Author: Prent Rodgers

This is a work in progress. The current version is a relatively straight forward performance of J.S. Bach’s first English Suite Allemande, first half. The tuning is from the 31-limit Partch Tonality Diamond, with a sort of major scale (shown here in the key of A) derived from the otonality using the following ratios:

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

The D- and F# are a bit weird. But the G- as the flatted 7th, and the 7th overtone, is very sonorous, as is the 5:4 5th overtone. The piece modulates from A major to E, F#, and B major. I don’t have those keys, so in this case it modulates from A to E+, to F#, and to B. And these keys are in the far reaches of the tonality diamond. If you consider C to be a 1:1, then the ratios for these keys are:
32:19 32:17 32:25 32:23 and the relationships between the keys are nothing like what Bach would have expected. Instead of a simple set of low number ratios as keys to modulate through, I’m in another place. I’m not saying Back wouldn’t have run away screaming at the way this sounds, but my plan is to radically transform his Allemande in the future, much like I did the Tango in the previous piece. We shall see.

Here is a comparison of Bach’s expectations with what I’m using:

or download here:
Allemande #2

Here is the score:

Here we have the final version of Prent’s Microtonal Slide Bosendorfers. Three of these monsters were assembled with my semi-patented whammy bars for this final performance. Gotta love those bass note slides.

This version only includes the utonality keys, but frankly since the major or minor third is only present in 1 out of 16 notes, it doesn’t matter much.

I spent an afternoon cleaning up the Bosendorfer sample files. There were several samples containing loud noises, door slams, and other detritus. I can’s believe people sell these samples with flaws like this. On the other hand, most people play them on the piano and learn by intuition to lift their fingers off the keyboard before the crap shows up. This version is free of chair moves and high pitched noises. It still has the punch in the low notes. It was really only the quiet samples that had artifacts.

or download here:
Tango #21

Keys the algorithm chose. He goes left, then right, then left, the right, then right.

• Cn-min
• D+-min
• Cn-min
• An-min
• Fn-min
• An-min
• Cn-min
• D+-min
• Gn-min
• D+-min
• Gn-min
• B–min
• D–min
• En-min
• F#-min
• En-min
• F#-min
• Ab-min
• A+-min
• Bn-min
• C+-min
• Dn-min
• E–min
• Dn-min
• C+-min
• Bn-min
• C+-min
• Dn-min
• C+-min
• Dn-min
• E–min

This one’s a bit longer. All major keys this time:

• D#-maj
• D–maj
• D#-maj
• E+-maj
• D#-maj
• E+-maj
• F+-maj
• G+-maj
• An-maj
• G+-maj
• F+-maj
• E+-maj
• F+-maj
• G+-maj
• F+-maj
• G+-maj
• An-maj
• Bn-maj
• An-maj
• G+-maj
• An-maj
• Bn-maj
• C#-maj
• E–maj
• G–maj
• E–maj
• G–maj
• A#-maj
• G–maj
• E–maj
• G–maj

The idea of a Tango came from Ravel’s Vocalise-étude en forme de Habanera

or download here:
Tango #17

This is a final version with some fixes to some envelopes and durations, and other challenges. It uses the following chain of utonanities (minor) keys. No major keys (otonalities) were chosen, just by chance.

• Dn-min
• C+-min
• Dn-min
• E–min
• Dn-min
• C+-min
• Bn-min
• C+-min
• Bn-min
• A+-min
• Bn-min
• C+-min
• Dn-min
• C+-min
• Dn-min
• E–min
• Dn-min
• E–min
• E+-min
• E–min
• Dn-min

There is a list of potential keys that can be picked, 16 otonalities, and 16 utonalities. The randomizer chooses a key, then moves to the next one it the list, then back again. The list is ordered based on the Partch Tonality Diamond. The Markov Chain Drunkard Walk can only go forward or back in the list. In this iteration, only five keys are picked across the almost ten minutes of execution, out of a set of 32 possible keys. This particular drunk seems to always come back to the same spot, or almost. He starts at Dn-min and ends there. (The n stands for natural).


or download here:
Tango #16

I’ve been working on adding the Tango part, and these are three versions with the bass part from Ravel’s Habanera. There are some strange artifacts in the samples I’m using. It sounds like when they recorded some of the longer samples someone was walking around the studio, or dropped something on the piano strings. This is going to be very hard to diagnose, since there are 28 samples in each of the 11 sample sets. That means listening to nearly 300 sammples, some of which are up to 21 seconds long.


or download here:
Tango #6

or download here:
Tango #7

or download here:
Tango #8

More keys, more variation in tempo. There are lists of durations, velocities, and notes, and the system uses a Markov Chain Drunkard’s Walk to navigate them. That is, they can only go forward or backward in the lists of lists of lists. Still not a tango, but I’m just getting used to the sounds of the piano now.


or download here:
Tango #4

More keys.

or download here:
Tango #3

Here is another iteration of the tango, which is not yet a tango.

or download here:
Tango #2

I’m just starting to work through two very new things. I bought a sample library of a Bosendorfer piano that included 11 different volume levels. To enable this, I’ve updated my source code to support a linkage between the requested volume and the sample chosen. It was actually only a few lines of Csound code that were required to add that capability. Finding those few lines was a bit of a challenge, but it was worth it.

I also have been incorporating a Partch tonality diamond to the 31-limit. That’s not 31-EDO, but rather the overtonality and utonality to the 31st overtone. Previously I had limited my work to the 15-limit, and frequently to the 11-limit. There is a whole world out there that I’ve only begun to hear for the first time. The current scale has 16 tones per o- or u-tonality, 216 in total per octave.

This piece is just an experiment to hear what it can do. It’s not yet a tango, but that will come later.

or download here:
Tango #1

I’ve been playing around with some impressionist composers of the late 19th century, including Chopin, Debussy, and Ravel. Mostly Ravel’s Habanera, which is a charming piece for piano and soloist. I’ve heard versions with clarinet, violin, and flute, and they are really lovely. I thought, well, let’s really mess it up by realizing a microtonal version. I tried some of my 15-limit scales, but quickly ran out of notes. Ravel is very chromatic, and an 8 note 15 limit scale is missing several accidentals, and the ones it has are a little strange.

To find some more of those missing notes that I’m sure Chopin, Ravel, & Debussy would use if they only had instruments that could play them, I moved up to a 31 limit. That’s 8 more notes per otonality and utonality scale to make 16 per octave per scale, with 16 scales to build. I’ll be trying to adjust my Csound sampler to accommodate the extra notes. The 31-limit in just has 217 distinct pitches per octave, quite a bit more than the 72-EDO scale I’ve used lately. (I add three notes at the top and bottom of the scale to make the first jump 1/3 less large. They are not in the diamond. While I’m at it, I plan to add the ability to automatically pick the right samples base not just on pitch but also volume. I bought a Bosendorfer sampler online, which has 5 or 6 different samples per note, depending on how hard the note is played. Most modern sample players handle that automatically, but mine, built with Csound, will take some more work. Not a lot, just some more.

Here is a picture of the 31-limit tonality diamond lined up with ratios in order from 16 to 31. It uses the following otonality ratios: 16:17:18:19:20:21:22:23:24:25:26:27:28:29:30:31. Each box in the diamond has the ratio in just, the pitch number in a non-equal 217 notes to the octave scale (1-217), and the note name in Sagittal notation. Click on the link below to enlarge it. As you might expect, 31 Limit is large. From a spreadsheet that I’d be happy to share.