An interesting idea. Following from the statement: Our previous work demonstrated that chords with frequency ratios 3:5:7: and 5:7:9: have many perceptual harmonic properties of major triads (4:5:6 ratios). The traditional diatonic scale can be constructed from three major chords, the tonic, the dominant, and the subdominant chords. I took some liberties with names and numbers to simplify the results. Build a 'C major triad' , C E G. ratio 4:5:6 The 'C' is the 5th of the subdominant chord, F, and G is the root of the dominant. Using this ratio to build the F and G triads, and using foldover octave equivalence, the C 'major' scale, [starting on the arbitrary frequency of 400 Hz], seems to come out as follows: C 400 D 450 E 500 F 533 G 600 A 666 B 750 C 800 This scale may already have a name. The three primary major triads would be beat free. I think that melodies constructed from here might be quite interesting for the general population. By extension up and down, F# and Bb would be introduced. Built on the D, the notes would be D, 450Hz, F# 562Hz and A 675. This A is higher than that in the F major triad. Maybe the solution would be to split the difference and tune A to 670Hz. It would be about equally inharmonic with both triads . . . Kevin On 2012, Jun 11, at 3:32 PM, Richard F. Lyon wrote:
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