Author: Prent Rodgers

I’m working on some variations on Arcangelo Corelli’s Folia Opus 5, a piece written just prior to 1700, for violin and continuo. Folia is a chord progression well used in the 15th and 16th centuries by a variety of composers. Think of it as the 12-bar blues of early classical music tradition. Corelli’s version is a theme with 23 variations. My version intersperses the theme with the variations, as I did with the Allemande. I still have more work to do, but this is a good introduction. This version is scored for my microtonal slide Bosendorfers, realized in Csound. The tuning uses two otonalities (based on C & F), one utonality (D), plus a few mixed tunings (an A major based on the F otonality, and G minor based on the C otonality).

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Follia-t2

This version includes the second part of the dance, which is more complex than the first. I’ve applied the same deconstruction to this part as previously. I have a set of rhythms, dynamic accents, and notes. If they are played correctly, then it represents the Allemande dance as written. But I can also assign the rhythm of one measure, the dynamics of another, and the notes of a third, as well as extend they time 2x, 4x, or cut it in half.

It’s really a theme and variations style, but the themes and variations are intermixed.

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Allemande #15

This is one of several recent versions that has some really nice parts. By next week I hope to have the second part of the Allemande ready. But for now, here’s some nice Sunday music for your consideration.

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Allemande #10

Today I reached the 16th measure. 16 more to go. I may stop here, because it’s getting long.

The preprocessor has the option to choose the durations from one measure, and the notes from another, and the volumes and accents from a third. Plus it can double or cut in half the speed. But first it is set to play the measure straight, then variations in the same key.

Imagine if Bach had spilled the stone manuscript on the floor into a thousand pieces and some musical archaeologist had to put it back together.

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Allemande #9

In DFW at the Hyatt for a meeting for four days. Haven’t seen the outside world in three days. But Allemande is never far from my mind. In this version I’ve doubled the speed, and still support the 1/2 and 1/4 speed versions. There is much more indeterminacy now, so I’m comfortable I can eventually come up with some music. Tonight I reached the 6th measure. 26 more to go.

Imagine if Bach had spilled the stone manuscript on the floor into a thousand pieces and some musical archaeologist had to put it back together.

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Allemande #8

I’ve rewritten the first part of the Allemande so that I can more easily manipulate different aspects of the piece. In this case, I’ve made it possible to stretch the time by two to four times. I’ve also made it possible to apply one measure’s rhythm to another measure’s notes, and a third measure’s dynamics. I’m just getting started making it work. Today’s version includes only the first seven measures. 

Next up is including double speed options, and then retranslating the rest of the 32 measures to increase the surprises. I love surprises. I already include two different F# major modes, one with a bad 6th and the other with a bad 4th. 

I should probably have sorted all the combinations by some sort of a scoring scheme. For every cent out of tune for a 5th, 5 points. For every 4rd out of tune, 4 points per cent. Every 3rd or 6th out of tune 3 points. Every second out of tune, 2 points per cent. 

There are hundreds of potential scales in a 31 limit diamond. I just have to find the right algorithm. Wish me luck.

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Allemande #7

This version uses some different chords for some of the measures. I’m still not comfortable with the transpositions. The chords are unusual distances from each other, which makes it rather jarring. For example, the A major is a nice 4:3 from the E major, and the D major is 9:8 from E. All good. But the two F# major chords available are either an 8:7 above the E, or a 28:25 above the E. Not good. It should be a 9:8, and neither really works here. B major is 8:7 from C# as well.

Here are the triads used in the piece, in a matrix that shows the relationships between the chords.

I’m getting the feeling I should have stuck with 72 EDO for this exercise.

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Allemande #6

I’ve finished the original transcription of the Bach 1st English Suite Allamende, parts one and two. To make this, I’ve expanded the number of modes in the 31-limit tonality diamond to 189 different triads, each with a 16 note scale derived from either an otonality or utonality taken at different starting positions. Previous versions used only the otonality or utonality right from the diamond. But the modulation from one key to another was rather jarring. Now I have many more keys I can chose from.

For example, I’ve created a relatively normal sounding A major diatonic scale from the notes in the F major Otonality by starting at the 3rd scale step, which is A at 5:3, then a 5:4 third above that as a C# at 23/12, and a 3:2 above the A as an E at 25:24. Relative to the A, we have 1:1, 5:4, 3:2 triad. Other notes in the 16 in the otonlality round out the other notes in the scales.

Bach used several modulations in the piece, from A major, B major, E major, and F# major in the first part, and a few other keys in the second. The D major needs work, as it’s not really where it should be to my ears. But this is a start.

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Allemande #5

Here is the first five measures of the score:

I took a side trip to find more triads in the 31-limit tonality diamond. With the diamond to the 11-limit, using either the otonality or utonality only, there are really only four valid triads, where valid is defined as having a pure major fifth, and four thirds: 7:6, 6:5, 5:4, 9:7. I systematically explored the 31-limit diamond and found many more. Here is a summary table of the thirds I found inside pure 3:2 fifths, in the otonality and utonality only.

Each of these can be transposed to any key in the utonality or otonality, depending on from which they were derived. That’s a total of 180 distinct triads across the entire diamond, after some duplicated ones were eliminated. I played each one with a keyboard to find a reasonable diatonic scale for each, plus two 7th’s, major and minor. Now I plan to use these to pick more sonorous keys for the Allemande dance by Bach. But that’s not for today.

What we have today is just all 144 unique triads, sorted by the 1st degree, then the 3rd degree, starting with the most subminor going to the highest bearable super major. In order. Straight through. This is not music, but it is interesting to listen to.

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Allemande #4

For this version, I enabled the entire Bosendorfer sample set, although it only uses the 5 moderate velocity samples. It adds a bit more color. Same tuning and keys. Next, I will begin work on the second half of the piece.

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Allemande #3

Here is the score: