I've been feeling sick for the past few days. :( But it'll pass.
Did you know that many theory books teach that a fourth and a fifth in a scale (ie F-C [5th], G-C [4th], Ab-Db [4th] as perfect intervals since they consist of the 1st-2nd and 2nd-3rd partials of a fundamental tone?
WAIT.
Just for reference, a fundamental tone is any pitch on a scale. Let's take C2 as an example. On a piano, when you strike a string, sympathetic vibrations will bring out families of pitches, called overtones in music, and partials in physics. And what's special about these is that each partial's number is the ratio of number of vibrations to the fundamental tone.
For example, the C2's 2nd partial is C3, then 3rd is G3, then 4th is C4, then 5th is E4, 6th is G4...etc.
Notice the same pitches on different octaves has a integral ratio between one another's frequencies e.g. C3 and C4 are 2:1. As a result, C4 and C5 will be 1:2 as well, and C3 and C5 are 1:4.
Back on topic.
P5 is, in truth, a major interval. P4 is a minor interval. If you looked at the partials, for P5, the base C is naturally on the bottom, giving a stable, finishing feeling to it. However, for P4, it is on the top, making it feel insecure. It's kinda like:
Source: http://www.stonebalancing.com/p7hg_img_1/fullsize/topheavy_fs.jpg
Top heavy. Liable to fall and hit your head any minute.
By the same classification, you'll see in the partials that a third interval is major as well, and the sixth is minor. Not only because of where the base C is, but also E-C is a true minor sixth.
The only place you can find a major sixth is between the 3rd and 5th partials. No base. Even more unstable.
To be cont'd.
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