Archive for the ‘Uncategorized’ Category

All the ways—

What scares you more: that I will talk of death, and injustice, and spiritual annihilation?  Or that I will explain how the equation

Pfi  = ∑ Γ(S)

affects your life?

Admit it.  You want death.  You want injustice.

You want spiritual annihilation.

I get it, I get it.  Math is an annoyance; math is anathema.  As it did for the learn’d astronomer, math makes you unaccountable tired and sick.

Maybe math scares you.  Or worse—maybe math bores you.  Fear you can take, and anxiety in equal measure; but boredom, never.  It wasn’t time but boredom that sunk Ozymandias into the lone and level sands.  Because—

Because (you say) math is about numbers.  That’s it.  It’s just numbers.  By enumerating, you take away a spark.  That which can be counted, can be dismissed.  A mathematician is a bean counter with a pocket protector, somewhere on the spectrum, digitizing nature, walling off the soul with a wall of 1’s and 0’s.

But it isn’t true.

I could plead that mathematicians don’t usually think of numbers.  They think about patterns, symmetries, interconnectedness.  They see math in the petals of a daisy, and in the predator/prey cycle of lynx and snowshoe hares.  Math is in the strength of nanowires, and the delicacy of hoar frost, and the oomph of an engine, and the whorls of a Spirograph.

I could plead that math is about connections, structures.  Math is the study of logical systems.  Numbers are beside the point.

Beside the point.

I’m looking right now at the white-board in my office.  Ignore the calendar with a picture of Crater Lake, and ignore the poster of Han in Carbonite, and ignore the Albert Einstein action figure, and the pamphlet which says “Welcome Aboard Marine One.”  Focus on the white-board itself: it’s covered with equations, in red and green and blue, with doodles, starts and stops, arrows and spirals, letters both Roman and Greek.  There are graphs of velocity vs. time.  There’s a derivative, and an integral.  There’s Newton’s 2nd Law, half-erased.

There are no numbers on the board.

I could plead still, but here is what I know: that math is beauty, and that the whole world is math.  Here in my ivory tower, I adhere to the Mathematical Universe Hypothesis, which posits that the multiverse is itself is “just” a mathematical structure.  It’s not infinite turtles, but math, all the way down.

Jump if you like: you’ll never hit the bottom.

And what of the equation I gave?  What does it say?  To whom does it speak?

It comes from a paper I wrote, across a gulf of years and disciplines.  It says, in English, that the probability of going from quantum state A to quantum state B is the sum of all the products of closed-loop amplitudes that include A and B.

I am A.

You are B.

To get from me to you, we have to count all the ways we can interact, including ways that go backwards from you to me.

We add up all the ways.

And in the end you don’t have a number, but possibilities.


Read Full Post »

I’ve talked in the past about the RGB color scheme, and about extra spectral colors.  Here I want to ask a specific question: why do some RGB color combinations have names, while others do not?

First, a review.  Most (but not all!) colors that humans can perceive can be represented (approximately) by a set of three numbers (R,G,B) where each variable runs from 0 to 255.  Roughly speaking, a 0 is “none” of that color and 255 is “maximum” of that color.  Thus (0,0,0) is black, (255,0,0) is red, etc.  What’s interesting is which combinations get names in English, and which do not.

Suppose two colors are maxed out.  (255,255,0) is equally red and green; if you’re familiar with color addition, you know this is yellow.  Similarly, (255,0,255) is magenta, and (0,255,255) is cyan.  So far, so good.

Now suppose one color is maxed, and another is at half value.  Here’s where things get interesting.  Consider (255,128,0), which is (in a sense) halfway between red (255,0,0) and yellow (255,255,0).  Not surprisingly, (255,128,0) is called orange.  But what about halfway between yellow and green, i.e. the color (128,255,0)?  Mathematically, this should be as unique a color as orange, but (sorry) it just looks like a different shade of green to me.  Why is that?  What’s special about (255,128,0), but not about (128,255,0)?

It turns out that (128,255,0) has a name: chartreuse.  But probably only one person out of twenty could identify chartreuse out of a line-up.

