Friday, December 24, 2010

Octaves roasting

It being the day before Christmas, it's time to air out the old interval song, which dates back to graduate school, with various tweaks and revisions since (I think Kathy Dupuy and I made up the first version in 1984 while walking in Princeton from a restaurant). Sung to the tune of Mel Tormé's Christmas song, and also available on my web page. Credit to Hayes Biggs for the second line, and maybe the fourth line, of the bridge. So get into the holiday spirit and learn your intervals. 

Or else.

For the uninitiated, I have put the intervals in red. Because you are worth it.

Octaves roasting on an open fire,
Major sixths nipping at your nose,
Major seconds being sung by a choir,
Chromatic alterations of the scale.

Diatonic scale.
A turkey and some mistletoe
Major sixths make the season bright.
Major seconds with their eyes all aglow
Will drop a perfect fifth tonight.

There's minor sevenths on their way.
They've loaded lots of minor seconds on their sleigh.
And every minor sixth will want to spy
To see the supertonic prolonged over five.

And octave offering this simple phrase
To major sixths one to ninety-two.
Although it's been said many times, many ways,
Meet the Flintstones. To you.


Eighth line the way Tormé sings it:
Will drop diminished fifths. Tonight.



Hence Judy Garland and Mel Tormé




Or you could go with the other gold standards — Nat King Cole



and Tony Bennett.


Saturday, December 4, 2010

How could I NOT have one? Part 4


See here, here and here for earlier chapters in the continuing nerd-a-saga. I used and shared the first three at Yaddo, and the results were decidedly mixed.

Thus, when shopping on amazon dot com, I was surprised to see not one, but two new Sound Machines in my Suggestions. Readers of this blog know that in 1967 or 1968 I kept buying Batman trading cards until I had them all. In that long and august tradition, then, I obviously must have one and exactly one of all the Sound Machines machines.

Football sounds — on their way. Just arrived this afternoon — behold.



One naturally wonders how they got the rights to use all those sounds. That one is not I.

Sunday, November 7, 2010

My Left Field


The organic approach is but one of many valid approaches to composition.

Thus spake a former colleague, when someone complained to him about a mix 'n' match so-called Postmodern piece that had been performed that evening. It's just not organic, he said.

Wait — did I type "thus spake"? Lordy. The pretentio-meter just a-sploded.

The piece in question contained a mishmash of fragments, as different from each other as possible, or so it seemed, and they came one after another, as if the piece had no collective memory. Thus the musical tension came from the startling juxtapositions, and perhaps the form from the proportions. The idea of the resolution of these tensions? The piece stops, I guess. Or maybe that's just the wrong question. It could be that one point of the piece was the connections the seasoned listener would make absent the conventional kinds of connections that pieces normally make.

The piece in question didn't do anything for me. Since everything was a non sequitur and anything could happen at any time, then there were no rules, and thus no expectations, no fulfilling or thwarting of expectations. I got bored. I leave the door open, though, that a better-written piece put together in this non-organic way, could be something I would love to listen to.

All music must be organic.

What's with one-sentence Italic paragraph guy?

Oh yes. He's holding up the straw man for us to knock down. Yeah, the metaphor of a kernel expanding like a seed that grows into a plant, etc. to explain how music goes, is a pretty popular one; and in traditional musical analysis, we reverse-engineer mercilessly to show that everything that happens in a piece must always have been destined to be so. Because it's in the DNA of the opening.

Speaking of straw men — once one is blown down, how come we never come back with a stick man, to be blown down again, and finally with a brick man? The second theorist built his theory out of sticks, we could say, and we blow that one down, too, but with more effort. And the (strangely ironically) iron-clad theory is built from bricks! See, that's what happens when you let squirrels applaud whenever they want. The only catch, though, is that you can't build any theory in this fashion unless you have hair on your chinny-chin-chin.

Well, music isn't a vessel into which substance is poured. We had that conversation already, even though it was only me talking, and already I'm having a dry heave over it. Very frequently, the most expressive, memorable, or affective moments in a piece of music are places where there's an anomaly — where it doesn't behave normally.

Not to mention (even though that's exactly what I'm doing — what's up with that?), most humor in music comes about bisociatively (I made that word up, but you recognize the root), when something outrageously wrong happens, based on the established normative (or as we called it in the early '90s, the Stormin' Normative). Case in point, the "Surprise" Symphony of Haydn, in which a forte dominant stinger (not a Vodka stinger, but I'm working on it) is tacked on to the end of an ordinary phrase played pianissimo. Squirrels, though, don't understand that moment.

