Reductio Fingerings II

Ha! This is my 200th post to MMM. Believe I'll celebrate with a brew or two. Anyway...

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The Fuga: Reductio ad Absurdum theme is now going to become a series of compositional/technical studies for the guitar, and not a variation set as I had previously thought (Except for in the wind quartet version, of course).

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I enjoy writing sets of closely related pieces, and have done a lot of it in the past. Previous sets I've written have included:


1) Six Studies on an E-Axis

Open string studies for guitar using the open high E-string in two-voice counterpoint.

2) Six Studies on a B-Axis

Ditto the above using the open B-string.

3) Six Studies on a G-Axis

Ditto with the open G-string.

4) Twelve Figuration Preludes

Homophonic studies for the guitar in five-part harmony. This will eventually be 24 studies, I think.

5) Three Lineal Studies

Another set I'm currently writing, which is linear compound lines based on four-part harmony using Schillinger circular transformation voice leading: Impossible on the guitar any other way. There will be between six and twelve of these eventually.

The Eighteen Axial Studies and Twelve Figuration Preludes make up the core of my set. MIDI and PDF files of them are here, if you'd like to download them.

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For this set of irreducible four-voice fugues, the final set will number twelve, as you will see.

Here is the first one:



The variation tactic I'm taking for the set has two essential primary variables: That of mode, and that of time. I'm being Hucbaldian about the whole thing by using the terms tempus perfectum and tempus imperfectum as the ancients did, but the concept of modus perfectum/imperfectum is something that is modern, and relates to post-modal harmonic practice.

I only admit of two modes: major and minor. The so-called modal degrees can be inflected in whatever way the composer wishes. The perfect arrangement has major triads on the cardinal degrees of I, IV, and V. Conversely, the imperfect arrangement has minor triads on those degrees, and inflections must be used to get leading tone/dominant harmony effects at cadential points. These two approaches give the modern Ionian and Aolean modes (Which are not the same as the old Church Modes of the same names).

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Logically, this one is now number two:



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Both of these work out so that the music can remain in its pure form: No concessions were required to play them on the guitar.

When I came up with the original version, I said it was like a musical Mandelbrot set, but that isn't really an accurate analogy. Now that we are working with dualities, they remind me more of the classic thespian masks.



The joker in the middle can only be me.

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Obviously the perfect/imperfect forms of mode and time can be mixed, which will yeild four variants. Since the fingerings for the major and minor will remain the same through the change in time signature, once first two are learned, the second pair are no problem. I'll be putting those together next.

Beyond the four versions I will have at that point, 4-3 and 2-3 syncopes can be introduced as well. That will add eight more variants for the total of twelve.

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Not only will this exercise reveal some compositional truths to me, and not only will learning them help my guitar technique out, but additional possibilities for the guitar itself will become apparent. As logic would have it, I wrote nothing but two-part counterpoint for the guitar for several years before anything with three voices occured to me. Now, I have gotten to a four-part contrapuntal theme - something I didn't really expect would ever happen - and so new horizons are opening up. This joins nicely with the five-voice harmonic technique I had developed for the guitar back in my jazz days, and furthered with the Figuration Preludes when I switched over to traditional writing.

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Even though the mistique of black holes may have vanished, the newly-categorized super-dense bodies will still be able to cause gravitational lensing, which this is an artist's rendition of. If there was a super-dense body between you and the Milky Way, it might look something like this.

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I think women ought to have hips, don't you?



Hips like those would cause gravitational lensing all on their own.

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P.S. I'm experimenting with my Smugmug display sizes because they reduced their default "Large" size so much that the music is hard to read. If your browser has any problems with the page, please comment or e-mail me. Thanks.

George

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Reductio Fingerings

I have now learned the Reductio theme and entered the fingering. There are not any position indicators, because the tessitura of the piece doesn't require anything above the fifth fret. Fortunately, I had to make exactly zero concessions to the guitar: The music remained absolutely pure, which is rare. Usually, something can't be sustained and attacks must be repeated &c., but not in this case.

The possibility exists for this to be played in either A minor or A major, and in either duple or triple time. I have yet to investigate whether the major mode version can be played in as pure a form as this minor mode example, but I believe that it can. Next, I plan to make two versions: This one in A minor and tempus imperfectum (Which I'll probably change to 4/4), and a second in A major and in tempus perfectum (In 3/4).