If you want to experiment, try the other “halfsies” using this RGB applet.  The combinations you should test are

(255,128,0) = ORANGE

(128,255,0) = CHARTREUSE

(0,255,128) = ?

(0,128,255) = ?

(128,0,255) = ?

(255,0,128) = ?

Only one of these is obvious to me, i.e. the color (0,128,255) which is halfway between cyan and blue.  That’s the color of a clear sky, and is known in English as azure.

Do any of these combinations have unique names in other languages?

Here’s a modern-day color wheel (thanks, Wikipedia!), which puts all of this into perspective:


[Note that “violet” here isn’t really true violet (as in a rainbow), which cannot be represented on an RGB computer monitor.]

Are these the names you came up with?  Personally, I called (0,255,128) “dark mint green” instead of Spring Green, but what do I know.

And here we get to the psychology of color, which is the main point of this post.  Look at the trifecta of red/orange/yellow: most people would classify those as three really distinct colors.  Now look at the trifecta chartreuse green/green/spring green.  Those all just look like green, to me.  They aren’t as distinct.  And I think the reason is completely in my mind.

Think back to when you studied color in kindergarten.  The “primary” subtractive colors were red/yellow/blue.  [That’s now known to be bullshit, of course; there are no three canonical primary subtractive colors; we instead make a choice of three primaries based on what colors those three could possibly make upon mixing (this is called the gamut) and  cyan/yellow/magenta gives a better gamut than red/yellow/blue.  Put another way, if you only had three crayons, then choose cyan/yellow/magenta instead of red/yellow/blue because more mixed colors will be available to you.]  Anyway, now look at the RGB wheel and find red/yellow/blue.  They aren’t equidistant.  Something is wrong.

Here’s my thesis: I think that the red/yellow/blue bullshit we lived through at the age of 6 has biased us towards thinking that red and yellow are more different than they really are.  Look at the wheel again.  In terms of RGB numbers, red and yellow are as similar as blue and cyan.  Hard to believe, I know, but that’s the way the cookie crumbles.

One final thought: in English, in kindergarten, when you mix white with red, you get pink.  What about mixing white with green?  Or white with blue?  How come there aren’t unique names for those colors?

(255,200,200) = PINK

(200,255,200) = ?

(200,200,255) = ?

Read Full Post »

There once lived a man who had strange dreams.

One of the dreams regularly involved a tennis tournament played on a mountaintop in Peru.  Another had an origami master who was the operator of an armored personnel carrier.  Yet another consisted of an Australian women’s rugby coach who moved to Serbia, opened a brewery, and wrote a novel based on the life of Python of Byzantium (Πύθων ὁ Βυζάντιος).

The worst of these dreams, however, was a nightmare which tormented the man periodically.  In this nightmare, there was a xylophone made from human bones: finger bones for the high notes on the right, down to an enormous femur for the lowest note on the left.   In this nightmare, the man was invariably tied to the xylophone with shigawire, while a demonic musician played something execrable (such as Vivaldi’s Four Seasons).  At the climax of the music, just when the man was on the point of being driven entirely insane, the ghost of Warren G. Harding poured grape juice onto the xylophone from an amphora made of jade.

At this point the man always awoke with a start, in a cold sweat, sometimes screaming, sometimes crying.

It goes without saying that the man developed a lifetime phobia of grape juice being poured onto xylophones.  And worse: he developed a fear of almost any juice product being dumped onto any percussive mallet-based instrument.

He avoided Kindergarten classrooms, for who could say that little Timmy might not pour his juicebox onto that glockenspiel?  He avoided performances of Danse Macabre by Saint-Saëns, for might not the percussionist have a flask of wine which could spill forth?  And forget ever going to see the Rolling Stones in concert: might not a band member spill a screwdriver onto the marimbas during “Under My Thumb”?  All told, the man’s phobia represented a very minor, but non-zero, inconvenience.

Our story would be of little interest were it not for the fact that the man became Emperor of the World.  How this was achieved is of no consequence to this parable; suffice to say that the man lied, preened, stole, and schmoozed his way to the top.  But once he was in power, the now-Emperor decided that he could now rid himself of fear, by passing a law.  The law was presented thus:

As Emperor of the World I hereby ban the pouring of grape juice onto xylophones.  Anyone caught committing such a traitorous, cowardly act, will face the full wrath of our justice system, and be imprisoned for not more than 33 years.

