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Take 10 is remixed with a bit less high brass, shorter holds, and more tuba. I like tuba.

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This is the final version of the piece. I’ve made a few small changes to the durations of some of the long and short notes. The long half notes can now end a bit early, leaving some space in the sonority, and the short mallet instrument notes last longer.

As I said when I started this hymn, the intonation I’m using is not attempting to be historically accurate. Dear JS would roll in his grave at the heavy use of the 7/4 ratio, for example. There is no evidence that he ever considered the interval in any way useful or musical.

I chose ratios with the single goal of using the lowest possible integers in each chord. Take a look at the first phrase below, where I use two different ratios for the tenor Ab, first 8/5 in chord number 3, then 14/9 in chord number 7, 3 72-EDO steps down:

In chord numbers 8 & 9, I switch from G on 3/2 to 40/27, in order to harmonize with the D 10/9, which was forced by the chord number 7. No sane composer would have a melody haphazardly change from one version of a note to another in a melody. But when you slow everything down, it makes sense harmonically. At least to me.

I used a spreadsheet to multiply all the ratios in a chord by all the other ratios, and then minimized the integers inside the chord. See the following chart for the first ten chords. Click it to make it bigger.

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This is a work in progress. The tuba had the wrong octave in take 6, so I removed it. I also added the ability to select a sample up or down from the one that matches the note, to allow more changes of timbre.

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This version is more or less complete. I’ll need to do some balance checks on different speakers to make sure the levels are correct.
Click to make the image bigger and see the note numbers in 72-EDO.

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This is a work in progress. Today’s version attempts to get back to some basics after wandering far afield over the past few weeks.

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This is a work in progress. Arpeggios mask the tuning. You’d hardly know it was 7-limit just.

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Today’s post is the complete hymn retuned to 7-limit just intonation, approximated by 72 EDO. I think I may have to do this again in true just, because there are some chords that beat. My goal was to have no interval in a chord beyond 7-limit, but I had to fudge a few. This is in no way a claim that Bach would have liked this. It’s just an experiment in some odd harmonies. Click to enlarge the picture and see the 72-EDO notes chosen.

The next step is some transformations of using slides and trills.

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This is a work in progress.

Today’s post is an arrangement of the first two lines of a hymn called Jesus, All My Gladness. It was harmonized by J.S. Bach. I can’t say that I remember it from my days as a soprano in the boy choir. I sang in St. Peter’s Episcopal Church in Albany, NY, from around the 3rd to the 6th grade. We must have screeched through it a time or two.

This is a very challenging tune to render in 72 EDO, 7 limit just intonation. I went through it and bent all the notes I had to to make it sound good vertically. I was merciless, and ended up with some very strange horizontal ratios, including 50/27, 40/27, and 35/27, which were necessary to keep the D at 9/10 and still have a decent minor chord. We are basically sinking down a step in 72 EDO to keep the notes sounding in tune, then just arbitrarily coming back up a step to return to the notes we started at.

The numbers in the image above in blue are the chord numbers, from 1 to 22. The numbers in green are the 72 EDO note numbers. I’ll add the ratios later if I can find room. I’m still considering what to do about the chord changes. I’ve used 18 pitches in what would typically be rendered in 12 EDO in only 9 different pitches. I have to be able to do better than that, I would think.

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I generally create many versions of a piece, and then listen to find one that has something special. Today’s post is the 13th pass through the algorithm, and it has a few new sounds to recommend it.

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I fixed up a few erroneous sustain timings and created a few more versions. This one is take #8, and has a nice busy opening with a Conlon Nancarrow feel to it. That is, it would if Nancarrow had better access to a slide player piano with a whammy bar. The intonation is in 72 equal divisions of the octave. As before, we go through the melody seven times with different levels of variation each time. There are lots of slides from the 7:9:11 to 4:5:6, at various speeds, including slides with pitch vibrato.

I take advantage of some new envelopes I created to enable longer sustain, and even crescendos of piano notes. For example, the normal piano sound has a characteristic waveform that starts loud and gets quickly softer. Here is the waveform of a grand piano played fortissimo on a G at the bottom of the bass clef:

And here is an envlope that will attempt to smooth it out:

And the result, when Csound is told to modify the sample by the chosen envelope:

The result is a note that not only has some serious sustain, but in many cases it will actually crescendo as it sits on the note for a while. The effect is much like that of an electric guitar player using the combination of sustain and feedback to allow a note to grow as it’s held.

There are many other possible envelopes that are applied at different times, resulting in sharp attacks and soft ones, depending on the choices available to each note in the piece.

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