Even though the performance time is only circa thirty seconds, the piece makes a nice and effective interlude between pairs of faster pieces on the same pitch level. So, the plan is to have one placed in the A minor suite in my set (Which is the opening suite that I play), and the other in the A major suite (Which is the last suite I play before my break).

There is also the possibility of using 4-3 and 2-3 suspension chains due to the series of parallel thirds in the theme, but that would preclude playing the piece pure, as some re-articulations would be inevitable. I'll explore that possibility, but first things first: When I have these both comfortably integrated into my set, then I'll worry about that.


Here it is, all eighteen bars of it:



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Anyone out there old enough and geeky enough to remember this?



Well, it turns out that there are no such things as black holes as traditionally defined: A singularity of infinite density. Evidently, there is another resistive force which precludes total gravitational collapse. There can still be super-dense bodies which are more dense than a neutron star - and they still have the property of gravity so great that even light cannot escape - but beneath the "event horizon" (Which may be similar to a "crust" it is now speculated) is an object with both mass and volume. Interestingly - to me anyway - Einstein did not believe that black holes could exist either, even though his theories predicted the possibility for them.

You know what this means, don't you? No, no: Forget the insignificant fact that there will have to be a wholescale revision of astrophysics; That's small potatoes. This means that the entire Star Trek universe will have to be re-thought!!! What will we do without singularities, wormholes, and cosmic string fragments?! I mean, Romulan ships are powered by an artificial singularity which provides the required gravity well.

This is a tragedy of epic proportions, the surface of which I have not even glimpsed (Because it does not reflect light!).

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Ever notice how chicks who ride horses have the most amazing buns? I have.

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Sonata Zero for Solo Guitar

Since I have now figured out the solution for the conclusion of the second movement Ricercare, this four movement sonata is essentially complete. I am already performing the third movement Scherzo at my gigs, and memorization and learning of the fugal finale is proceeding nicely.

For a history of the development of this Ricercare, see my four (!) previous posts on it here, here, here, and - finally - here. These posts were back in January, so I obviously have had quite a bit of "trouble" with this piece, and it has taken a long time to come up with the solution. The "wait" has been worth it.

The previous finale was a relative major version of the stretto which concludes the final Fugue and the Sonata. As I listened to the entire four movements, this became unsatisfactory for two reasons: 1) Hearing this stretto here in the second movement diminished its effectiveness in the finale, and 2) The vioces at the top in measure 47 - the beginning of the ultimate episode - were not connected with and/or "brought down" in the Shenkerian compositional sense. The more I listened to this piece alone - and the sonata as a whole - the more I noticed those things, and the more they bothered me.

Instead of reviewing the entire piece yet again, I will simply post the new final page:



The final episode has not changed: It still reaches the tonic at the beginning from a C# dominant seventh chord interpreted as a subV7/I at the end of the previous page (A German Augmented Sixth chord in trad lingo), and it still presents a harmonized form of the subject of the Ricercare in augmentation to arrive at the dominant of G for the beginning of the recapitulation.

Now, however, I have replaced the stretto with an inverted and slightly modified version of the entire exposition: Even the mode is inverted. The "Eureka!" moment was when I realized I that could play the inverted form of the subject in the high octave while sustaining the dominant pedal if I used harmonics: It's actually fairly easy. Unlike the exposition, the recap has suspension chains in it, and the inverted Ricercare subject morphs into the rectus Fugue subject over its three iterations. The decending chromatic line in the middle voice of the penultimate measure is a nice bit of whacky weirdness which fits with the overall outlandish nature of this Ricercare (Compared to the stately and noble concluding Fugue, that is).

I have put MP3's and PDF scores of all four movements of Sonata Zero on my Downloads Page if you'd like to hear it.

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The resolution leaves much to be desired, but the idea of this "Mandelbrot Canyon" is great.



I'd like to see a larger version with several times the resolution.

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Got to remember to work on my flexibility.

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Further Glissentar Modifications

Sorry for the infrequent blogging. It's not that I don't have plenty to blog about, it's just that I've been busy with various non-musical "chores" this month. In any event...