Many, many pieces by Bach have endings in which the tonic resolution of a dominant pedal is delayed by said resolution being, instead, the secondary dominant of the subdominant — thus incorrectly resolving the leading tone down a half step, instead of up. The result usually makes this listener (that's third person Davy) feel briefly as if he is floating on air, as one must wait still longer for the dominant and its correct, final resolution.

There are those little anomalies and then there are the really big ones. A popular one to bring up being the tutti forte C-sharp that Beethoven tacks on after the half-cadence — in F major, on C — that ends the first section of the finale of the Eighth Symphony. That moment of C-sharpness is both funny and kind of tragic, since it is such an ugly duckling at that moment. The really cool thing about that anomaly is how Beethoven spends so much of the remainder of the movement splaining it, or more accurately, gradually bringing it into the piece such that it isn't anomalous. Thus a lot of really kooky things that happen in the piece — substantial episode in the distant key of F-sharp minor, tonicization of D minor, respelling to D-flat to resolve correctly down to the structural dominant — get to happen in a kind of non-organic way.

Beethoven? Non-organic? Get outta town!

I myself have used a few of the WTF-type anomalies in some pieces recently, and getting around to the splaining part is always fun. My current favorite splain is to have the anomaly happen in the middle of a seemingly ordinary phrase much later, as if the original anomaly was a teensy-weensy window that let you see the future. Call me Simile Guy.

And then there is the musical pun. I call it a pun because it's about a harmony that "sounds like" a harmony that could potentially have a different function. The most mundane pun chord is the pivot chord in a modulation, in which, say vi (minor) of the old key is recontextual eyesed as ii (minor) of the new key. In chromaticville, all the textbooks love to point out how the Italian and German sixths "sound like" dominant sevenths (and by the commutative law of "sounds like", vice versa) and thus can be used as pivots for very odd-sounding modulations themselves. Well, whoa — when your big honkin' dominant seventh chord suddenly acts like the Augmented Sixth in the key of the leading tone — it's very rare to write "now there's a composer with taste".

Or you could go the other way. Like our old friend Bobbie did.

Now there's a composer with taste.

As I mentioned in that previous post, the long-unresolved E-sharp from the end of the first song of Dichterliebe finally gets something of a resolution, eleven songs later. By which point we've probably forgotten we ever wanted it. Bobbie, though, makes it the bass note of the German augmented sixth chord of B-flat major — whoa doggies, starting on a dissonant sonority! What's more, since it's going to resolve properly to the cadential six-four, the note usually spelled D-flat is spelled C-sharp — since it's going to move up a half-step to D. This is only a detail, but it's cool to note that by the rules of chords, C-sharp is the root of a chord spelled C-sharp, E, G-flat, B-flat. That's nutty! The fifth of the chord is doubly diminished with its root! And the squirrels have applauded that.

So we're now twelve songs in to the poet's sixteen-song odyssey. Rejection — so two months ago. Resolution — dude, it's 1840. And what's happening in this song? It's a beautiful summer's day! — no longer May, as in the first song. And poet-guy now imagines that the flowers in the garden are talking about, and then to, him.

I see a vast potential for compositional anomalies. And a potential for vast compositional anomalies.

And Bobbie doesn't disappoint. But since he is a composer with taste, he is going to grow his anomalies organically.

Really? I thought anomalies couldn't be organic.

Then read on. Or read off. Whichever, I can't tell the difference.

So we already mentioned that Bobbie starts out using the oddly spelled German augmented sixth to begin the song, and that it properly resolves to the cadential six-four  to introduce the song. As the singer simply sings that it's a beautiful day in the garden, an ordinary chord progression with a smooth bass line accompanies — I IV V4-3/ii ii V7 I. The applied dominant to ii provides a bit of nice chromatic color, as well as a three-note chromatic melody (B-flat, B, C) at the top of the piano part. The phrase finishes with another German sixth properly resolved, introducing the new phrase.

Now in the second phrase, the poet notices that the flowers are whispering about him. To commemorate this odd feeling, Bobbie puts a German sixth right after the tonic, and spells it wrong — as if it were the dominant seventh of the raised tonic (or Neapolitan, or something). Of course, we listeners have heard the chord before, twice, spelled in its German manifestation, so we think little of it.

