis. The...

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