Home Again

The vacation was brief, but good and much needed. This marks the beginning of the second year of my three year musical career plan, so the getaway made a nice seam in the process, and I feel refreshed and ready to get back to work.

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I love hanging out at Stately Smith Manor. Brian designed and built it himself (He restores historical landmarks for a living), and it really is magnificent.



Now, back to the matters at hand.

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I have finally came to the ultimate conclusion of Fuga: Reductio ad Absurdum. If you'll recall, I reduced the fugue subject to a single half-note, and the four-voice exposition to four measures of 2/4. The first version was a simple fugue.



Though this was nice, there was an ultimate solution awaiting me, and this wasn't it.

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The second idea I had was for an even simpler double canon.



This was less satisfying, but it lead to the breakthrough I was looking for.

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Ta da! Using the simple process of quadrant rotation, I made the entire fugue out of nothing but the exposition: Original, Retrograde Inversion, Inversion, and Retrograde. If you number the quadrants clockwise in the usual manner, that means it is a 1, 3, 2, to 4 progression.

The piece is a double pallindromic canon as a whole, and each half is a double pallindromic canon in inversion (Double mirror crab canons).



I have color coded the voices to make the canon(s) easier to see. Red and blue voices are canonic, while the green notes are free additions to fill out the cadential elements. In measures one through nine, the leading blue voice and the folowing blue voice read the same forwards and backwards respectively, but they are in inversion (A mirror crab canon). Likewise, the leading red voice and the following red voice read the same forwards and backwards respectively, also in inversion (A second mirror crab canon). Therefore, measures one through nine are a double mirror crab canon.

Measures ten through eighteen are simply measires one through nine backwards, for a second double mirror crab canon. Finally, the entire piece creates a larger double crab canon, since it reads the same forwards and backwards (With the exception of the green notes, of course), but it is a true pallindrome and is not a mirror.

Humorously, I came up with this while driving east on I 40 between Memphis and Nashville Tennessee last Monday morning: That would be "Music Highway" in case you have never driven that route. OK fine, I guess you had to be there, but I thought it was funny.

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There is something deeply and irresistably compelling about this musical structure. It is an irreducible musical truth. Since even before Bach, Western Art Music has reflected the so-called Golden Mean ratio in its idealized proportions, but research I did years ago intimated to me that there was a bi-fold symmetrical way to approach musical structure - for music in general, and fugue in particular - and this is it. I plan to use this structure as the framework for larger pieces, which I will realize by elaborating on it: After twenty years of reducing fugue down to this primordial kernel, I can now build it back out.

Imagine this as the classic Mandelbrot formation at the heart of this fractal image: The image has bi-fold symmetry running crosswise through the axis of the central Mandelbrot figuration, and everything exterior to that is self-similar elaboration. Now that I have the musical version of the Mandelbrot formula, I can now begin to add the fractal elaborations to it.



This is a huge breakthrough for me.

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Vacation is over, so...



I can now concentrate on music again. Or something.

Vacation

Well, Springtime is in the air, and this young man's mind has turned to... motorcycles, shotguns, and machine shops. So, I'm going to my best bud's spread in SW Virginia tomorrow, and we're going to blast around on the Blue Ridge Parkway, shoot clay pigeons, and apply redneck tech to one of my motorcycles as well as my truck. You never know what we're going to create, but it will be cool because I'll get to use all of his super-cool power tools, his lathe, and a bunch of other zippy-widget stuff

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We built this out of four different BMW motorcycles over the course of the last three years:



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This is my other bike, which Brian and I have modified as well:



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Brian and my truck the last time we got together: Hunting groundhogs (On a horse ranch, where their burrows are a severe injury hazard to the equine population).



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I'll return... whenever the hell I feel like it.



Toodles.