Here's where the pun comes in, as said dominant seventh resolves to — to — to what, really? A delayed suspended something or other to the Neapolitan? To an F-sharp minor triad over a B-natural bass? Theory students trying to do a Roman numeral analysis go nuts here. They write "N9" or N7", or they write in a brief modulation to B with the German sixth as the pivot chord — well, I suppose it's all of them and none of them. but it shonuff makes the vocal line tortured, and that's kind of the point, isn't it?

I mean, okay. Look at the flats and the canceling naturals in the vocal line above a piano part in sharps. Nutty! and when the "N7" or whatever it is kind of slides into a more normative V7/V, that causes a bunch of weird stuff to happen. The octave between the singer and the bass (well, not an octave ‚ C-flat and B-natural) is "resolved" to a seventh! Both voices must be spelled that way because of the voice leading — raised tone going up, lowered tone going down. It is exactly the opposite of how the augmented sixth resolves (in opposite directions to an octave). Hmm.

So when the voice "resolves" to B-flat, ah! Back inside the key, and the seventh that it forms with the bass will resolve down, properly. After all, in first year theory I have reiterated time and time again — so frequently that I always note which iteration it is — that sevenths resolve down by step. Always, always. Except when they don't.

And Bobbie/the poet's resolution of that seventh? Up by step! Nutty! How can Bobbie get away with that?

I'm sure you thought of the same thing; The bass line was B-flat (then F-sharp), B, C, as another manifestation of the 3-note chromatic line noted earlier. The voice, too, accomplishes the same line on slightly longer time scale — B-flat to begin the phrase, the C-flat "resolution" and the completion of the motive by the move up to C-natural.

Well, things return to normal soon thereafter, and the German sixth is once again a German sixth and B-flat major is back where it belongs. Now it's apparently normal for flowers to whisper, since the poet then sings those words again, to the "normal" chords of the beginning of the song.

Okay, reality has changed. Flowers talk. The important thing, though, is — what do they say?

Luckily, the poem ends with the flowers talking, and of course they can't be in the same key as the poet. How does Bobbie decide what key the flowers will be in?

Ah, here's an idea! Project the 3-note chromatic line on another time scale! Vocal line cadence in B-flat; have the flowers start on B, and finish on C! Oh, how's that going to happen?

And anyway, aren't we accustomed to vocal phrases being introduced by augmented sixths? Let's give the flowers their own augmented sixth, one not even associated with a country! In another breathtakingly slidy move, the chord with the A-flat bass moves smoothly. if strangely, into the Key of the Flowers: G major. A perfect place for a B-natural in the voice. And that augmented sixth? B-flat D F-sharp A-flat. The fifth with the root? Augmented!

That one isn't quite German and not quite French, either. I usually call it the Alsacian sixth in class, and am always entertained by how many ways the students spell "Alsacian" when they write about this song. Alsacian wines are very nice. Alsacian sixths are very weird.

And what do the flowers say, in their very own key? Don't be angry with our sister, you sad pale man. Flowers are name-callers. And sad pale man gets the old German sixth treatment again, with another chromatic slide in the bass to G-flat from the G of the flowers; but this time resolving directly to the dominant, and initiating a long dominant pedal for a piano postlude. Bobbie narrowly avoids parallel fifths by resolving D-flat to C early — thus making the augmented sixth very briefly French.

This piano postlude is a bit nutty, too — what with all the vagrant harmonies moving stepwise. And the postlude to the postlude will also be the postlude to the whole cycle, in D-flat.

And that long-unresolved E-sharp from eleven songs ago? Dude, it's 1840.

Monday, October 25, 2010

The Means Justifies the Ending


It was the first year of graduate study in composition. I was learning a few incontrovertible things about high-level academic programs, especially factoid #18b: the best programs have very few self-esteem issues and thus don't insist on formalities. Thus the faculty were addressed by their first names. It took a few weeks before I could ask for a lesson time with Milton without walking away blushing, and giggling.

At Beff's first full-time continuing position, her colleagues insisted that students call her Dr. Wiemann. At her current job, she is Beth.

I give my students two choices: Davy or Herr Professor Doktor Davy. I make sure they distinguish the "k" sound in Doktor from the softer "c" sound to which they are accustomed, and to roll the r's. Advanced students can call me Egrrrrrrrrrigio Maestrrrrrro.

