Gavotte II #1

Today’s creation is a realization of the 2nd Gavotte in Bach’s English Suite #3 BWV 808 on Prent’s Microtonal Slide Bosendorfers. There are two Gavotte’s in the suite. The first is in G minor, and the second in G major. The score indicates several repeats, including the request to repeat the first after the last repeat in the second. I’ve only completed the second Gavotte, in G major. The tuning is taken from the 31-limit tonality diamond. I used a G major scale derived from the 16 notes in the C otonality. The are a nearly perfect diatonic just scale, with the exception of the F#, which should be a 15:8 above the G tonic, but is actually 23:12, 38 cents sharp. And out of tune with the perfect 4:3 C. It has a perfect F tuned to 7:4, but alas that’s a note that Bach did not include.

Here is the complete scale:

Degree Name Ratio
1 G 1:1
2 A 9:8
3 B 5:4
4 C 3:2
5 D 4:3
6 E 5:3
7 F 7:4
G F# 23:12
1 G 2:1

Gavotte II

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Gavotte #1

Berceuse #3 in Db Major Opus 57

I’ve continued work on the lullaby by Frédéric Chopin, his Berceuse opus 57 published in 1843, when he was 33. This version includes the entire movement, 70 measures long.

The scale I used is mostly diatonic, with a few extra notes to achieve what I think Chopin might have done, had me been as twisted as me. The notes are all derived from the Otonality on C#. My names for the 16 Otonality degrees in 31-limit are, starting at the 1st overtone, 1 through 9, then A, B, C, D, E, F, G. In this piece I did not use the 6th degree, 13:8 or the Gth degree, 31:32. The 14 I did use are shown below.

Degree Name Ratio
1 Db 1:1
9 D 17:16
2 Eb 9:8
A E 19:16
3 F 5:4
B Gb 21:16
4 G+ 11:8
5 Ab 3:2
D A 25:16
E Bb 27:16
F B 29:16
7 Cb 7:4
8 C 16:15
1 Db 1:1


or download here:
Berceuse #3

Berceuse #2

I’ve continued work on the lullaby by Frédéric Chopin, his Berceuse opus 57 published in 1843, when he was 33. Here are measures 56-71, the ending that I found so transcendent when I first heard it. I made the C flat a 7:4 above the D flat major key. I also tried some other odd ratios here, including replacing the 6th degree (now a 27:16) of the scale with a 13:8, and the 4th degree (now a 21:16) with an 11:8, but my ears would have none of it.

or download here:
Berceuse #2

Berceuse #1

I’ve started work on a lullaby by Frédéric Chopin, his Berceuse opus 57 published in 1843, when he was 33. There is one passage towards the end that is truly transcendent. I’m starting at the beginning. Today’s offering is measures 1-16. The tuning to represent the 12-EDO Db major is derived from the Otonality of Db, but the notes I’m using in this part are a typical diatonic just scale:

  • Db 1:1
  • Eb 9:8
  • F 5:4
  • Gb 21:16
  • Ab 3:2
  • Bb 27:16
  • C 15:16
  • Db 2:1

The Gb is 27 cents flat, a 64:63 off. But the rest are a relatively sweet diatonic major scale.
There are a total of 16 notes in the 31-limit Otonality. I’m picking them carefully. I think Chopin only chose notes other than these diatonic ones as chromatic stepping stones when he moved from one major scale note to another.

or download here:
Berceuse #1


Chaconne #8

I’ve revised the arpeggios and fixed a few wrong notes in my version of the Chaconne by J.S. Bach as transcribed for piano left hand by Brahms. I previously didn’t make the arpeggios flow from bottom to top, but they do now. It sounds more pianistic this way. The tuning is still based on three scales:

  1. D minor based on the Utonality on D
  2. A major based on the Otonality on F, starting a 5:4 above the F
  3. D major based on the same Utonality on D, but picking different notes

More info on this work can be found here, here, here, and here.

or download here:
Chaconne #8

Sarabande #5

I completed the 9th through 24th measures of Sarabande and this version is more or less complete. I may run a few more iterations of the randomizer and see how that changes things. I divided each measure into three, a quarter note per choice. For each quarter not, the preprocessor picks either a straight version, or one with arpeggios of different speeds and directions (up, down, or random), with quick moving pairs of notes turned into a glissando, and whacked out arpeggios far into the upper ranges of an otonality or utonality. For this version, I’ve made it possible to change to a different base otonality or utonality in the middle of a measure, instead of forcing it to stay for a whole measure in one scale. For example, measure 23, the second to the last, foes from F major otonality, to Bb major otonality, to F, then C major otonality. This forces some different Bb’s, some as the 7th overtone of C, some as a 16/9. It just sounds Just to me.
See more information on this piece here, & here.
I made the trills have the same number of steps as those recommended by C.P.E. Bach “trillo”, but through bending instead of discrete notes. Because I can, I guess. Some will find this strange.
C.P.E. Bach Trillo
Here’s a picture of the pitch modifier used in Csound to match the Bach recommendation.
New trills to match CPE Bach
See measures 4 & 5 for their use.
Sarabande Sheet Music

or download here:
Sarabande #5

Note: There was a bug in my Csound code that affected measure 11. It was an occasional reference to an invalid table. I reran the preprocessor, and it escaped this time without the error.
For geeks, here’s the source code to the preprocessor,
Here’s the Csound score it produced.

Sarabande #2

This version is similar to yesterdays, except for the keys used and some additional variations on the held chords on the second beat of the measures.

I moved the F major and C major keys to become based on their respective Otonality. I did not use the 11:8 as the 4th degree of the scale, but rather the 21:16, which is closer to a normal 4:3. Likewise the 6th degree of the scale is not the 13:8, but rather the 27:16, which is closer to a 5:3, a sweet sounding just ratio for the 6th degree of a scale. In sum, for a major scale, the ratios for the keys of C & F are:

  • 1 C 1:1
  • 2 D 9:8
  • 3 E- 5:4
  • 4 F 21:16
  • 5 G 3:2
  • 6 A 27:16
  • 7 Bb 7:4
  • 8 B 15:8
  • 1 C 2:1

Sarabande Sheet Music

or download here:
Sarabande #2

Sarabande #1

Today’s work is a realization of the first eight measures of Bach’s English Suite #3 (BWV 809) Sarabande movement. The sarabande dance was first mentioned as a dance performed by Spanish colonists in the new world in the 16th century, thought indecent by some. Jesuit priests claimed it incited bad emotions in even very decent people.

By the time that Bach composed his English Suites, perhaps around 1718, it was considered a slow traditional dance form. What interested me about the piece is the interpretation of ornamentation. In the version that Glenn Gould recorded in 1977, he goes really wild with improvisational transformations of the written score. He has trills, rubato, glissando, and other ornaments that are not to be found in the score I have. Since I like to transform things, I decided to try my hand at it.

For this version, I created five or six variations for each quarter note beat in the 3/4 time signature. The software selects which 1/4 note duration to play at any given time. Some alternatives include glissandi (real ones), others have rubato, stretching notes across beats, and other changes.

The tuning is taken from several otonal and one utonal 16 note vectors in the 31-limit tonality diamond.

The keys of F, Bb, and D major are derived from the otonality of A#. The C and A major are derived from the otonality on F. G major is derived from the otonality on C, and the D minor is from the D utonality.

Sarabande Sheet Music

or download here:
Sarabande #1