The 2006 Delian Games: "In the Witch's Head"

The Delian Society, a group of contemporary tonal composers of which I am a member, is currently holding the 2006 Delian Games; a friendly composition non-contest. This year's theme is Ghost Stories, or otherwise "scary" music, and this post is about my entry. Entrants - calling us contestants would not really reflect the spirit of The Games - are to submit: 1) An MP3 of their piece of music, 2) a PDF file of the score, 3) A JPG image to go along with the music, 4) a PDF file of a description of the piece, 5) a JPG picture of the composer, and finally 6) A link to where this can all be found. Though everything concerning my entry will be presented in this post, the source files can be downloaded at my File Share page here.

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The Witch Head Nebula.

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In the Witch's Head is a five-voice perpetual canon at the octave for string choir. Since it is a piece of absolute music, there really are no overtly or covertly programatic elements present in the piece. Rather, it was the musical result of the work which inspired certain associations, and those in turn lead to the title.

Originally, this piece was to be a five-voice fugue for orchestra with a five-measure subject composed in canonic stretto at one measure of delay. While composing said stretto, I noticed that the head of the subject would also work in stretto at a half-measure of delay, and that if I made the chromatic mid-section of the subject diatonic, that would work at a half-measure of delay as well. Eliminating the tail figure then gave me a second closer stretto of a varied and truncated form of the subject. Finally, I noticed that if I used this modified form of the subject in augmentation - thereby making the stretto's delay an entire measure again - the original and varied augmented forms of the subject would dovetail perfectly while maintaining technically correct counterpoint. This dovetail worked with either the original or modified augmented form appearing first, and so the five-voice perpetual canon was born.

Due to the fact that I employed a deceptive resolution to the major seventh chord residing on the minor sixth degree of the minor key of the piece with the varied augmented form, and because I allowed for inversions of that major seventh in which the root was above the seventh, highly dissonant harmonic structures were produced via the resulting minor ninth intervals. This lead to an interesting effect wherein the chords of resolution were more dissonant than the preceding dominant function chords. Coupled with the chromatic elements in the original form of the subject, this lead to the music creating a very uneasy effect that I could only describe as "creepy" or "diabolical." I liked the effect so much that after writing a conclusion for the canon, I decided against going ahead with writing it out as a fugue: The perpetual canon said all that needed to be said about the subject and its variant in it's brief two minutes of stage time.

While pondering whether or not it would be worthwhile to orchestrate such a brief piece, the Delian Society decided that for its 2006 suite of music composed by members, the theme would be ghost stories or more generally "scary" music. Quite independent of this in one of my non-musical interests, astrophysics, I came across a series of haunting images of the Witch Head Nebula. That was it: The perpetual canon and the images of the Witch Head Nebula went together perfectly, and that all fit in with the theme of the 2006 Delian Suite.

The title In the Witch's Head has more than one level of meaning, as it can be thought of as being inside the mind and thoughts of a witch, or traveling in a ship within the aforementioned Witch Head Nebula, or even - if your taste runs toward the ribald in humor, as mine does - making use of the water closet on a ship named The Witch. I'll leave any further ass-ociations to your imagination.

As is the case with many of my favorite compositions, In the Witch's Head was arrived at by my stumbling blithely through a series of happy accidents.

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An MP3 of In the Witch's Head is available for download here.

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Hucbald

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Now that's what I call a witch!

John Lanius, Come On Down!

I absolutely, positively love life's humorous little synchronicities. My blog recieved hit number 5,000 the other day, and instead of it being some anonymous surfer, it's a friend of mine! Well, an e-mail buddy, at least. Fellow Texan and proprietor of the eclectic blog Texas' Best Grok (Heinlein fan? Ya think?) John Lanius. Too funny!



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In a "DO'H!" moment I realized I could incorporate all three versions of the reductio into a single version. I gave the second version the rhythm of the third, and I liked something about each of them, so I used them all.



That about does it.

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Oh, yeah. John, your wife says "hi."

Reductio ad Absurdum

I consider myself a minimalist, but not in the usual way that minimalism is thought of vis-a-vis the music of Phillip Glass et al. Rather than taking a small musical idea and repeating it ad nauseum as Glass is wont to do, I am always striving to find the irreducible musical truth at the root of whatever musical subject I'm dealing with: For harmonic voice leading that is circular and crosswise transformations of the chord tones, for root progression patterns it is the relationship with the primordial falling fifth that the overtone series gives us, for counterpoint it is the set of laws disallowing paralel intervals that are superparticular ratios in both inversions, also from the overtone series. You get the idea.

