In the overtone series, which pair of intervals follows after the octave?

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Multiple Choice

In the overtone series, which pair of intervals follows after the octave?

In the overtone (harmonic) series, after the fundamental the overtones appear at whole-number multiples of the frequency: 2f, 3f, 4f, and so on. The interval from the fundamental up to the first overtone is an octave. The next interval, from the octave (2f) to the next partial (3f), is determined by the frequency ratio 3f/2f = 3/2, which is a perfect fifth. The following interval, from that partial (3f) to the next one (4f), is 4f/3f = 4/3, which is a perfect fourth. So the two intervals that come after the octave are a perfect fifth and then a perfect fourth. The option that lists these two intervals together matches this pattern. (The upward sequence goes P8, then P5, then P4, etc.)

In the overtone (harmonic) series, after the fundamental the overtones appear at whole-number multiples of the frequency: 2f, 3f, 4f, and so on. The interval from the fundamental up to the first overtone is an octave. The next interval, from the octave (2f) to the next partial (3f), is determined by the frequency ratio 3f/2f = 3/2, which is a perfect fifth. The following interval, from that partial (3f) to the next one (4f), is 4f/3f = 4/3, which is a perfect fourth. So the two intervals that come after the octave are a perfect fifth and then a perfect fourth. The option that lists these two intervals together matches this pattern. (The upward sequence goes P8, then P5, then P4, etc.)

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