The Emperor released this edict and went to bed content, confident that his nightmares were over.

But there were unintended consequences.

Most people had never, in their wildest fantasies, entertained the notion of pouring grape juice onto xylophones.  The whole concept never crossed their minds.  But now, with the Emperor explicitly banning the practice, the pouring of grape juice onto xylophones (PGJOX) became A THING.  Suppose you wanted to irk the Emperor, get under his skin, be a gadfly, protest his policies.  What better way, than PGJOX?  Whereas before the Emperor clawed his way to power, there was not a single case of PGJOX, after the edict there were thousands of such cases.

The Emperor was too dense to realize that his law had caused all that grape juice to be poured.  Indeed, the ballooning of PGJOX cases reaffirmed his pre-conceived notion that PGJOX was A THING, and had always been A THING, and so his law was justified.  There was a vicious cycle: the more he railed against PGJOX, the more people performed the act he hated; this in turn caused him to rail against PGJOX all the more.

What became of the Emperor?  And what became of the law?  And what became of pouring grape juice on xylophones?  In the first case, his nightmares returned, his dreams became indistinguishable from reality, and we are still to this day (centuries later) recovering from the 30-year rule of the Mad Emperor.  Of course, the law banning PGJOX was repealed eventually, but (interestingly) pear juice is still poured onto vibraphones every Nov. 30 in parts of Alberta and Saskatchewan (on Banff Day).

Moral: if you’re a lawmaker, and there’s some strange act that makes you uncomfortable, then shhhhhhh…don’t do anything.  Don’t bring attention to it.  Passing a law against your pet peeve is just lighting a match and handing it to your opponents.

But don’t trust me.  Trust the ghost of Warren G. Harding.


Read Full Post »

There’s a lot of talk these last few days of how horrible it would be if, for example, Penn State wins the Big Ten championship but doesn’t make the college football Final Four playoff.  This would happen if, say, Washington (the current #4) loses to Colorado in the Pac-12 championship.  Presumably, then, Michigan (now currently #5) would move up into the #4 slot, leaving the Nittany Lions crying into their Wheaties.

Why would this (ostensibly) be horrible?  Well (the argument goes) you’d then have two Big Ten teams (Ohio State and Michigan) in the playoffs who didn’t even win their conference.  Some people think this would be a travesty.

I disagree.  Winning (or not winning) a conference is essentially meaningless.  That’s because it’s entirely possible to win the conference with a shitty record.

Image result for big 10 trophy

First, we have to discuss how the Big Ten champ is chosen.  There are 14 teams in the Big Ten, not 10. (We’re already in Twilight Zone territory here).  7 of the teams are in the West division, and 7 are in the East.  Each year, each team plays 4 non-conference games, and 8 conference games; of those 8, 6 are in the same division, and 2 in the other division.  The winner of the West will play the winner of the East to determine the Big Ten conference champ.

Suppose, in the East, Michigan, Ohio State, and Maryland all post 11-1 records; each losing only one division game to one of the other two.  Based on arcane tie-breaks, one of these (presumably) good teams will be invited to the Big Ten championship.  Let’s say it’s Maryland.

In the West, however, imagine that all 7 teams have identical 3-9 records.  They achieve this by losing all non-divisional games, and splitting their West division games 3-3.  One of these (crappy) teams will go to the Big Ten championship game by tie-break.  Let’s say it’s Iowa.

So it’s Maryland (11-1) vs. Iowa (3-9).  Maybe Iowa wins on a fluke (Maryland’s QB gets the flu, or a ref gives the game to Iowa by awarding a 5th down…these things happen).   Despite this head-to-head result, is anyone really going to rank the now 4-9 Iowa Hawkeyes over the 11-2 Maryland Terrapins?  Of course not.

Here’s the mathematical reason that conference championships are meaningless: all they tell you is that you’re the best team out of a subset of teams.  And that doesn’t really tell you much at all.

