Author: Prent Rodgers

I took a side trip to find more triads in the 31-limit tonality diamond. With the diamond to the 11-limit, using either the otonality or utonality only, there are really only four valid triads, where valid is defined as having a pure major fifth, and four thirds: 7:6, 6:5, 5:4, 9:7. I systematically explored the 31-limit diamond and found many more. Here is a summary table of the thirds I found inside pure 3:2 fifths, in the otonality and utonality only.

Each of these can be transposed to any key in the utonality or otonality, depending on from which they were derived. That’s a total of 180 distinct triads across the entire diamond, after some duplicated ones were eliminated. I played each one with a keyboard to find a reasonable diatonic scale for each, plus two 7th’s, major and minor. Now I plan to use these to pick more sonorous keys for the Allemande dance by Bach. But that’s not for today.

What we have today is just all 144 unique triads, sorted by the 1st degree, then the 3rd degree, starting with the most subminor going to the highest bearable super major. In order. Straight through. This is not music, but it is interesting to listen to.

or download here:
Allemande #4

For this version, I enabled the entire Bosendorfer sample set, although it only uses the 5 moderate velocity samples. It adds a bit more color. Same tuning and keys. Next, I will begin work on the second half of the piece.

or download here:
Allemande #3

Here is the score:

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.

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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

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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).


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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.


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Tango #6

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Tango #7

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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.


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Tango #4

More keys.

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Tango #3

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

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Tango #2