How do I use the 'white-key method' as an aid for memorizing intervals?
I'm working my way through the Open Music Theory digital textbook (http://openmusictheory.com/).
There is a chapter that describes intervals and how to determine their quality. The introductory method given is a table with Chromatic Intervals along the side and Generic Intervals along the top. The table is depicted below:
Using the table, we can see that C-G is a P5 because of the five diatonic steps from C to G (C, D, E, F G) and the seven semitones (i7) from C to G (C#, D, D#, E, F, F#, G).
The author goes on to recommend a more intuitive method for memorizing intervals called the 'white-key method' (http://openmusictheory.com/whiteKeyMethod.html).
Using the logic of the white-key method, all fourth intervals are perfect with the exception of F-B which is augmented. By inverting the intervals and by extension of this method, are all fifth intervals therefore augmented with the exception of B-F, which is perfect?**
**I know there is a flaw in my logic because looking at C-G, I come to the correct solution using the table (P5) but using my understanding of the white key method, I see it as an A5.
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You're working under the misapprehension that the inverse of augmented is perfect. It isn't. The rule of nine helps with P5 inverted = P4. (M7 inverted =m2; m3 inverted = M6, etc). But the point of Perfects is they remain as such - perfect (P).
Augmented inverts to diminished - aug4 = dim5; aug6 = dim3 etc.
Your F>B is an aug4, as F>Bb is P4, now enlarged by one semitone. So, B>F will be a dim5.
Yes, it's true that all the other 'white key' 4ths are P4, except F>B, just as all 'white key' 5ths are P5, except B>F. Which is dim5...
How do you arrive at the conclusion that all white-key fifths are augmented (except B-F) by using this "white-key method"?
Perfect fourths invert to perfect fifths, and augmented fourths invert to diminished fifths. This seems to be what the page you link is suggesting: starting from the fact that all white-key fourths are perfect, except for F-B which is augmented, the conclusion is that all white-key fifths are perfect, except for B-F which is diminished.
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