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Fugue has recieved the same treatment from me, and after fifteen years during which my subjects have become increasingly elemental (For the most part), I have reached the ultimate reduction of the subject to a single note, and the four-voice exposition to four measures. This may not seem particularly significant to you the reader, but for me as a composer and contrapuntist it is like stumbling onto some sort of ultimate musical truth. It's really kind of earth shattering for me.

As an initial experiment with this idea I decided to write as short a fugue as possible and make it... a guitar piece, natch: Exposition, transition 1, counterexposition/middle entry in the relative, transition 2, recapitulation, and a codetta is all there is to it. It comes to just twenty measures of 2/4 and takes only 30 seconds to play.




We're in A minor here, and as you can see the top system is the exposition, and the subject is a single half note which is answered at the fifth. The answer is obviously real (ha, ha). Note also that up until the middle of measure five, the exposition is a double canon at the octave. I plan on following that possibility in an upcoming exercise.

If the subject is the irreducible minimum, then it follows that the counterpoint should be the most obvious as well. Under the first answer the counterpoint is a 2:1 ratio that makes a 4-3 resolution: There is no more hallowed entrance setup for an answer than a prepared fourth.

Over the second subject in measure three there are both 4-3 and 6-5 resolutions, and the harmony is a plagel iv to i progression. Finally, in measure four, there is a 7-6 and 5-4 over the answer and a 4-3 under it, which creates a modal progression ending on a i(6/3) chord. It's a lot like a v(4/3) to i(6/3), but the v has no third. The killer is the downbeat of measure five: It's a vii(d4/3).

Measures five and six were originally composed in the version you see in measures eighteen and nineteen which end the piece. By simply allowing the G in the bass to remain natural I was able to effect the modulation to C, and the counterexposition/middle entries are essentially the same except for the mode.

To add to the absurdity of the piece, I had voices one and two exchange places, as well as voices three and four. This must be reflected in the notation from a theoretical standpoint, but it isn't something my ear seems concerned about.

The added part which voice four has in the middle maintains the basic 1/4 note pulse, and also allows for the dissonance climax to coinside with the pitch climax in measure nine (The 50% point, excluding the measure of repose after the final resolution).

For the second transition back to the tonic an extra measure was required, and the sixteenth note figuration was allowed a bit of development.

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Once the initial idea struck me (And, struck is the operative word), it took all of two to three hours to put this together. After pondering it for the afternoon, however, I came up with the following slightly elaborated version.




This is better in almost every way: The subject begins on an upbeat, which makes the 4-3 resolution (And the rest of the compound resolutions) both better prepared, and also more effective. There is also much more rhythmic drive to this version of the piece, and that's part of the problem. The eighth note articulations create an expectation of a continuance, which is not delivered when the quarter notes reappear. There is something less than perfect about this, but the articulation idea itself is OK: It just needs a better execution.

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So, I came up with a third version.




Adding the leading tones provides some colorful contrapuntal effects, as well as some directional impetus to the piece. The lilting dotted-eighth/sixteenth rhythm eliminates the expectation of continuous eighths, which allows the piece a range of rhythmic space in which to breathe. This is a really cool little ditty.

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Obviously, this idea will eventually lead to a much larger piece - I can already see it modulating to E minor to outline the tonic minor triad - but for now this will be enough food for thought to keep me occupied.

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Reductio ad Absurdum, indeed™.

Never. Again.

No more wedding ceremonies. Two out of the last four I've done have been disasters; not because of any failing on my part, but simply because they have been "over-planned" by the clients. The more details you ask for, the greater the chances that something won't go according to plan. Not only that, but the work of learning the musical requests gets in the way of my personal musical agenda, which includes learning the music for my next CD. Receptions are OK, but no more ceremonies! *spit*

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This brief hiatus has given me a chance to figure out a few things about the blog, and so I'm going to expand it's horizons a bit. Don't worry, I'm going to keep the pinup girl tag, but I'm going to blog about some other musical and non-musical interests I have. Don't worry, politics is not important to me: I consider myself to have evolved beyond the whole nation-state "thing" and I'm just waiting for the rest of the world to catch up with me.