Suppose we had a tournament for BIG COUNTRIES.  Who would you rank among the top BIG COUNTRIES?  My top four would be Russia, Canada, USA, and China.  “But wait!” says Algeria.  “I won the Africa division!  And the USA is smaller than Canada and so didn’t even win its division!”

If we want to pick the BIG COUNTRIES, then being the biggest country in your continent is meaningless.  Similarly, if we want to find the best teams, finding the best teams in conference divisions is meaningless.

One way to mitigate this problem is to eliminate conference divisions entirely.  In the hypothetical scenario mentioned above, if the Big Ten just had one 14-team division, then Iowa would stay home and Maryland would play Michigan (say) for the conference title.  Still not perfect, but we’d definitely know then that a good team had won the conference.

I’m not lobbying for any sort of change in the NCAA playoff selection rules.  I have every expectation that the committee will do the right thing, regardless of whether Washington wins or not.  Their ranking Ohio State #2 despite not even going to the Big Ten title game is indicative of that.  What I am advocating for is for people to shut up about conference champions.

Hey, Algeria: just because you’re the biggest country in Africa doesn’t make you a top-4 country.

Image result for algeria flag

Read Full Post »










Huang Gongwang: Dwelling in the Fuchun Mountains (Part)

Read Full Post »

The music you need today

If you listen to one piece of music today, let it be this:

When I need comfort, this is the best piece of music I can imagine. It’s one long movement. It’s one continuous narrative. There is no suspension of disbelief required, by which I mean you don’t really hear individual instruments as instruments, or hear the whole orchestra and think “that’s an orchestra”. You forget you’re listening to a performance at all. You forget you’re listening to something man-made called “music”. It’s almost as if you’re listening to perfection, translated into the medium of music. The notes swell and ebb, and you wander through a beautiful yet haunting landscape. When every climax is reached, when every section finds its conclusion, the music evolves gradually, and a new summit is attempted, a new path is taken. But the previous sections don’t end; they become (in turn) the backgrounds for what lie before you. Listening to the 7th is like hiking a ridge line in the mountains, cresting apex after apex, but your previous climbs are always behind you, receding only gradually into the past. At many points in the journey, you think you’ve reached the top of the mountain, only to see the sun glint off a snowy peak in the distance, and realize you can yet climb higher. The ending is abrupt and resigned, like freezing to death on the mountaintop. If you cry, it’s just the cold wind in your eyes.

Read Full Post »

Here’s something that will never happen, but it would be awesome:

The NCAA should go to a Swiss-system for college football.  And I don’t mean for the playoffs; I mean for the entire season.

First of all, here’s a brief primer on what the Swiss-system is.  I don’t think I can explain it better than the hive mind on Wikipedia, so here’s a quote:

“A Swiss-system tournament is a non-eliminating tournament format which features a predetermined number of rounds of competition… In a Swiss tournament, each competitor (team or individual) does not play every other. Competitors meet one-to-one in each round and are paired using a predetermined set of rules designed to ensure that each competitor plays opponents with a similar running score, but not the same opponent more than once. The winner is the competitor with the highest aggregate points earned in all rounds.”

Such systems are very common in chess tournaments, and also used in backgammon, squash, and eight-ball tournaments.  I’ve never heard of them being used in team sports, which is a pity.

Image result for bern

If I were Emperor of the World, here’s how I would implement the Swiss-system for college football.  At the beginning of the season, I’d rank the 128 FBS teams (teams that normally are bowl eligible) from #1 to #128.  (Well, I probably wouldn’t rank the teams personally, but I’d have a computer and/or a committee rank the teams much as the BCS does now.)  The great thing is that a ranking of #1 vs. a ranking of #5 (say) at the beginning of the season wouldn’t matter much at all.

The first week of the season, #1 would play #65, #2 would play #66, and so on.  For illustrative purposes, if we based seeding on the current NCAA rankings (as of Nov. 7, 2016), we’d have Alabama (#1) playing Southern Mississippi (#65), Michigan (#2)  vs. Texas Tech (#66), Clemson (#3) vs. Georgia (#67), Washington (#4) vs. NC State (#68), and so on, down to California (#64) vs. Florida Atlantic (#128).  Every higher-ranked teamed would be favored of course, but you’re going to get plenty of upsets: every one of the matchups I just (arbitrarily) presented would be a decent game.  Gone would be the days when an Alabama would play a non-FBS Western Carolina for their first game and win 49-0 to pad their resume.

