This one is another trip down the drunkard’s walk. Some earlier versions are here, here, & here. This is a work in progress.

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Gavotte II Transformed #4

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# Author: Prent Rodgers

## Gavotte II Transformed #4

## Gavotte II Transformed #3

## Gavotte II Transformed #2

## Gavotte II #1

## Berceuse #4

## Berceuse #3 in Db Major Opus 57

## Berceuse #2

## Berceuse #1

## Chaconne #8

## Sarabande #5

This one is another trip down the drunkard’s walk. Some earlier versions are here, here, & here. This is a work in progress.

or download here:

Gavotte II Transformed #4

This one is another drunkard’s walk, but with the addition of making choices between two different 6th degree ratios (the E in the piece), and two different 7th degree ratios (F#).

The algorithm switches between E as 5:3 above G, and E+ as 7/4 above G. It can choose F# as 23:12 or F+ as 11:6 above G. Sometimes they can pick two different tunings at the same time. The difference is pretty minor but it does sound more harsh this time. This is a work in progress.

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Gavotte II Transformed #3

This is a transformation of Bach’s English Suite #3 Gavotte II movement, BWV 808. The original is here. For the transformation, I allow my preprocessor to chose which measure to play using the Markov Chain Drunkard’s Walk algorithm. I have a list of all the measures in order, and let the preprocessor choose which one is next, constrained to either the next or previous in the list. For example, if measure 5 is chosen, then the next measure to be played can be either 4 or 6, forwards or backwards in the list. If I’m at the end or beginning of the list, it wraps around. There are only 19 measures in the movement.

I start the piece by playing the first five measures in order, then start the randomizer. The next ones chosen for this run through were the following:

- Measure 19
- Measure 01
- Measure 02
- Measure 03
- Measure 02
- Measure 01
- Measure 02
- Measure 01
- Measure 19
- Measure 01
- Measure 02
- Measure 01
- Measure 02
- Measure 03
- Measure 02
- Measure 03
- Measure 02
- Measure 03
- Measure 04

Eventually our drunk wanders across the entire piece after about 100 choices. At the end, I play the last five measures straight.

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Gavotte II Transformed #2

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 |

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Gavotte #1

This is a revision only to fix some spurious volume errors and add a trill to a note in the 45th measure. I left it out by mistake.

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Berceuse #4

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 |

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Berceuse #3

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.

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Berceuse #2

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.

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Berceuse #1

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:

- D minor based on the Utonality on D
- A major based on the Otonality on F, starting a 5:4 above the F
- 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

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.

Here’s a picture of the pitch modifier used in Csound to match the Bach recommendation.

See measures 4 & 5 for their use.

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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.