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Today I want to give you some cool sites related to Antonio Stradavari, luthier and maker of the Stradavarius violins, violas, and cellos which bear the latinized version of his name.

I've always been fascinated by the mistique these instruments have, though I personally believe they are stupidly over-valued and that contemporary luthiers make instruments that are superior in every way. But that's just me. I mean, his instruments were made for gut strings, for crying out loud, so any great "tone" they have in modern setups with steel strings is purely accidental, if it is not simply a subjective bias on the part of the listener (Which I'm positive is the actual case). But anyway...

There is an absolutely fascinating site which lists every single instrument he made that is still extant, gives the names they are known by, and has photos of many of them. I spent hours kicking around on that list the other night. You may get lost there as well.

Most people don't know that old Antonio made a few five-course Baroque guitars circa the 1690 as well, and that three of them still survive, at least one of which is still in playable condition. Not only that, but a few modern master luthiers have copied that design and John Ainsworth actually markets a copy. It is devastatingly gorgeous.



This is something I will have to aquire at some point. Absolutely, positively.

It is not quite as amazing as my Anthony Murray though.



That German Spruce top is as highly figured as they come, and it was harvested back in the late 40's: There is no more like it.

Tony was the one who informed me of the technique that modern luthiers have developed, and he was always shaking his head at people who spent fortunes for "old axes" as he called them. Modern instruments by the best builders are simply better, and that's all there is to it. You may not like that idea, but it's true (I'm sure the Strad Guitar Copy is better than the original was as well).



It's all in the greater levels of precision measurements that are possible these days.

Ode to Joy

Well, this turned out better than expected. One of this month's clients wanted Beethoven's Ode to Joy, and after looking at a bunch of lame-ass guitar transcriptions, I decided to make my own. This is cool enough to lead to a set of variations.



I could pick worse subject matter.

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I love daylight saving's time.

Hiatus (Not an April Fool's Joke)

I'm going to take a couple of weeks off of the blog. Not because I really want to, but just because I have to. Between now and the fifteenth I have a TON of music to learn, and a BUNCH of gigs to attend to, so it will just be easier if I don't pressure myself to come up with any weblog entries during that time. If I can sneak one or two in, well then fine, but I'm just not going to worry myself about it.

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Wednesday night's Eric Johnson concert was a rip-roaring blast. The Railroad Blues only has a standing capacity of about two-hundred (All of the usual tables and chairs - even the barstools (!) - were removed for this show), so it was an absolutely tiny venue to see someone of that stature at. Virtually every guitarist in a one-hundred mile radius from Alpine showed up, so we had a collective blast, and since it was a Wednesday night, it was almost exclusively an audience of the cognoscenti. I went with a few of my students, and we were able to stand stage right and just a couple of feet away from Eric. Yes, we were copping licks all night, and he played some pieces I've never heard him do before: Everything from The Wind Cries Mary by Jimi Hendrix to Crazy Train by Ozzie Osborne, for crying out loud.

Unfortunately, one of my guitarist-friends brought a bottle of whisky, and I couldn't resist having some. Man, I used to be such a hard-core party animal; now I'm just a wussy old fart. So while they hung out for a while afterward, I had to make the two mile walk home while I was still physically able to.

Hell of a lot of fun, but it took me all of Thursday to recover (Fortunately my usual Thursday gig was preempted due to a party at the venue).



Did manage to get an autographed copy of his latest album, Bloom as well as the first album which was never released until 1998, Seven Worlds, which was actually recorded in the late 70's!!!

Oh yeah, the business card: Picked up yet another gig at my gig tonight. When it rains...

OK, back to frickin' Pachelbel.

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That's what I need: A convertible.