Specific examples vs Abstract generalities

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take5_d_shorterer
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Re: Specific examples vs Abstract generalities

Postby take5_d_shorterer » 10 Jan 2018, 14:38

It's easy to see this on the piano. See below.

Image

Now consider a major 7th chord like C major 7th with notes C,E,G,B.

You can find this in exactly 2 major scales, C and G.

The other three 7th chords are the the dominant 7th, half-diminished 7th, and diminished 7th.

The dominant 7th (such as C,E,G,Bb) is found in exactly one major scale, F. That means in practice that if you have a dominant 7th chord and you are dealing with major key tonality, you are saying very clearly where you are going.

The half-diminished 7th (such as B,D,F,A) is found in exactly one major scale, C.

The full diminished 7th is found in no major scale.

An easier way to remember this is as follows:

Consider the white keys which constitute the C major scale.

Construct 7th chords on each degree of the scale.

You get

C major 7
d minor 7
e minor 7
F major 7
G dominant 7
a minor 7
b half-diminished.

There are 3 minor 7th chords, 2 major 7th chords, 1 dominant 7th, and 1 half-diminished.

Using a "double-counting" argument from discrete mathematics, you can show that every minor 7th chord must be in 3 major scales.



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Back to "Giant Steps". Barry's main point is that although you start on B major, you need to move immediately to D dominant 7. Don't wait until that D7 chord appears on the 3rd beat of measure 1.

You might think it sounds dissonant, but go straight to D7 and use the common tone in D7 and B (i.e., F#) to smooth things out.