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So I'm trying to wrap my head around intervals. I know that, for instance, a major chord is made up by the fundamental (I), a perfect third (III) and a perfect fifth (V). So, the "important" third interval is called major, but the fifth is called perfect. I've searched for why it is that, and I found two possible explanations:

  1. in the natural temperament (IIUC, way back to Pythagoras), a fifth is perfect in the sense it is in a very very simple ratio with the fundamental (3:2). This makes the waveform simpler than the third, which in a sense is then "less perfect" then the fifth interval.
  2. in the usual arrangement of notes (diatonic scale, C D E F G A B), the distance covering a perfect fifth is almost always that of free diatonic notes (except for B - F#), whereas with the thirds this is not the case. So the term "perfect" refers to "how well this nomenclature fits well with the way we chose to call the important (diatonic) notes".

Now, are those examples correct? Historically, do you know which is the reason the names "perfect" and "major" were distinguished (as if they were two different things)?

Thanks!

EDIT: this is indeed a duplicate question. After being redirected to the relevant previous ones, it turned out the answer is not completely certain, but most probably the number 1: "perfect fifth" is a term much more tied to the frequencies of the sounds than to the names of the notes; moreover, the terms "major" and "minor" arose from they being not perfect, in the previous sense, and they refer to the longer and shorter third. Thanks to the community!

Alessandro Bertulli
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  • [related](https://music.stackexchange.com/q/22525/3032) – anatolyg Jan 21 '23 at 15:13
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    Seems to me this is best addressed by the answer by Athanasius here: [What makes an interval "Perfect"?](https://music.stackexchange.com/questions/22525/what-makes-an-interval-perfect) – Andy Bonner Jan 21 '23 at 15:25
  • That accepted answer is incorrect. Perfect intervals are so called simply because they only come in one size (ignoring diminished and augmented, which came later). In medieval theory, a fifth above G is D, unambiguously, but a third above G could be B natural or B flat. One is bigger; one is smaller. Latin for "bigger" and "smaller" are "major" and "minor." – phoog Jan 22 '23 at 10:42
  • Well, but isn't that true for all intervals? I mean, also every major third is always the same distance between two sounds (on the chromatic scale). On the diatonic scale, I can see there is a difference, but then also the fifth is no longer ALWAYS perfect, as the perfect fifth of a B is actually an F# (if that's what you meant, please correct me if I'm wrong) – Alessandro Bertulli Jan 23 '23 at 14:00

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It was indeed Pythagoras who 'discovered' the interval of P5 - the ratio being 3:2, after he established that the octave had a ratio of 2;1. So the perfect fifth was 'born'. C>G is one such. Turn that on its head, G>C and it becomes P4, with a ratio of 4:3, the next simple ratio available.

As far as major is concerned, it doesn't bear a lot of relationship to major scales. Here, major refers to 'most important', 'bigger' where the basic scale, with its intervals, is the datum point. Hence M3 is a larger interval than m3, M7 is larger than m7.

Tim
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    Pythagoras surely did not "discover" the fifth but rather identified it with the 3:2 ratio -- or at least was the first person whose knowledge of this association has survived to the present day. But I don't believe the adjective "perfect" was yet in use. That terminology must have arisen in the late middle ages or perhaps even in the Renaissance. I'm not sure when it was, but it r was certainly after Guido in the 11th century. – phoog Jan 22 '23 at 10:37
  • @phoog - yes, it's like who 'discovered' America, Australia, et al!! I just missed the second apostrophe. Unlike me with my dislike of misuse of them... – Tim Jan 22 '23 at 10:41
  • Ah, I didn't notice! Also I should have noted that the "important" sense of "major" is figurative and not particularly relevant to intervals. It literally means "bigger" in Latin. – phoog Jan 22 '23 at 10:44