In this grad program, I was working on a massively complicated Septet, and learning about computers and computer music. I quickly had enough computer facility to write programs in EXEC that would, for instance, type the word fuck at you if you typed the word shit. And vice versa. As Steve, the EECS student next door noted, It's just like getting your mother to say 'Fuck'. Years later, Martler designed similar programs that enabled the following exchange between user and computer: Lick. Lick? Yes. Oh.
The Metropolitan Opera was doing its first production of the newly restored Lulu, and Claudio had sufficient connections there to get those of us who wanted into rehearsals for it. He even supplied transportation. I would say I went at least five times and got to know the music very well. Twice afterwards, Claudio even had his fingers on enough strings to get us a brief private meeting with Maestro Levine, or as Claudio called him, Jimmy. Claudio wanted to talk musical stuff with Jimmy while we watched, and Jimmy was very friendly and engaging with us. He was shorter than he looked on TV.

The first time we met with him, Jimmy might have been a little tired of talking Lulu, made a big gesture with his hands at us lowly grad student composers and said: Send me your stuff! I want to know what you're writing! He was sincere, as far as we could tell, and one of us — Scott, from Pittsburgh — took him up on the offer. He sent his giant and very short orchestra piece with a structural part for the lion's roar to Levine at the Met, and, of course, never got so much as an acknowledgement. It's hard to pierce the apparatus of great thickness around people with the stature of Levine. There was no good way for Scott to put on his package "of the fifty or sixty scores Mr. Levine receives in today's mail, this one is the special one. For you see, Mr. Levine, who probably wouldn't remember me, specifically asked to see it..."

Donald Martino told a story that after he had won the Pulitzer Prize, a second- or third-tier orchestra sent him a letter requesting scores and recordings for their programming consideration. He complied, and shortly they sent his package back with a note, "We apologize that we cannot accept unsolicited scores."

The very last time we were able to get into the Met for a rehearsal was the actual dress rehearsal, and we weren't the only scruffy onlookers in the audience – there seemed to be various levels of funding people scattered about, as well as the understudies. Whenever Lulu had a very high melisma, I started to notice the same melisma happening an octave lower right in front of me – and I realized that I was sitting right behind the understudy, singing along. Later to be the one who was on the classic Lulu broadcast, and who went on to great success in the movie of Carmen. Yes, it was Julia Migenes-Johnson.

After the four or five hours of that last rehearsal, Claudio insisted we get to see Jimmy again, and damned if, all sweaty but wired, Jimmy didn't come right out to see us again. We (Claudio) had a few issues with the production: first, near the beginning of the last scene, Lulu was seen soliciting her first client, and we thought that was gratuitous. Damned if they didn't cut that out! And finally, we had an issue with Berg himself and how he chose to end the opera. Berg was wrong, and it was up to Jimmy to fix it.

Famously, the last chords of each of Lulu's three acts summarize the musical materials of particular characters — A major over an F bass at the end of act I to signify Dr. Schön, A minor over F bass in act II for Alwa, and at the end of the opera, both of those chords (duh, just move the C-sharp to C), followed by Esus4 over F to signify Grafin Geschwitz (move C to B — facile comme un gateau). Geschwitz had just been stabbed by Jack the Ripper and ends the opera by singing a last heartfelt paean to Lulu, with a vocal range that exceeds even the Star Spangled Banner. Berg wrote a soft dynamic for the orchestra to end the opera — at least he did in the short score — perhaps trying to be subtle. In the Suite from Lulu that would feel fine because it ends only about twenty minutes of music from the opera. We felt, though, that after three hours of death and deception and all the other stuff that happens in operas, that the emotion had accumulated to a point where it had to end loud, and tragic — stereotypical, yes, but in the moment it was right. Jimmy agreed. We made a difference, and Berg made a quarter-turn in his grave. Which was, ironically, more comfortable.

Geoffy and I were once suppering at the Quarterdeck Restaurant, and somehow we got the idea to make a binary list: Davytudes that end loud, and Davytudes that end soft. The classic setup of two columns on a napkin from so many movies — or maybe from one — revealed that soft beat loud by a large margin. One wonders what the focus group would think, and what conclusions they would make. We also wondered what was for dessert. Alas, the fateful napkin will not be available for purchase at auction.

Loud endings are confident. Soft endings are cop-outs.

