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Minor Scale
    

The minor intervals and the frequency ratios their correspond to are the second (9:8), minor third (6:5), fourth (4:3), fifth (3:2), minor sixth (8:5), minor seventh (9:5), and octave (2:1). The minor scale is sometimes also called the "natural" minor scale. The minor scale is constructed from minor triads in an analogous manner to the construction of the major scale by major triads. A minor triad is a group of three notes played together with the ratios of frequency 10:12:15. Within an octave, three such minor triads can be constructed as follows:

C D E F G A B C' D'
10 ... 12 ... 15        
      10 ... 12 ... 15  
        10 ... 12 ... 15

interval steps half steps ratio
prime 0 0 1:1
second w 2 9:8
minor third wh 3 6:5
fourth whw 5 4:3
fifth whww 7 3:2
minor sixth whwwh 8 8:5
minor seventh whwwhw 10 9:5
octave whwwhww 12 2:1

Therefore, the minor scale, like the major scale, also has just intonation. The minor scale was also used by the Greeks, and was called the aeolian mode. Note that the same intervals are present in the minor scale as in the major scale, although the order is different. However, the notes of the two do not correspond in frequency (E, A, and B are different). That is, notes defined according to 1:1, 9:8, 5:4, 4:3, 3:2, 5:3, 15:8, and 2:1 (major scale) and 1:1, 9:8, 6:5, 4:3, 3:2, 8:5, 9:5, and 2:1 (minor scale) differ in the third, sixth, and seventh note. The problem becomes more obvious with a numerical example. Defining C as 264 Hz, the major and minor scales can be seen to require different frequencies for the three notes mentioned above:

Key C D E F G A B C' D'
Major 264 297 330 352 396 440 495 528 594
Minor 264 297 316.8 352 396 422.4 475.4 528 594

This difficulty can be ameliorated in a combined scale by adding additional notes for the minor scale frequencies which do not correspond to major scale frequencies. Notes must be added between major notes D and E (D$\sharp$ or E$\flat$), G and A (G$\sharp$ or A$\flat$), and A and B (A$\sharp$ or B$\flat$), for a total of 10 notes per octave: C (1:1), D (9:8), D$\sharp$ (6:5), E (5:4), F (4:3), G (3:2), G$\sharp$ (8:5), A (5:3), A$\sharp$ (9:5), and B (15:8). However, the only way to resolve these difficulties completely is to use equal temperament.

see alsoHarmonic Minor Scale, Melodic Minor Scale


© 1995-2005 Eric W. Weisstein