For fun, and in spare moments, I am putting the entire Hindemith classic, “Traditional Harmony” in Sibelius – something I’ve long wanted to do. While I’m at it, I’m beginning to incorporate some of the Schillinger technics as well. Here’s a little 4-part harmonization from a Hindemith exercise of Chapter 10 (Secondary 7th Chords) using Schillinger’s non-fractioned resultant from 4:3 (in this case the exercise supplied the Figured Bass – the student then realizes the melody and inner parts).
r4÷3 = (3+1)+(2+2)+(1+3)
And here’s another using the Expansion technic on the 8:5 resultant.