Starting with week #2, things are already interesting.  Every week after the first, each team plays another team with the exact same record (if possible).  Continuing with my example, and assuming that all the higher ranked teams won in week 1, you’d already have on the table Alabama (#1) vs. Troy (#33), Michigan (#2) vs. Tulsa (#34), Clemson (#3) vs. Minnesota (#35), etc.  None of these games are cake-walks by any means (for perspective, the current records of Alabama, Michigan, and Clemson are all 9-0, but the current records of Troy, Tulsa, and Minnesota are 7-1, 7-2, and 7-2, respectively.)

Here’s the thing: starting with week 2, every single game in college football is a competitive game.  And starting around week 4, every single game is almost evenly-matched.  We’ve eliminated the all-too-common problem with the current system: that the top teams really only play 2 or 3 meaningful games a year.

Suppose we were using the Swiss-system, and we were making the matchups for the coming week’s games (Nov. 12).  What games would be on tap?  Well, there are currently 5 undefeated teams, which in a Swiss-system would be very unlikely after 9 weeks.  Just for fun let’s assume that it’s possible, but let’s ignore Western Michigan (no way they’d go 9-0 if they faced a few good teams).  With Alabama, Michigan, Clemson, and Washington all 9-0, this week’s marquee matchups would be Alabama vs. Washington, and Michigan vs. Clemson.  It’s likely that next week you’d have Alabama facing Michigan.  This, in early November!

The good matchups continue all the way down the line.  One-loss teams would all face each other, and you’d perhaps have games like Louisville vs. Ohio State.  Even at the bottom of the barrel, with a Rice playing a Florida Atlantic, the games would be evenly-matched.  This would be great for fans, because as it stands, when a Rice fan attends a game, they fully expect a loss; but with a Swiss-system, that same fan can be hopeful for at least a 50-50 shot at winning.

At the end of the season, an undefeated team would be almost impossible.  It’s likely you’d have 3 or 4 teams that were 10-2, and they’d all have already played each other.  That’s when a playoff would kick in.

For the playoff, we’d have the 4 (or better yet, 8) teams with the best records play each other in a standard elimination format.  At this point, it wouldn’t matter if they’d already faced each other in the regular season; rematches at this point would be desirable.  The great thing is that these teams would all be excellent teams.  In a Swiss-system, if you go 10-2, facing tougher opponents every single week, no one can argue you aren’t one of the best teams in the country.  Built into the Swiss-system is an important feature, which is that basically, every team at the end with a similar record faced a similar strength of schedule.

This is important, for in the current system, teams which are 12-0 can be left out of the playoff discussion if they’d didn’t play any good teams.  That’s never struck me as particularly fair.  If my team goes 12-0 and doesn’t get to the playoffs, then that means the team never even had a theoretical shot at making the playoffs to begin with.  What’s the point, then?  It’s a sordid fact that in the current system, there are only 30 or so teams that can ever even theoretically make it to the playoffs in a given year.  I’m sorry, Florida Atlantic, but if you go 12-0 next year you ain’t playing in a major bowl game.

There are obviously a few objections one could raise to my brilliant scheme.  Let’s address them.

  1. What about logistics? How in the world could you have teams flying around the country, facing each other, planning trips on only a week’s notice?  Well, as Emperor, it wouldn’t be my problem.  But in any case, it’s the 21st century for Xenu’s sake, so I think with some 747’s and the internet, it could be done.
  2. What about revenue? If Western Carolina doesn’t get to play and get crushed by Alabama, then Western Carolina loses out on some big time TV money!  OK, sure, but the games will in general be much, much more competitive, and many more fans will go to see WCU home games since they finally have a chance to win.  I really believe TV revenue would be up across the board.  We could even implement a TV revenue-sharing scheme, but that’s a topic for another day.
  3. What about rivalries? Well, what about them?  The current system doesn’t give a fuck about them in any case.  I can’t even keep track of who’s in what conference these days.  (Syracuse is in the ACC?  When did that happen?  They’ll always be a Big East team to me.)  With a Swiss-system, conferences become meaningless, and I say good riddance.

