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C Major Scale
Fig. 1        1  2   3  4     5  6  7  8  
Figure 1 shows the C Major Scale. The notes are simply: C D E F G A B C. Each letter has a degree or number associated with it: 1 2 3 4 5 6 7 8. A chord consists of three notes or more. Two notes can sometimes imply a chord but this is only the suggestion of a chord.
C Major Scale In 3rds
Fig. 2         1  2   3  4     5  6  7  8  
Figure 2 Western music is tertiary - based on thirds (C=1, D=2, E=3, the distance of C to E is therefore a third). We can build chords on each degree of a scale in order to arrive at the chords derived from the scale. Start by stacking a third on each degree of the scale, in this case the C major scale. The notes are C and E (built on the 1st degree), D and F (built on the 2nd degree), E and G (built on the 3rd degree), F and A (built on the 4th degree), G and B (built on the  5th degree), A and C (built on the  6th degree), B and D (built on the 7th degree), C and E (built on the 8th degree, a repitition of the  third built on the 1st degree).
C Major Scale Triads
Fig. 3         1  2   3  4     5  6  7  8  
Figure 3 shows what happens if we stack another stack of thirds on top. Now we have built chords in the key of C. These particular 3 note chords are called triads. The notes are as follows: triad 1 is CEG, triad 2 is DFA, triad 3 is EGB, triad 4 is FAC, triad 5 is GBD, triad 6 is ACE, triad 7 is BDF, triad 8 is the same as triad 1.
c major scale
Fig. 4         1  2   3  4     5  6  7  8      9 10 1112    131415
Figure 4 is the "C Major Scale" extended to two full octaves.The notes are C D E F G A B C D E F G A B C. The degrees are 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. The most common degrees used in chords above the octave (the 8th degree) are 9th, 11th, and 13th.
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