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→Intervals Above vs. Intervals Below and Inversions
The 7ths/2nds, 3rds/6ths, and 4ths/5ths swap. This makes sense - the further a note is from some root note, the closer that note will be to the root note's octave. Yet notice the '''major intervals' inversions are minor intervals''', the perfect intervals' inversions are also perfect intervals, and the tritone's inversion is also a tritone.
The major/minor swap may seem a little counter-intuitive at first. "Major" is often associated with harmonious and happy, while "minor" is associated with dissonant and dismal. That's more true of the major and minor keys scales than the intervals; however, I would even contest such a general statement. Songs in major keys can be sad and songs in minor keys happy given how they are written. Intervals are more basic, however. The major/minor label has less nothing to do with their consonance and dissonance, then whether they are present in ''but the size of the major or minor scalesinterval''. All It so happens that all the major/minor intervals in a major key against the root note are major, while 3/4 of the major/minor intervals are minor in a minor key.
Chords can be inverted without changing their harmonic function (although it does affect their percieved qualities), but intervals are a bit more sensitive. See the example below.
P5 P4 m6 M3
In the tab above, the low E string and higher D string are always playing an E, and the A string plays B, then C. This demonstrates an E-B P5 interval and its inversion, a B-E P4 interval, then an E-C m6 interval and its inversion, a C-E M3 interval. Inverting the perfect intervals only create a slight difference in perception, while inverting 3rds or 6ths has a larger impact. The composer cannot simply swap them willy-nilly - they clearly have different qualities in terms of overall harmony although they do sound related.
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