Image result for army navy game 1963

As for the handful of actual rivalries that still exist, and haven’t become jokes, such as Army vs. Navy (come to think of it, that has become a joke) or Alabama vs. Auburn, you could have the teams play an extra game in mid-December that doesn’t really count for anything.  If you think it’s unfair that a team has to play an extra game compared to other teams, well then, why not have every team pick a greatest rival that they have to play every year?  Hell, these games might even be the first games of the year, a sort of pre-season-type game, and the results don’t affect the Swiss-system per se, but the results might inform the seedings.  So Navy plays Army (a joke game, usually) but if Navy loses, we might initially rank them a little lower than otherwise.

Would any of this ever happen?  Not one chance in a million.  But it’s fun to speculate about.  And mark my words, in the universe(s) where I actually do become Emperor, initiating an NCAA football Swiss-system is one of my first magnanimous acts.

Read Full Post »

Many Worlds Puzzle #5

I proved a theorem in number theory last week.

Don’t get me wrong; the theorem is fairly useless.  The proof itself is trivial.  But the fact that I came up with the proof, in my head, makes me proud…mostly because I’m a physicist, not a mathematician.

Here is the theorem:

Square any odd integer greater than 1, and then subtract 1.  The result is evenly divisible by 4.

I’ll leave the proof to you, for fun.  Do it in your head!

This is what theoretical physicists daydream about on 7 hour car rides.

Image result for pinnacle park sylva

Read Full Post »

I spent a ridiculous amount of time writing my last blog post.  I mean, it was almost 5000 words.  Who writes 5000 words just for fun?  But luckily, all that work will yield not just one, but two (or maybe even more) blog posts.  Just as PhD’s mine their dissertations for journal articles, I will mine the last post for more nuggets of symphonic information.  We will count down the 100 symphonies ever written.  Most of the work has already been done: I’ve ranked every numbered symphony I could think of (spoiler alert: Sibelius has the top 2 spots!) but there are some symphonies I’ve left out.  We need to add some works numbered 10 and beyond; and we need to add a few symphonies without numbers at all.  Likewise, we need to get rid of some of the “throwaways”.  Sorry, Haydn #9.

What, exactly, is a symphony?  I consider it a large-scale work for orchestra, for which soloists don’t play a major part.  That’s a pretty broad definition, but it excludes things like Bartók’s Concerto for Orchestra, Bach’s Brandenburg Concertos, and Beethoven overtures.  There’s some subjectivity here: why exclude Lenore III when, in actuality, it’s longer than some Mozart symphonies?  I don’t have a good answer except to say that Lenore III wasn’t meant to stand on its own…it was meant to be part of an opera.  A symphony should be self-contained.

One further point.  I’m not going to rehash all of the symphonies from the previous post.  I am going to use the scores from that post, but in order to keep this post under 5000 words I’m going to limit myself to one sentence only for each symphony.

Here’s the countdown:

  1. Bruckner Symphony #1

Not the strongest Bruckner symphony, but worth a listen for the promise it conveys.

  1. Schumann Symphony #4

Schumann’s best symphony is well-constructed but kinda forgettable.

  1. Beethoven Symphony #6, “Pastoral”

Most people like it, but it’s too cheery for me (in a “drunken centaur” kind of way).

  1. Tchaikovsky Symphony #1, “Winter Dreams”

Not Tchaikovsky’s best, but sprightly and with a triumphant ending.

  1. Shostakovich Symphony #15

A demented toy shop: just listen for the quotes from the William Tell Overture.

Image result for helnwein paintings

Gottfried Helnwein, Untitled

    95. Borodin Symphony #2

Good and bad in equal measure, it depends upon your mood.

  1. Beethoven Symphony #3, “Eroica”

The first memorable Beethoven symphony, but the funeral march is boring.

  1. Tchaikovsky Symphony #2, “Little Russian”

More serious, slightly improved version of Tchaikovsky’s 1st.

