Drei Equale

This is a work in progress. I've made a few updates to the ratios of some of the notes to take the advice of some microtonalists. My ratios are shown on the JPG below in blue, Marcel de Velde's in black. I tried to eliminate the wolfs. The differences are small to Marcel's choices, a 7/6 instead of an 6/5 at chord 12 to enable the 7th overtone, and several choices that are 81/80 or 64/63 different. What's a 225/224 among friends? (chord 27: I like the 7/5, he has 43/32. I'm trying to make sure that when you hear a 3/2, it is a 3/2, and not a 20/27 or a 45/64, or something like it. That's my rule for now. See measure 5, where I've changed the 9/8's to 10/9, to keep a 3/2 instead of the 20/27.

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O Sacred Head, Now Wounded - #14

For this version, I switched from 72-EDO to pure just, to hear the effect. The samples I use are as in well tuned as I can get them, but I still hear beats in some chords, even with pure just intonation. Some of the samples move around in pitch as they transition from the attack to sustain. I can imagine those poor guys in a room playing into a microphone trying to hit a pitch. There's only so much you can do with human beings, I guess.

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Drei Equale - Beethoven Trombone Quartet

This is a work in progress. Marcel de Velde has asked several microtonalists to apply our intonation efforts to retuning Ludwig Von Beethoven's Drei Equale for trombone quartet. Here's my first pass at the first 21 measures. I used Csound and a trombone sample from the McGill University Master Samples library. I don't have any midi tools available.

I've used some strange ratios, especially for the diminished triads. Measure 12 starts with a D minor, which I use 10/9 4/3 5/3. In the next chord, the A becomes an Ab to make a diminshed triad. I chose the ratio of 14/9. That makes a 5:6:7 ratio, as in the otononality scale. How else to chose? Where did the diminished triad originate?

There is another diminshed triad in measure 17, last note. I chose 6:11:13 here, and it really sticks out. Maestro LVB would not approve. Any better ideas?

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Now Thank We All Our God #9

This is a work in progress. This is the current ninth take. It's shorter than the others, at just under eight minutes. The algorithm chooses how long to stay on each chord from a list of choices, one to five beats, then repeats it zero to two times. That way, it can be as short as one beat to as long as fifteen beats on each chord.

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Now Thank We All Our God

This is a work in progress. Today's version is mostly complete. I've generated four and will pick one as the final version.

This version is another of my Transformed Hymns, which take a familiar hymn tune and stretch it out a bit. Each chord of the hymn becomes a measure or several measures of the transformation. Now Thank We All Our God is a Felix Mendelssohn harmonization of a 17th century tune. There are many unusual chord voicings in the arrangement I have, from the Center for Church Music. There are sevenths in the bass and other unusual arrangements. There are also some challenging comma issues, which I work through by switching from one note to another to preserve the harmony. My goal is to make a good just chord, and so I sacrificed melodic consistency sometimes. If a note starts out as a 16/9 to go with a 4/3, then drifts down to a 7/4 as the 7th in a major chord, it does it. No questions asked. Listen at around 1:45 in this version for the gradual 2 step in 72EDO fall in the Bb. Here it is in score form:

Here is a chart of the notes that I used in the piece. Notice how often the C, F, G, A, Bb are used, and that lonely G# passing tone as a major third to the E natural.

The piece is scored for flutes, clarinets, french horns, trombone, tuba, finger pianos, regular pianos, harp, marimba, and vibraphone.

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