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Music Theory for Computer Musicians by Michael Hewitt

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Perfect Concords

The most concordant interval of all is the octave—discussed in Chapter 2—where the ratio of the two frequencies is virtually the simplest possible: 2:1. Here the two notes are so concordant that they register to us as being virtually the same. Harmony by octaves occurs naturally when, say, men and women sing the same song. Women sing in a higher register, while men sing in a lower register. Both sing the same notes, but separated by one or more octaves.

After the octave, there are two very important intervals that also have simple ratios. These are the perfect fifth, which has a ratio of 3:2, and the perfect fourth, which has a ratio of 4:3 (see Figure 8.1). Both intervals produce a very natural, distinctive, and strong harmony. ...

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