  1. Bax Symphony #7

Bax tries to emulate Holst’s The Planets, but only partly succeeds.

  1. Piston Symphony #7

Almost like a movie soundtrack, with hints of Copeland.

  1. Haydn Symphony #94, “Surprise”

Stereotypical late Haydn, which can be good or bad.

  1. Mahler Symphony #3

A glorious, epic mess; the singing parts are just weird.

  1. Schubert Symphony #6, “Little”

Even a weaker effort of Schubert is better than most people’s best.

  1. Shostakovich Symphony #2, “October”

Experimental, random, chaotic, but ultimately triumphant.

  1. Mahler Symphony #1

All-encompassing journey to a primordial alien world, marred by the presence of an insipid children’s song.

  1. Glass Symphony #9

This is what happens when Glass tries to sound more like Sibelius or Bruckner.

  1. Bax Symphony #6

This muscular symphony could be the soundtrack to Conan the Barbarian.

  1. Brian Symphony #1, “Gothic”

Gargantuan, beautiful, and over-long.

  1. Mahler Symphony #8

Mahler tries to make his own “Beethoven’s 9th” but dispenses with the foreplay.

  1. Bruckner Symphony #3, “Wagner Symphony”

The first fully mature Bruckner symphony…serious and masculine.

  1. Dvorak Symphony #8

Happy and mature…a hike for grown-ups.

Image result for hikes on isle royale

  1. Tchaikovsky Symphony #4

“A sleigh ride through Siberia”, and proof that Tchaikovsky just kept getting better.

  1. Mozart Symphony #39

Underrated Mozart symphony that matches the heft and polish of the more famous last two (#40 and #41).

  1. Prokofiev Symphony #7

Melancholy and percussive, and proof that Prokofiev wrote more than just the “Classical” symphony and Romeo and Juliet.

  1. Shostakovich Symphony #12, “The Year 1917”

Some call it a film score looking for a movie, but it sounds good to me.

  1. Sibelius Symphony #1

The first sign that Sibelius is The Chosen One.

  1. Mendelssohn Symphony #4, “Italian”

It’s like crème brulee that’s been sitting out for an hour or so.

  1. Glass Symphony #3

The best symphony by Philip Glass.

  1. Haydn Symphony #88

This takes refinement to a whole new level.

Image result for vienna in 1787

  1. Vaughn Williams Symphony #8

Great and otherworldly, but the ending has me thinking of all the Who’s singing down in Whoville.

  1. Prokofiev Symphony #1, “Classical”

Hey, look Ma, I can write a classical Haydnesque symphony in the 20th century!

  1. Vaughn Williams Symphony #5

Pastoral and Faux-Sibelius, with Hobbits.

  1. Vaughn Williams Symphony #6

Hey, I know, let’s just depress everyone with this “nuclear wasteland” ending.

  1. Mahler Symphony #6, “Tragic”

It’s got some hammer blows in there somewhere?

Image result for mjolnir

  1. Mahler Symphony #5

A sublime Adagietto padded by an hour of epic Mahlerian mush.

  1. Sibelius Symphony #3

Leaner and more focused, this is a new direction for Sibelius.

  1. Shostakovich Symphony #10

Tense and colorful and oppressive, like a Soviet propaganda poster brought to life.

  1. Mahler Symphony #7

Strange, bleak, demonic, and then…triumphant?

  1. Mozart Symphony #35, “Haffner”

Mozart tries something a little…bigger.

  1. Hovhaness Symphony #63, “Loon Lake”

I have no idea where Loon Lake is, but I want to go there now.

  1. Haydn Symphony #82, “The Bear”

My favorite lesser-known Haydn symphony.

  1. Bruckner Symphony #6

Like Bruckner’s 5th on Xanax.

  1. Bruckner Symphony #4, “Romantic”

The age of chivalry made into music.

  1. Shostakovich Symphony #9

Goofy, sinister, vigorous, and off-putting.

  1. Tchaikovsky Symphony #5

Despair gives way to triumph.

Image result for helnwein

Gottfried Helnwein, Midnight MIckey

  1. Schubert Symphony #5

You could call this “Mozart’s 42nd”.

