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Old 10-17-2008, 12:11 PM   #2 (permalink)
Mathemusician7
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Join Date: Oct 2008
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I'm not sure if you are saying "I dont think so" to the inversion method, but it really does work for any major or minor three note chord, meaning I am excluding all seventh, diminished, or any other more complicated chord. It's actually quite easy to show that this is true. There are 12 notes in the chromatic scale, C D E F G A B, plus all the accidentals. So if we just write them as numbers rather than letters, then we get 0,1,2,3,4,5,6,7,8,9,11 (I just realized a mistake I made in my previous post; I should have started C on 0 rather than 1). There are 24 three note chords using these notes and the rules of constructing chords. 12 major and 12 minor. I can just write it in list form to show that what I said earlier is true.

C Major - (0,4,7) - (0,8,5) - F minor (another mistake I made, it is not rooted on the minor third)
C# Major - (1,5,8) - (11,7,4) - E minor
D Major - (2,6,9) - (10,6,3) - D# minor
D# Major - (3,7,10) - (9,5,2) - D minor
E Major - (4,8,11) - (8,4,1) - C# minor
F Major - (5,8,0 - (7,2,0) - C minor

I'm going to leave it at that because there is actually a really nice little pattern that is coming out of this. Once the pattern is found it is very easy to figure out the rest.
Also, if you inverted the minor chords, you would get the same major chords out as above.
So F minor inverted is C Major and so on.
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