f1 = 440.00 1 2 3 4 5 440.00 880.00 1320.00 1760.00 2200.00 f2 = 440.00 1 2 3 4 5 440.00 880.00 1320.00 1760.00 2200.00 R= 1 1/2 2/1 1/3 2/3 3/2 3/1 1/5 2/5 4/5 3/5 5/4 5/2 5/3 f3 = f1*R 440.00 220.00 880.00 146.67 293.33 660.00 1320.00 88.00 176.00 352.00 264.00 550.00 1100.00 733.33 f3 = f2*R 440.00 220.00 880.00 146.67 293.33 660.00 1320.00 88.00 176.00 352.00 264.00 550.00 1100.00 733.33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 CT: F1-F2 Doubly degenerate |f2-f1| f2+f1 F3 = 0.0 880.0 CT: 2F1-F2 Singly degenerate 2f1+f2 |2f1-f2| 2f2+f1 |2f2-f1| (f1+f2)/2 |f1-f2|/2 F3 = 1320.00 440.00 1320.00 440.00 440.00 0.00 CT: 3F1-2F2 No degeneracy (3f1+f2)/2 |3f1-f2|/2 (3f2+f1)/2 |3f2-f1|/2 (2f1+f2)/3 |2f1-f2|/3 (2f2+f1)/3 |2f2-f1|/3 F3 = 880.00 440.00 880.00 440.00 440.00 146.67 440.00 146.67 0.0 880.0 1320.00 440.00 1320.00 440.00 440.00 0.00 880.00 440.00 880.00 440.00 440.00 146.67 0.00 200.00 400.00 600.00 800.00 1000.00 1200.00 1400.00 Print to PDF without this message by purchasing novaPDF (http://www.novapdf.com/)

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f1 = 440.001 2 3 4 5

440.00 880.00 1320.00 1760.00 2200.00f2 = 440.00

1 2 3 4 5440.00 880.00 1320.00 1760.00 2200.00

R= 1 1/2 2/1 1/3 2/3 3/2 3/1 1/5 2/5 4/5 3/5 5/4 5/2 5/3f3 = f1*R 440.00 220.00 880.00 146.67 293.33 660.00 1320.00 88.00 176.00 352.00 264.00 550.00 1100.00 733.33f3 = f2*R 440.00 220.00 880.00 146.67 293.33 660.00 1320.00 88.00 176.00 352.00 264.00 550.00 1100.00 733.33

0 0 0 0 0 0 0 0 0 0 0 0 0 0CT: F1-F2 Doubly degenerate

|f2-f1| f2+f1F3 = 0.0 880.0

CT: 2F1-F2 Singly degenerate2f1+f2 |2f1-f2| 2f2+f1 |2f2-f1| (f1+f2)/2 |f1-f2|/2

F3 = 1320.00 440.00 1320.00 440.00 440.00 0.00CT: 3F1-2F2 No degeneracy

(3f1+f2)/2 |3f1-f2|/2 (3f2+f1)/2 |3f2-f1|/2 (2f1+f2)/3 |2f1-f2|/3 (2f2+f1)/3 |2f2-f1|/3F3 = 880.00 440.00 880.00 440.00 440.00 146.67 440.00 146.67

0.0 880.0 1320.00 440.00 1320.00 440.00 440.00 0.00 880.00 440.00 880.00 440.00 440.00 146.67

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00 1400.00

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