Blog

Chaconne #3

This is a new piece I’m just starting to work on. It’s based on Bach’s Violin Partita No.2 in D minor, BWV 1004, transcribed by Brahms for piano left hand. This piece has been performed and written about for centuries. Here’s a short essay, “About the Piece” as prepared for the LA Philharmonic by Grant Hiroshima.

Bach’s Chaconne for solo violin is a summit of Western music: as a technical and musical challenge, the violinist’s Everest. But musicians have not been content to leave this masterpiece solely in the fiddle’s intimate four-stringed domain. The famed conductor Leopold Stokowski created an immense orchestral version in the 1930s. And pianists have long made the Chaconne a concert favorite in the elaborate and virtuosic transcription by the legendary Italian pianist Ferruccio Busoni.

But they say tennis is no fun without a net. And in crafting his austere and perhaps more reverential vision, Johannes Brahms was seeking a different musical truth. Presenting his transcription to Clara Schumann (his friend and the widow of Robert Schumann), Brahms wrote: “The Chaconne is, in my opinion, one of the most wonderful and most incomprehensible pieces of music. Using the technique adapted to a small instrument, the man writes a whole world of the deepest thoughts and most powerful feelings. If I could picture myself writing, or even conceiving, such a piece, I am certain that the extreme excitement and emotional tension would have driven me mad. If one has no supremely great violinist at hand, the most exquisite of joys is probably simply to let the Chaconne ring in one’s mind. But the piece certainly inspires one to occupy oneself with it somehow…. There is only one way in which I can secure undiluted joy from the piece, though on a small and only approximate scale, and that is when I play it with the left hand alone…. The same difficulty, the nature of the technique, the rendering of the arpeggios, everything conspires to make me feel like a violinist!”

Majesty and vastness are easily conjured when two hands and a grand piano, or for that matter a full symphony orchestra, are called into service. But it is far more challenging to recognize that the true genius of the Chaconne is that it achieves its immenseness within the confinements of a single violin, and then to seek to inhabit on the piano this achievement with just the left hand alone.

Never shy to follow in the footsteps of giants, I’m venturing off to see what I can do to the piece with my 31-limit tonality diamond and my microtonal slide Bosendorfers.

I’ve only completed the first 16 measures, as written by Brahams below. The basic idea is to take the notes, durations, and velocities, and mix them up using the drunkard walk. The keys are well represented by the the Otonality and Utonality, with some modes taking the scale from different origins. The Chaconne is a four measure ostinato in the bass, more or less. And it soons get very complex.

or download here:
Chaconne #3

Chaconne

Scales in 31-limit tonality diamond

I have sets of 16 note scales derived from the 31-limit tonality diamond. The Otonality is the overtones, the Utonality are the undertones. Otonal scales have the ratios of 8:9:10:11:12:13:14:15:17:19:21:23:25:27:29:31. The Utonal scales are the opposite: 32 over 16:17:18:19:20:21:22:23:24:25:26:27:28:29:31.
That gets me a matrix that is 16 by 16, or 256 notes. Click the following image to enlarge it.

Diamond

Elimintating duplicates, there are 216 unique pitches per octave. Right out of the gate I have 16 major 16-note scales based on the otonality, and 16 minor scales based on the utonality. Otonality is read up and to the right, Utonality is read down and to the right, except the scale starts at the note a 3:2 below the starting point. For example, Utonality of F is on the row starting at C 1:1, and the root of the scale is F 4:3.

When I was working with the 15-limit diamond, I noticed that there were other scales, in addition to major and minor, that could be found in the diamond. In 15-limit diamond, there are two additional scales with very good 5th’s. I called one the sub-minor with a 7:6 3rd, and the other a super-major with a 9:7 3rd.

When I took a systematic look at the otonality and utonality scales in the 31-limit diamond I found other modes that could be used to construct scales with perfect major 5ths. By other modes, I mean out of each 16 note scale, start at different points in each to find interesting scales. Limiting the search to only those with perfect 5ths, I found 22 distinct modes, and with the 16 otonal and 16 utonal scales, that left a total of 191 unique and interesting scales.

The 3rds are anywhere from 7:5 subminor to 31:24 sensi supermajor.
3rds in 31-limit scales with perfect 5ths

I then checked the other notes out for closeness to major or minor just. I evaluated the 2nds, 4th’s, 6th’s, and two different 7ths to see how many cents off each was, and then sorted them by distance from just. I ended up with 40 that were pretty good. In the chart below, the first column is the scale name. The first letter of the scale name is the root, the second two numbers are the third ratio, and the last two numbers are the root of the otonal (O) or utonal (U) from which the scale was derived.

For example, the first in the list starts on C, and has a 5:4 major third, and is derived from the otonal scale in the key of F. In the tonality diamond, the F otonality starts in the 9th position along the axis starting at C 1:1, then B 32:17, then A 16:9, then A 32:19, A 8:5, G 21:21, G 16:11, F 32:23, F 4:3. So the F 4:3 otonality, read up and to the left from the F 4:3, is G 17:12, G 3:2, G 19:12, A 5:3, A 7:4, B 11:6, B 23:12, C 1:1. Start the scale at that C as root, and pick the best 12 notes from all in the F otonality 16 to create a mode that is relatively close to Just major scale.