Huh? Where did that come from? Actually, I've heard that from exactly one composer, who will remain anonymous. In his defense, however, it came in a grad seminar as rigid philosophical positions were being staked out, and that one hadn't yet been taken.

Hmm, the more I write about grad seminars here, the less flattering they look. All in all, they were good — they made my brain expand sideways, though it never got any taller.

A number of years ago, and not long after I had become a professional teacher of composition, an old friend had sent me some cassettes of his music, which I listened to in as fastidious a way as I could, given the width of my brain. Since I was a newly anointed full-time composition teacher, it was hard to switch off composition teacher mode when I wrote him back for the feedback that he had requested ("I'm curious to know what you think" he had said, which with the burden of life experience I now know always includes the understood but unwritten ending "unless there's anything you don't like").

One of the things I wrote was "at least half of your pieces don't end. They just stop." The response was predictable: "What do you mean by that?"

Wow. Composition teacher mode means you have to splain stuff. You don't just proclaim it. Oh, right. I'm not European.

In retrospect, I should have just said it was all great and please sir may I have some more. Instead, I had to gather statistics from the unused portion of my brain to say what I meant: "By which I mean your pieces stop. They don't end."

Realizing my tautology (yes, my ology is very taut — even self-taut), I added "it doesn't feel like the musical thoughts, whatever they are, are completed. There's no inertia that I can sense. Things feel like they end in the middle of something." Aw, man it's about feelings? What's up with that?

In May 2003 Amy was airing out part 2 of the 'tude recording project on the AmerKlavier thing that DePaul University was putting on. That's not a typo, and every time anyone said AmerKlavier out loud, an angel got schmutz on his wings. I came out to do the Amy 'n' Davy show and introduce the two dozen 'tudes she was playing. Much of the audience was faculty and piano student types, and they got to ask questions after the show. One of them remarked, "some of the études don't seem to end. They just stop."

Luckily, I had exactly two feet, giving me an extra one for the shoe. I acknowledged that some endings felt weak but not necessarily wrong (parents always love even their ugliest children), I said it was a fair criticism, and if he would identify one such ending, perhaps I could explain why he was wrong, or why I was wrong, or how Amy could play it differently such that it ended in a way that was satisfactory.

He zoomed in on Wiggle Room, (two YouTubes, here and here!) and I agreed that the ending had seemed unsatisfactory. This is the one that, as Amy's original idea, takes off on the texture of the WTC 1 C minor prélude, and in recognition of Bach, leaves tempo, articulation, pedaling and dynamics to the performer.

Looking at the last four bars (here you are informed that the excerpt is © by C.F. Peters), I could explain what characteristics this passage has that signify that it's over!

  • After covering much of the piano, the range contracts to a very tight space, as in the beginning, where it lingers for two bars.
  • The right pinky is obliged to sustain a B-flat for almost four bars — the longest sustained note of the piece.
  • The left-hand wiggling gets antsy and syncopated, and slowly, then quickly, descends to the bottom of the piano, thus doing a space-opening gesture that should scream I'm ending, dammit!
  • At the last attack of the piece, the space-opening left hand ends at the low B simultaneously with the sustained B-flat moving, in a voice-leading way, to another B.
  • The opening-up to that wide octave should sound like a resolution, and make the B-flat sound retrospectively like a leading tone to B.


Amy was interpreting the ending — absent any Davynamics — as a fadeaway gesture. It was beautifully subtle, even if the left-hand thing wasn't. And the resolution to the upper B was perhaps too subtle. There Amy decided to instill an equally subtle crescendo to the last moment, and emphasize the octave. All in attendance were satisfied that it was now a suitable ending.

You will note in I-Chen's performance, it ends forte with the resolution slam-dunked. Both approaches work.

My first exposure to the chamber music of Dvorak was at a concert in San Francisco, and I fervently hope it will be my last. For you see, the finale of the piece I heard ended no fewer than five times.

I've also been fortunate to hear, in concert, plenty of modern works that kept ending. Over and over again.

Thanks to the magic of the radio format, pop songs don't have to end. Like old soldiers, they can simply fade away. Grad seminar or no grad seminar, I say that's a copout ending. Though I guess it creates work for arrangers when groups tour and need concert endings for their hits that do the fadeaway. Within that tradition, such as it is, however, there are some tunes I know of that are constructed such that they can never end — the harmonic progression ending Borderline, what with its cleverly placed secondary dominants and all, can never finish. Thus it has to ride off into the sunset.