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Working the fretted Glissentar into my set is going according to plan. I have hit some sort of critical mass point with it, and it has suddenly become much more managable to play. Accordingly, I'm now starting off my performances with it - my indoor performances, anyway: It's too much of a PITA to keep in tune outside - and it "works" fine through the first two suites (A minor and C major as my set is organized). Then I switch to the Grand Concert SA.

The problem is, and has always been, that I don't care for the sound I get from the Glissentar. I didn't care for it fretless, and it's not much better in the tone department fretted either. If I simply play the instrument unamplified - as when I'm practicing - it has a fine sound with the string set I have put together for it (Savarez Alliance High Tension Carbon Fiber B's and E's, the standard Godin Glissentar A's, D's and G's, and a Hannabach .047 Super Hard low E), so the problem is definitely the L.R. Baggs ribbon transducer pickup system (The rest of my amplification system consists of a Lexicon MPX-G2 Preamp/FX unit, a Bryston 2B-LP stereo power amp, and a pair of Yamaha AS108-II mini PA speakers).

This piezoelectric transducer is the same unit which was half of the L.R. Baggs Duet system on the first Godin Multiac Grand Concert guitar I had, and it wasn't very successful in that application either. The internal condenser mic was better, and I used the sound mixed on that guitar about 60/40 in favor of the mic. The problem with the tone of this regrettable unit is that it is thin and has a nasal quality no matter how you EQ it. It is also prone to feedback.

The RMC Pickups Polydrive system on my Godin Multiac Grand Concert Synth Access is positively brilliant by comparison: It has a gargantuan sound which is deep, broad, and smooth, and I've never been able to MAKE it feed back. I've never used it to drive a synth, and I wouldn't care if it didn't have that feature: It's simply the best pickup system for electric nylon string guitars I've ever experienced. By far.

Well, Ed Reynolds (The luthier who made the fretted neck for my Glissentar) is always ranting and raving about how good B-Band pickups are, so I decided to check them out. I like that the system is based on electret film technology - I had a pair of electret headphones back in the 80's which required that they be plugged into the speaker posts (!) of my stereo, and they were BY FAR the best headphones I've ever heard for fidelity - and I think this simple fact will give the B-Band system a better chance of sounding similar to the RMC Polydrive I like so much.

The problem is, I don't want to rip out the current amplification system: It would be much better if I could just add a second pickup to the guitar. As I perused the B-Band product line, I came across the UST (Under Saddle Transducer) and the A1 preamp, which is an endpin unit for acoustic guitar.

As luck would have it, the UST comes in steel string and nylon string versions, so... I ordered both, of course. Hey, I don't care if a unit is designed for steel string guitars, if it sounds better on the Glisentar, that is all that matters. I'm going to experiment.

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Fortuantely, there is plenty of room inside the Glissentar for all this stuff:



As you can see, the units are tiny. I have to remove the screw-on shell from the preamp, and it will have to be glued into the axe, but there is juuuust enough room for it before it encounters the stock pickup system's battery housing. I'll simply use some hook-and-loop tape to Velcro the new battery under the bridge plate, and then if you don't look closely, you won't even notice that there are two pickup systems in the guitar.

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I did have to drill a hole for the endpin preamp:



No problem.

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I'll let you know how this all turns out, but it will be a while: The steel string units were on hand, but the nylon string variety had to be special ordered.

Let's just think happy thoughts:



I like the far-away perspective of this fractal image: The central Mandelbrot figure is very small.

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One of the things I've been spending a lot of time on recently is exercise: Two hour-long walks every day plus 1,250 reps on my Bowflex every other day. I'm sure some of the ease with which I can now play the Glissentar is due to my strength training (Which was part of the point).



Now I just need a workout partner like this.

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Happy "Blogversary" to Me/Palindromic Variations

Well, here I am: One year, 196 posts, 5,601 visitors, 8,035 page views, and 1,295 profile views later. Not impressive traffic, actually, but that was never the point of the blog. MMM has always been and will continue to be an autodidactic aid which allows me to organize my thoughts. As a result of that, lots of things - such as the B's 9th analysis and the Taneiev transcription - will be taken up and abandoned as suits my personal goals. The Beethoven project lead to a nice sonata process piece, and the Taneiev project lead to the Axial Fugue for Solo Guitar (An amazing piece, if I do say so myself, which you can download here). This is the purpose of study for me; to launch new pieces.

