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I am reading an entry book titled Music Theory: From Beginner to Expert by Nicholas Carter.

He says that Perfect 4th is found at 3rd overtone at a frequency of Fundamental note + P5 + P4(which is a frequency of two octaves).

But other sources tell that Perfect 4th interval is not found in overtone series as below.

https://music.stackexchange.com/questions/82682/how-can-a-perfect-fourth-interval-be-considered-either-consonant-or-dissonant

A book titled "Melody in Song Writing" by Jack Parricone also says Perfect 4th is not found in overtone series.

So, is P4 considered to be found in overtone series or not?

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  • Btw, I'm not familiar with Carter's book and shouldn't judge it on this small excerpt. But, on the continuum "from beginner to expert," talking about the overtone series in any depth is farther from the "beginner" endpoint. Most music theory 101 classes tell about intervals but don't go into great historical, mathematical, or philosophical depth about how they're derived or what they signify. If you don't already have it, I recommend starting with the kind of broad knowledge you can gain in one day, like at musictheory.net/lessons, and then enriching with details beyond that. Feb 29 at 12:49

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There is no note which is a perfect 4th from the fundamental, or from harmonics 2, 4, 8, etc. However the 4th harmonic (C) is a perfect 4th above the 3rd harmonic (G). Apparently Nicholas Carter considers that this means that the perfect 4th appears in the harmonic series, while Jack Parricone does not.

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    Yep. Terminology issue. Plus, "appears in the overtone series" is usually just a tool to use dubious psychoacoustics to justify some music theory opinion... like what intervals are most natural, most consonant, most whatever, so you get a lot of disagreement about what "in the overtone series" entails.
    – user45266
    Feb 29 at 5:18
  • I agree with user45266, the overtone series supports the idea that a major triad is fundamental consonant and stable harmony, but after that the overtone series has little relevance to harmony practice. Feb 29 at 17:16

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