Here is another version with some arpeggios and more interesting dynamics and timbre from Prent’s Microtonal Slide Bosendorfers.
The tuning is Just Intonation for each measure, but it changes from measure to measure, so the are many comma-sized changes from one measure to the next, where a note from one measure changes by a comma in the next.
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Dox #3
This is a realization of a hymn known as the “Old 100th”, originally written by Loys Bourgeois in the early 16th century. When I was growing up, we called it the “Doxology“, as the tune was heard most frequently as the setting for the following lyrics:
Praise God, from Whom all blessings flow;
Praise Him, all creatures here below;
Praise Him above, ye heavenly host;
Praise Father, Son, and Holy Ghost.
In my youth I sang it just about every Sunday in the Episcopal choir in Albany, NY, as a soprano.
Today’s version is a combination of the actual hymn, together with transformations where the next measure played is either the one before or the one after the current measure. It’s the Drunkard’s Walk Markov Chain, going either forward or backward through the measures.
The tuning is mostly conventional just intonation, with scales derived from the tonality diamond to the 31 limit.
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Dox #2
This is the 2nd movement of Mozart’s Sonata #6 K 284, Rondeau. It’s scored in the key of A major, unlike the D major in the other movements.
The tuning I use is similar to what I used for the other movements, with the addition of a new scale for the E major measures.
Stream online:
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Rondeau #1
Here is a version of the first movement of the Sonata I’ve been working on lately. It uses the same four scales derived from the Partch Tonality Diamond taken to the 31-limit.
Click on the image for a larger version:
For each measure in the piece, I chose which of the four scales to deploy based on how well it plays the notes in the measure.
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Mozart K284 Allegro #1
This is another realization of yesterday’s post with more tempo variability.
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Mozart K284 Theme and Variations #13
I’ve been working on this piece for a few months, and have finally completed the theme and all 12 variations. The piece is a masterpiece, in my opinion. That it was written when Mozart was only 19 years old is astonishing. That he was never paid for it is one of the many injustices done to poor Wolfgang. Wiki for more info.
The piece is in D major, with the exception of the 7th variation, which is in D minor. The basic harmony includes the chords D major, B minor, E minor & major, and A major and some diminished chords.
The tuning is taken from the tonality diamond to the 31-limit. I chose three 16-note scales from to utonality, and one from an otonality.
| O/U | Root | Key | 3rd | |
|---|---|---|---|---|
| O | 16:9 | Bb | D | 5:4 |
| U | 5:3 | A | D | 9:7 |
| U | 5:3 | A | B | 7:6 |
| U | 5:4 | E | A | 9:7 |
To derive a scale I used three 16-note utonality or otonality scales from the 31-limit diamond. The first column in the table determines if the scale is either otonal or utonal. The root is the base note for the 16 note scale.
The first row shows 16:9 Bb otonality as the origin of the 16 note scale. I derive a mode from that scale based on choosing the D (10:9) as the root of the scale in the piece.
The next row shows the 5:3 A utonality as the origin of a 16 note scale, with the root on D 10:9. The next one is from the same 5:3 A utonality, but with the root on 15:8 B. The last row takes a mode from the 5:4 E utonality with A 5:4 as the root.
This generated several scales:
| D maj 1 | ||||||||
| Note | D | E | F# | G | A | B | C# | D |
| Cents | 0 | 242 | 386 | 520 | 702 | 919 | 1111 | 1200 |
| Ratio | 1:1 | 23:20 | 5:4 | 27:20 | 3:2 | 17:10 | 19:10 | 2:1 |
| D maj 6 | ||||||||
| Note | D | E | F# | G | A | B | C# | D |
| Cents | 0 | 204 | 435 | 498 | 702 | 933 | 1106 | 1200 |
| Ratio | 1:1 | 9:8 | 9:7 | 4:3 | 3:2 | 12:7 | 36:19 | 2:1 |
| B min 1 | ||||||||
| Note | B | C# | D | E | F# | G# | A# | B |
| Cents | 0 | 1732 | 267 | 471 | 702 | 898 | 1119 | 1200 |
| Ratio | 1:1 | 21:19 | 7:6 | 21:16 | 3:2 | 42:25 | 21:11 | 2:1 |
| A maj 2 | ||||||||
| Note | A | B | C# | D | E | F# | G# | A |
| Cents | 0 | 204 | 435 | 498 | 702 | 933 | 1106 | 1200 |
| Ratio | 1:1 | 9:8 | 9:7 | 4:3 | 3:2 | 12:7 | 36:19 | 2:1 |
The D major 1 scale, in addition to a decent D major, has a fair A major with neutral/sub minor third, a good B major and minor scale, and a good G major scale. When these chords are needed, I chose the D major 1 scale.
The D6 major has a great A minor, with a 6:5 minor, and 409 cent major third. It has a nice G major, with a 9:7 very sharp but usable major third. It also has a decent B minor,
The B minor 1 scale has a good F for the D minor variation.
The A major 2 scale has the best E major and minor, which are frequently used in the piece. The minor is 6:5 and the major is 24:19, 4 cents above a 12-TET major third, which is what was common at the time. This scale also has a decent D major and A major scales, a little high on the major third.
As you can see, there are lots of strange notes in this set of scales. I like to call them puns
on the target ratio. I have one 5:4 third, and two 9:7’s and a 7:6, not ordinarily trusted as major and minor thirds. The fourths should be 4:3, yet I have a 27:20, 21:16, along with two 4:3. All four have a good 3:2 fifth, but all were selected to have perfect fifths.
To chose which of the four scales to use for each measure, I played them to see which sounded best for each measure. This lead to situations where an F# might vary by 50 cents from one measure to another, so I would often go back and choose a different scale instead of the one chosen originally.
I don’t mean to imply that this is a good
or historically relevant tuning for this piece. I’m sure the maestro was rolling over in his grave at the heresy of this ahistorical tuning of the piece. But this is 2018 and Trump is President.
I did it as an experiment and found that the tuning appears less grating the more you listen to it, and it can grow on you if you don’t run screaming from the room too quickly.
The performance was realized in Csound using Prent’s Microtonal Slide Bosendorfer (commercial Emporer
samples). The only slides are in variation #11, where they are frequently used as grace notes and sometimes as trills.
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Mozart K284 Theme and Variations
Here’s the 10th variation.
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var 10
Here’s the 9th variation.
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var 9
Here’s the eighth variation.
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var 8
Here’s the seventh variation.
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var 7
