### Fugal Science: Vol. 2, No. 4 - Five-Part Ricercare for Orchestra

EDIT: This is part 8 of 8. Here are the links to the entire series:

Index of Fugal Science, Volumes 1 and 2Here is today's audio. It's just a string choir arrangement, as I still have to make digital fair copies of this piece, as well as the five-part grand fugue of volume one, in the orchestral arrangements. That will be my next project, and since I have to start by making a new Encore template, it could take a while.

Five-Part Ricercare for Orchestra

I apologize for the left side of the mix being hotter than the right, but I'm chasing some balance gremlins and ran out of patience with it. So no, it's not your imagination - or your system's fault - that the balance is out of whack.

We're back up to a-minor now, but the tempo is a slow 63 BPM to really bring out the super-hot dissonance points. Otherwise, this part of the exposition is exactly like the three- and four-part versions.

This page is exactly like the four-voice fugue as well, with the third entry and the required linking episode.

Whereas the four-part fugue left us on the dominant level, this ricercare finally has the fifth entry on the tonic. Note how the simple means I limited myself to produce a magnificent and moving effect here: The fourth entry of the answer on the dominant has the highest note of the piece at f-natural in measure twenty-one, and then the basses get the lowest note of the piece at e-natural in measure twenty-nine (The lowest note on four string basses without the extension to get c-natural, which is what I'm figuring on for when I hire an orchestra to play it).

With the exposition behind us - a relatively vast twenty-nine measures - we transition back to four voices with the second appearance of the episode, and then the six measure interlude comes along. This sets up for the middle entries.

For the overall plan of this fugue - a ricercare is just a particularly large fugue, or one that goes to distant keys - I chose to go back down to two voices and build back up from there, presenting the extensive canonic possibilities of this amazing subject as I go. Here, we get the two-part canon at three measures of delay/two measures of overlap, that is also a perfect dovetail: The countersubjects require no modification to work, they are just interrupted or joined in progress. This was the same canon I presented all the way back in the guitar version, by the way.

This dovetail sets up the two-voice version of the episode, which leads to the three-voice canonic possibilities, which are amazing.

We directly modulate to the dominant, as in the four-part fugue, and this three-part Escher morph/perpetual canon is exactly as before: The canon at two measures distance morphs into itself in augmentation - this does not work in more than three parts - and then into the doubly-augmented subject with the original head figure and diatonicised tail, and back.

On this page we get the dovetail into the doubly augmented version of the subject.

And now that sublime series of searing dissonances - what I've come to call a dissonance flow - that seem so poignant to me, and then the re-transition back to the augmented subject. I think a good conductor could have a field day with this piece.

Then the head of the doubly-augmented form of the subject reenters, proving the perpetual part of the canon - going back to the original note values does not work - and right at the point where the beautiful dissonance flow would appear again, the contrabass makes a dramatic entrance and a direct modulation back to the tonic. As I mentioned in the previous post, stacking the canon up from the bottom produces some wonderful conflicts that I was able to take advantage of.

The top line breaks the canon by repeating the subject, and then the final conflicts are set in motion in a dissonance flow that is evocative of boiling water to me.

These conflicts come to a head when the cello and bass arrive on a unison f-natural in measure 113. The cello then dips below the bass to play the e-natural, f-sharp, and g-sharp against that f-natural, and that is the climax of the section.This is much more dramatic with the bassoon and trombone doubling the cellos, and the contrabassoon and tuba doubling the basses.

The augmented subject head then reenters, the tension ebbs, and we get our episode again.

That's the second episode since the previous interlude, so now comes the final interlude, lengthened to seven measures this time to get the caesura that prepares for the introduction of the final five-part perpetual canon. The introduction is the anacrusis made with the diminished triad at the top.

Finally, with five voices, we get the full harmonies I intended. At 136 it's a **bVI(M7)** in first inversion, reading, bottom to top; a-natural, a-natural, c-natural, e-natural, and f-natural. It's the minor ninth between the top voices that makes it so astringent. Then at 137 we get the same **bVI(M7)** in first inversion, but this time it reads up as; a-natural, c-natural, e-natural, f-natural, and e-natural. This puts the minor ninth between the violas and second violins, so that dissonance is moving down through the voice pairs as the canon unfolds. By 138 the **bVI(M7)** has become a second inversion sonority reading up as; c-natural, e-natural, f-natural, e-natural, and c-natural, with the minor ninth between the tenor and bass voices. In 139 - bet you guessed it - we get the third inversion of the **bVI(M7)** reading up as; e-natural, f-natural, e-natural, and a-natural. Finally, we get the root position **bVI(M7)** in 140, reading up as; f-natural, e-natural, c-natural, a-natural, and c-natural. Now the minor ninths are played out, and we get the root position chord. This logical canonic progression makes this dissonance flow seem profound to me. Also, the note doublings are modal, and not tonal, so that adds to the eerie effect.

Now we re-transition to the original subject, and back, proving the perpetual nature of the canon.

And so we wind down over the ostinato of the tail figure, revisiting the descending minor ninth sequence as we do so, and end up with all five voices on the tonic: the pluperfect resolution.

As I mentioned above, I now need to do digital fair copies of the two orchestrated pieces, which could take a lot of time. In the meanwhile, I'll link these posts together so that anyone who finds one will have the links to all of them.

Back sometime next month.