Notes on a Modulating Just Scale

I have now had the chance to play a keyboard tuned to the scale I proposed here.

The difference between the Fourth of 4/3 and the Super Minor Third of 27/20 was perceivable but too small to be of any value. I would suggest that a piece composed with many II chords and few IV chords would do well to adopt 27/20 rather than 4/3, but that otherwise 4/3 is quite suitable. For example, much Godspeed You! Black Emperor would benefit from this adjustment. I think the powerful identity of 4/3 (it is after all the complement of a very low numbered partial) is such that one tends to hear 27/20 as an out of tune 4/3. This relative identity is an interesting concept that should be explored further.

Two Bbs were used, 7/4 and 9/5. The 7/4 was indeed useful and appropriate, although it did not ring as clearly in the I7 as I would have expected. In some ways it had more of the quality of a 7th chord, and in another way it did not. I think by denying the minor seventh an identity as the complement of the wholetone, part of the leading feeling of the 7th chord is lost, but that by isolating and perfecting the identity of the minor seventh as the seventh partial, another aspect to the character of the 7th chord is distilled and amplified. This is a tool to use with discretion. The two tones were readily identifiable and it was entirely appropriate to have both on the same instrument. I would consider placing the 7/4 on the B and the 9/5 on the Bb and doing away with the major seventh altogether.

I would like to make more observations of the two As in the scale.

Overall, the whole thing held together and rang beautifully. The modulations worked just as I had intended, and it was very pleasant as a melodic scale. This proves that the ideas I have about abstract numbers on paper translate properly into real world musical situations. I know what I am doing.