My much-maligned-by-me first symphony ends big and thick and loud. Not because the piece demanded it. But because George Rothman asked me not to end it slow and soft. Opposites attract.

How can a composer get an ending wrong? So far it looks like pieces either don't end at all, or they end too much. I see the seeds of a trashy novel here — The Quartet That Ended Too Much. Can Dvorak realize the folly of his ending philandering and choose only one of them? And the right one? What will the other endings do when he rejects them? You won't be able to put it down; but you won't be able to sit through it, either! Ironically, it's a never-ending story!

Okay, yes, it's really aggravating for the composer to tell you he's finished and then to keep going. I've sat through my share of speeches that do the same thing. Poems, too.

Speaking of poetry, I have encountered more than a few poems with punch line endings. And then I cried. Aren't we all like that after all? It made me think of my mother. Perhaps we can agree that the problem with such endings is that they are too obvious — they don't leave any of the work of thinking to the reader. I wonder if there are endings analagous to punch line endings in music.

Well, okay. Sticking Shave and a Haircut at the end of a piece. But that's a joke. It could be irono-funny. More likely, it'd just be dumb. And so totally eighth grade, dontcha know.

Perhaps the endings are too heavy? Too downbeaty? How about an example of a very heavy ending, then? The Beethoven 5 — it's both Teutonic and its homonym, too-tonic. This heavy ending, though, feels earned, especially when taken in the context of the entire symphony. First there had been the seeming ending of the first movement that is hijacked by thirteen hammered Neapolitan and then thirteen hammered applied diminished seventh chords, going off into la-laville, thus making the movement's actual ending seem a bit weak in comparison. Plus, there's all the stuff that happens in the movements that follow, which seem — at least to ol' Ludwig — to require an ending heavy enough to stomp out all dissent — and that includes Neapolitans and diminished sevenths. That ending is so heavy that it seems overbalanced if the fourth movement is played by itself.

Okay, so endings have to be scaled to their pieces. Fair enough. A 40-bar prelude doesn't get a 30-bar ending. And you don't start pieces with the end. Or do you? Is there a piece of music with a structure similar to that of the movie Gandhi? It starts with Gandhi's assassination, then does glacially paced stuff for three hours, and when you finally wake up and the assassination scene happens again at the end, you know what's going to happen. Ah, foreshadowing. Perhaps all music contains in its beginning the seeds of its endings? Just like life contains the seeds of death?

Nah. Cosmic doesn't work here.

As Bobbie showed us, endings of pieces within larger collections of pieces can end weakly, as questions — a little bit like chapter endings in novels prepare the subsequent chapters. That is, they can end such as to defer to the later movements for the real, stronger endings. Which also makes such pieces a little harder to excerpt. Who claps when a piece ends on the dominant seventh? That's right — only squirrels do.

And as theorists say, some of whom were in the same room as me when they said it, much of the music of Brahms doesn't end until there's a cadence in every register. And presumably a car in every garage and a chicken in every pot.

Since the ending is the last thing you hear in a piece (uh, by definition), it's pretty memorable when the composer gets it wrong. So what do endings do anyway? Other than the tautological answers, that is.

I am proud to say that once the list of what endings do is finalized, notarized and certified by the composer commissions of at least fifty countries, I will be the first in line to write an ending that does something else. Because, you know, that sort of thing is one hundred percent perspiration.

In another blog post, I said that I do the two endings: the fadeaway and the a-splode™. In Davyworld, they both release a tension of sorts, accumulated by what happened before. Fadeaway is letting the air out of a balloon slowly, hopefully without the squeaky sound; a-splode™ is letting the air out of the balloon by popping it, thus making a big noise.

Thus perhaps at DePaul, Wiggle Room seemed still to have the fingers closing the aperture of the balloon with the air still in it. How did I get to this crappy metaphor? It's, like, even worse as a simile.

So, is the ending of a piece the strongest cadence? The largest release of tension? The resolution of all tension? The rhythmic nexus? The ultimate release after the structural downbeat?

I am pleased to offer the answers to these gnarly questions: Depends. Depends. Depends. Depends. Depends.

That's right. It's context-dependent.

And can a piece end convincingly if it's clearly in the middle of something?

Yes.

Cosmic question: if my piece ends convincingly, how do I get the critic to write It left me wanting more!?

For some reason, I'm feeling really self-conscious about how I end this blog post.

Aren't we all like that, after all?