And so, I will continue in this vein.

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Today's piece is v2.0 of a variation set built around the Fuga: Reductio ad Absurdum theme, which I have blogged about previously and most recently here.

As I have mentioned before, this theme is a four voice fugue distilled out to it's irreducible essence: The subject and answer are a single note, and the four-measure exposition is presented in a series of quadrant rotations so that a compound double palindromic canon is created: Original, retrograde inversion, inversion, and retrograde is the sequence required to pull this off.

So, the theme is an antecedant/consequent phrase duplet as well. This means the two halves can be separated in a series of variations on the theme so that the entire variation set is a gigantic double palindromic canon!

Basically, the antecedent of variation one is the first phrase in the set, and the consequent of variation one is the last phrase in the set; the consequent of variation two is the second phrase in the set, and the antecedent of variation two is the next-to-last phrase in the set, and so on. Setting the piece up this way makes the canonic voices of the entire variation set read the same forwards and backwards. It's really cool, it's totally fractal, it's symmetrical, and I like it a lot.

For this initial experiement I wrote pairs of variations: The first is "straight ahead" and it's pairing contains 4-3 suspension chains. The first set is in 4/4 time, the second pair is in 3/4 time, the third pair is in 2/4 time, and then there are three in 3/8 time. The third 3/8 variation is necessary to get a "keystone" at the top of the arch, and it has 2-3 suspension chains in it.

This simple mechanical variation scheme nonetheless yeilds fascinating results.

What has captivated me the most are the rhythmic implications. Over my twenty some-odd years of contrapuntal writing, I have never employed the retrograde or retrograde-inversion orientations of any theme I've come up with. The few times I've tried it, the results were sucky, to say the least. Well, as I've discovered, the problem is non-retrogradable rhythm/melody combinations, with rhythm being a prime culprit (Truth be told, I don't care for Bach's experiments with "crab" canons and other retrogrades because it seems he's just forcing them to work, and not particularly tactfully at that).

Dealing with this situation is forcing me to concentrate on rhythm as I never have before. For decades I've been looking for a unique and systematic approach to rhythm - as well as a crucible in which to pulverize it - and so I've finally found it. I was never really convinced of Schillinger's symmetrical resultants of interference, but in this context breaking up the entecedents and consequents of those rhythms works quite well. As usual, I use them freely, the musical result always trumping any rigorous systematic approach.

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So, here it is: (If you would like to download an MP3 and a PDF of the score, they are here, as usual). These are so simple and self-explanitory that I will present them without further comment.



















This particular theme is going to be one of those which takes months or even years to come to full fruition, but it sure has got me thinking more than anything I've come up with in the past few years.

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Though the gold is a bit too "Liberace" for my taste, in a royal blue this would be nice embroidered on a comforter/pillowcase set. LOL!

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No need to wrap my present.

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Dear Brave Anonymous

First of all:



Now that's posing. In style. On a $20K BMW motorcycle. Have you even made $20,000.00 in your entire life? I'm doubting it based on your command of the English language.

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Secondly:

The rules are simple: If you can compose a better fugue than I can, then - and only then - will I listen to what you have to say about music. If you can't, then SHUT THE F#@* UP and BACK AWAY FROM THE KEYBOARD! "My own counsel will I keep!" - Yoda

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For those of you wondering what's going on, I have a... "fan" ;^) I picked up this fan by doing a hit-and-run slam over at "Pretenza 21" (Better Navel-Gazing through Electron Microscopy!). You can see the inane thread here in the comments to the idiotic "Decline and Fall" article.

I know, I know. I shouldn't have. It's like making fun of Mongoloid Idiots - oops - "people afflicted with the polyploid genetic defect known as Down's syndrome." Ahem. But there's just so much head shaking and chortling I can do sometimes before I'm forced to respond. Those guys remind me of the hilarious insanity on parade over at DU and Daily Kos. None of them have any clue about music, and they are all WAY too self-conscious to make any kind of an honest musical utterance.

At least when they are writing about music they aren't writing what passes for music in that gaggle of the guilt-ridden.

So, Brave Anonymous decides to alert me that someone has responded to my cut in the comments (I'm betting it was HIM alerting me to HIS response, but I couldn't prove that). I duly checked it out, and got a few laughs out of it. Big whoop.