The next columns in the chart are the closest 24-EDO root of the scale, the actual root as a ratio, and the name of the o/u tonality 16 note scale that was used to derive a new scale. The next column, labelled “Mode” is which of the 22 modes are applied to determine the 12 note scale in use.
Diversions In Cents from Just major and minor ideal scale

For Follia, I only needed C, d, A, F, and g. Easy peasy. C, and F were straight otonal scales. D minor was a straight utonal scale. G minor was the 7:6 subminor based on the C otonality starting 3:2 above the root. A major was derived from the F otonal scale, starting at the A a 5:4 above the fundamental and going up from there.

Allemande was much more complex. For this piece, I needed nine keys, and almost none were straight otonal or utonal. I tried many different modes and scales before settling on a set. The challenge of finding reasonable sounding keys was very time consuming, so I resorted to sorting the potential scales based on how close it was to an ideal Just major or minor scale.

Follia #4

Another run through the algorithm produced these variations on Arcangelo Corelli’s Folia Opus 5, a piece written just prior to 1700, for violin and continuo. Folia is a chord progression well used in the 15th and 16th centuries by a variety of composers. Think of it as the 12-bar blues of early classical music tradition. Corelli’s version is a theme with 23 variations. My version intersperses the theme with the variations, as I did with the Allemande.

This version is scored for my microtonal slide Bosendorfers, realized in Csound. The tuning uses two otonalities (based on C & F), one utonality (D), plus a few mixed tunings (an A major based on the F otonality, and G minor based on the C otonality) from the 31-limit diamond.


or download here:
Follia #4

Follia

Follia #6

I present here some variations on Arcangelo Corelli’s Folia Opus 5, a piece written just prior to 1700, for violin and continuo. Folia is a chord progression well used in the 15th and 16th centuries by a variety of composers. Think of it as the 12-bar blues of early classical music tradition. Corelli’s version is a theme with 23 variations. My version intersperses the theme with the variations, as I did with the Allemande.

This version is scored for my microtonal slide Bosendorfers, realized in Csound. The tuning uses two otonalities (based on C & F), one utonality (D), plus a few mixed tunings (an A major based on the F otonality, and G minor based on the C otonality) from the 31-limit diamond.


or download here:
Follia #6

Follia

Follia #2

I’m working on some variations on Arcangelo Corelli’s Folia Opus 5, a piece written just prior to 1700, for violin and continuo. Folia is a chord progression well used in the 15th and 16th centuries by a variety of composers. Think of it as the 12-bar blues of early classical music tradition. Corelli’s version is a theme with 23 variations. My version intersperses the theme with the variations, as I did with the Allemande. I still have more work to do, but this is a good introduction. This version is scored for my microtonal slide Bosendorfers, realized in Csound. The tuning uses two otonalities (based on C & F), one utonality (D), plus a few mixed tunings (an A major based on the F otonality, and G minor based on the C otonality).


or download here:
Follia-t2

Follia

Allemande #15

This version includes the second part of the dance, which is more complex than the first. I’ve applied the same deconstruction to this part as previously. I have a set of rhythms, dynamic accents, and notes. If they are played correctly, then it represents the Allemande dance as written. But I can also assign the rhythm of one measure, the dynamics of another, and the notes of a third, as well as extend they time 2x, 4x, or cut it in half.

It’s really a theme and variations style, but the themes and variations are intermixed.


or download here:
Allemande #15

Allemande #9

Score of the first 16 measures
Today I reached the 16th measure. 16 more to go. I may stop here, because it’s getting long.

The preprocessor has the option to choose the durations from one measure, and the notes from another, and the volumes and accents from a third. Plus it can double or cut in half the speed. But first it is set to play the measure straight, then variations in the same key.

Imagine if Bach had spilled the stone manuscript on the floor into a thousand pieces and some musical archaeologist had to put it back together.


or download here:
Allemande #9

Allemande #8

In DFW at the Hyatt for a meeting for four days. Haven’t seen the outside world in three days. But Allemande is never far from my mind. In this version I’ve doubled the speed, and still support the 1/2 and 1/4 speed versions. There is much more indeterminacy now, so I’m comfortable I can eventually come up with some music. Tonight I reached the 6th measure. 26 more to go.

Imagine if Bach had spilled the stone manuscript on the floor into a thousand pieces and some musical archaeologist had to put it back together.


or download here:
Allemande #8

Allemande #7

I’ve rewritten the first part of the Allemande so that I can more easily manipulate different aspects of the piece. In this case, I’ve made it possible to stretch the time by two to four times. I’ve also made it possible to apply one measure’s rhythm to another measure’s notes, and a third measure’s dynamics. I’m just getting started making it work. Today’s version includes only the first seven measures. 

Next up is including double speed options, and then retranslating the rest of the 32 measures to increase the surprises. I love surprises. I already include two different F# major modes, one with a bad 6th and the other with a bad 4th. 

I should probably have sorted all the combinations by some sort of a scoring scheme. For every cent out of tune for a 5th, 5 points. For every 4rd out of tune, 4 points per cent. Every 3rd or 6th out of tune 3 points. Every second out of tune, 2 points per cent. 

There are hundreds of potential scales in a 31 limit diamond. I just have to find the right algorithm. Wish me luck.

or download here:
Allemande #7