If you read an article about the Just Scale, you learn that the three major chords each have the simple frequency ratio 4:5:6
1 9/85/44/33/25/315/8 2 9/45/2 C D EF G A B C D E
C : E : G = 4/4 : 5/4 : 6/4 ; F : A : C = 4/3 : 5/3 : 6/3
G : B : D = 3/2 : 15/8 : 9/4(x 8/3) = 4 : 5 : 6
but that for the minor chords ...
E : G : B = 5/4 : 3/2 : 15/8(x 8 ) = 10 : 12 : 15
A : C : E = 5/3 : 6/3 : 5/2(x 6 ) = 10 : 12 : 15
For Nature's most harmonious sound of a major chord, the simple ratio (1:2):3:4:5 makes joyful sense But a minor chord is Nature's next most harmonious sound, so why the more complex ratio 10:12:15
If we take the reciprocal(inverse) ratios and multiply them by 60 …
Major and Minor chords are the inverse of each other (Maybe that should have been obvious from the fact that the major 3rd and minor 3rds are inverted)
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Anglophone, HA 64 Win.10, amateur composer. La musique classique est ce dont vous attendez toujours qu'elle se transforme en mélodie
Oh Tony, you solve the question before raising it!
In addition, a 7th chord (C E G Bb) présents the ratio 4:5:6:7
This "just scale" aspect is very interesting indeed (I found that out a couple of years ago); as a mathematician, I enjoy to see something physical using integer numbers (yes rational (fractions) ones, but at least not real ones).
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André Baeck, de retour en Belgique après 12 ans passés dans le Gard. Windows 11, HA 997e (et précédents)