Then he got offended that I deleted his comment on MMM - I'm guessing (Which had nothing to do with the topic of the thread) - and revealed himself as a punk.

Oh, well.

I still say the best chance any of the Pretenza 21 crowd have of going down in music history is if they wind up in footnotes in the book that will be the story of... my life, so nya-nya Brave Anonymous.

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Finally, today's babe is for The Brave Anonymous as well:



I just knew those pix would come in handy someday. LOL!

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Fugato for Chamber Orchestra

My Fuga da Camera set is taking shape nicely. This fugato is now planned to be the next-to-last piece. My friend David pointed out that if you translated the title literally, it would (or could) mean "flight from the chamber." It had been a while since I was reminded that the root word for fugue is "flight" or "pursuit" but that certainly is a good way to describe the process. As a result, I'm going to end the set with a fugue for full symphony orchestra after this fugato. The set will flee from the chamber ensembles into a full symphony piece by steps.

With a run time of almost exactly sixty seconds, this little ditty has a humorous aspect to it. Long time visitors of this blog may remember that I originally wrote this to be a small part of a larger sonata-process piece (and it still might end up in one at some point), but I ditched all the rest of the movement. David said it was "like Bach and Mozart got together for a quick whiskey", so I'm going to give it the title "A Quick Whiskey" of course.

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First of all, this is a concert pitch-score, so the instruments are not transposed. Just as "there is no crying in baseball" there are no transposing instruments in MIDI. Also, the horn part is inside of the winds because I just put them in the general order of the ranges. Tradition, schmadition.



For this fugue subject, I wanted something athletic with a big, wide range, so I came up with the root to fifth to octave head figure first. I also wanted a super-tight stretto between the subject and the tonal answer, so I wrote them in canon:



As you can see from the score, a simple repeat of the tail figure harmonized out gives a nice place for an orchestral interjection, and it is sorta-kinda Mozartian in its effect.

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There couldn't possibly be anything brilliant about the orchestration - I'm certain it's quite pedestrian, in fact - because I've never really understood what all the fuss is about: You get whichever instruments you want to play whichever parts you want them to, and then you put them into some kind of a logical order. How hard can that be? Rimsky-Korsakov, Chintzy-Schmorsikov I say.

What I do like here is how I got a decending chromatic tetrachord into the beginning of the counter-answer, and an ascending chromatic tetrachord into the end of it.

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Of course, then it was inevitable that I would get an ascending chromatic tetrachord into the countersubject on the next entrance. The running effect that this chromatic counter-answer and countersubject set produce is actually quite jazzy, but without the swing. I like it.

By simply not raising the sixth and seventh degrees of the scale in the last repeat of the tail figure during the orchestral interjection, I effected a modulation to the relative at the end of it. Though sudden, it's perfectly smooth.

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For the first major key entrance, I used a diatonicised variant of the countersubject for contrast. I know the oboist will hate me, but in the words of Gary Solt - one of my Jazz Theory and Composition profs from Berklee, "That's the way I heard it (comma) man." And it really does sound cool with the horn down below it.

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Even cooler is the clarinet working down into its chalmeau register for the answer with the clear highs of the oboe above. Hey, it just worked out that way.

I again used a simple linear device to effect a modulation back to the tonic minor at the end of the orchestral statement - the last of this micro-miniature series of episodes - and with the appearance of counter-answer two, all of the materials of the expositions have been presented.

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Here is the super-tight stretto for the recap, which creates quite a powerful effect if the listener is in tune with fugue listening, and the free voice in the bass gives a heavy duty cantus firmus vibe to the passage.

The one-beat delay also means that the tail figures are moving in contrary motion to each other at the end of this statement, which sets up a final, more powerful episode as well. Combine all of that with the octaves in the orchestration, and the extra voices in the harmony, and you have one rockin' passage.

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A little bit of sixteenth-note action over a driving countrapuntal chord progression, and you've slammed that shot of scotch!

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I'd like this pattern embossed on floor tiles. Wouldn't that be too cool?

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Then a tasteful area rug with a little bit of bling decorating it. Yeah baby.

The Fugato and some improved versions of the String Trio and String Quartet are now posted on my FileShare page here. As John pointed out in the comment to the post below, the Soundfonts I used for the improved versions are quite a bit better (Thanks John).

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