The diatonic scale (octave) is divided into 6 intervals (4 full tones and 2 half-tones) between its 8 tones from beginning to end. How to do it, to have the frequency ratio between beginning and end 1:2?
There are two well-known ways: the major and the minor scale. They differ in the positions of the two half-tones. But why is the major scale perceived as happy fulfillment and the minor scale as sad disppointment? Why should the placement of the half-tones correspond so universally to human moods? This is true transculturally, I believe. Even the do-mi-sol triads have these mood differences.
Do any cultures anywhere use the other possibilities of placing the 2 half-tones? As combinations of 2 out of 6, there should be 13 others, for a total of 15. What would their mood correlations be, if any?