Here is another variation #6 of People. The only change is that I ensure that the chord progression is played in order at least three times. That is, the string of G minor, C major, F major, Bb major is selected in that order three times. All the other changes follow the drunkard walk Markov chain. If it selects to play a measure in C major then the next measure is G minor or F major, but never Bb major. Backwards or forwards only, with loop around.
Here is variation #6 of People. It’s based on the harmonies of measures 13 & 14. Out of the 1:1 Otonality I derive a just G minor and C major. Out of the 16:9 Otonality, I pull a just F major and Bb major.
This set of chords share many of the same notes, except for D which moves from 182 to 204 cents like variation 5, and F, which moves from 471 to 198. G and C are stable at 702 and 0 respectively.
Here is a proposal for variation #5 of People. It’s based on the harmonies of measures 11 & 12. Out of the 5:4 Utonality I derive a just E minor and D minor. Out of the 4:3 Otonality, I pull a just A major. Inside the 16:9 Otonality, there is a just D major.
Unfortunately the most prominent note is D, but it shifts from 182 to 204 cents depending on the tonality I’m in. The same is true of other notes, like F, which goes from 460 to 498 cents. And Bb from 969 to 983 to 996. G stays at 702 cents, which is nice.
Here is a proposal for variation #4 of People. It’s based on the harmonies of measures 9 & 10. Out of the 4:3 otonality I derive G minor and C major, and out of the 16:9 otonality, there is a nice F major and Bb major.
I’m stepping my way through the theme one or two measures at a time. This is the second variation, which uses the keys of measures 5 & 6, which are derived from the 16:9 otonality, and the 4:3 otonality. There are more features of Prent’s Microtonal Slide Bosendorfer in this one.
This is the fourth try at a tuning that sounds reasonable. I’m using the same two utonal and three otonal 16 note scales as the source for the notes. I start at with the 9:8 utonality, which has a very nice D minor and A minor modes. In measure 6 I shift to the 5:4 utonality to play a sweet G minor and A major, the D minor and F major modes. Each is unique and charming, to my ears.
Rzewski used this theme as the vehicle for 36 variations that explored the range of pianistic techniques that he was so famous for. It’s really a wonderful piece. I don’t plan to transcribe his variations at this point. I may come back to variation 13, my favorite. My intention is to explore the tuning in different ways. I’ve been playing along on my little Midi keyboard in the various tuning, and have found some delightful keys that I plan to explore. And I can transpose the tunings in interesting ways as well.
I made a few changes to the tuning. It’s still very rough. This will take some time.
Basically, I use the following five 16-note scales which are either otonal (overtone based) or utonal (undertone based).
The 16-note utonal scales four “minor”, one neutral but close to major, and one major scales. The otonal scales can create 3 major and three “minor” scales. From all those scales I pull the tones I need to make each measure as consonant as I can.
This is a version of the first movement of the Rzewski piece with some altered tuning based some otonal and utonal scales derived from the tonality diamond to the 31 limit. I’m not happy with some of the tuning and will continue to work on some different chords.
The piece is a set of 36 variations for virtuoso piano on the Chilean song “¡El pueblo unido jamás será vencido!” by Sergio Ortega and Quilapayún, which was popular in the 60’s and 70’s in Chile. Rzewski wrote his variations in 1975 as a protest against the repressive regime of Augusto Pinochet. Some say the U.S. had a major role in the coup that lead to Pinochet’s rule, which lasted from the 70’s into the 90’s.
The first movement is just a statement of the theme. I like the romantic harmonies, which sound ironic in a protest song. I hope to take the tuning into interesting areas as I continue to learn the piece.