  1. Schubert Symphony #8, “Unfinished”

Pristine, flawless, menacing…then peaceful.

  1. Shostakovich Symphony #1

A stroll through a museum of artworks by mental patients.

  1. Haydn Symphony #26, “Lamentatione”

Why didn’t Haydn write more symphonies in a minor key?

  1. Hovhaness Symphony #22, “City of Light”

Harmonious and magisterial.

  1. Mozart Symphony #38, “Prague”

The first Mozart symphony with real gravitas.

  1. Bruckner Symphony #7

Great Adagio, even if Hitler liked it, too.

Gottfried Helnwein, Epiphany I

  1. Sibelius Symphony #6

It’s like waking up to a foggy dawn in the Smokies, to discover autumn’s first frost.

  1. Beethoven Symphony #4

The most underrated Beethoven symphony.

  1. Tchaikovsky, Manfred Symphony

This is so good, how come no one has ever heard of it?

  1. Nielsen Symphony #4, “The Inextinguishable”

Eclectic, disturbing, psychological, with a timpani battle!

  1. Khachaturian Symphony #3

“Raw and strident” …it’s a single movement, dominated by an organ and 15 (!) trumpets.

  1. Shostakovich Symphony #8

Like a vacation in East Germany.

  1. Schubert Symphony #3

I challenge you not to like this.

  1. Mahler Symphony #10

 Ah, what might have been…

  1. Bizet, Symphony in C

Here’s a teenager putting the rest of us oldsters to shame.

  1. Nielsen Symphony #5

Nielsen tops his 4th with an even more war-like symphony.

  1. Rachmaninoff Symphony #2

A harmonic mosaic that somehow conveys poignancy, joy, and sadness at the same time.

  1. Dvorak Symphony #7

My favorite Dvorak symphony other than the 9th…I wish I knew why.

  1. Ives Symphony #4

It’s like a church service with goblins besieging the place.

  1. Haydn Symphony #49, “La Passione”

Haydn + minor key = good.

  1. Mozart Symphony #40

Mozart + minor key = good.

  1. Górecki Symphony #3, “Symphony of Sorrowful Songs”

Threadbare songs of infinite sadness.

  1. Tchaikovsky Symphony #6, “Pathetique”

Tchaikovsky’s best; there’s just so much going on here.

  1. Haydn Symphony #39

Strum und Drang…must I say this was in a minor key?


  1. Strauss, Also Sprach Zarathustra

OK, maybe this isn’t a symphony, but holy shit….please, please, listen to more than just the cliched opening two minutes!

  1. Mahler Symphony #9

Funny, how much of the best Mahler is the Mahler that sounds most like Bruckner.

  1. Franck, Symphony in D minor

A French organist tries his hand at symphonic writing, and scores a home run.

  1. Mozart Symphony #29

Maybe the best opening movement of any Classical symphony.

  1. Mahler Symphony #2, “Resurrection”

Mahler’s best.

  1. Beethoven Symphony #5

Skip the first movement if you want to hear this with fresh ears.

  1. Mozart Symphony #25

Agitated, syncopated, minor key…are we sure this was written in 1773?

  1. Shostakovich Symphony #7, “Leningrad”

Trump’s ascent made into music: the banality of evil.

  1. Shostakovich Symphony #11, “The Year 1905”

Highly visual and emotional tour-de-force.

Image result for the year 1905

  1. Dvorak Symphony #9, “From the New World”

Maybe the catchiest symphony of all time.

  1. D’Indy, Symphony on a French Mountain Air

Like a picnic in the Alps, in springtime.

  1. Brahms Symphony #1

Some call it “Beethoven’s 10th” and that’s not far off the mark.

  1. Brahms Symphony #4

Better than the 1st, by a hair…Brahms proves here that rigid structure and control can still yield immense beauty.


  1. Saint-Saëns Symphony #3, “Organ Symphony”

The organ’s entry in the finale is spectacular…and is that a fugue?

  1. Bruckner Symphony #8

Apocalyptic in every sense of the word.

  1. Berlioz, Symphonie Fantastique

A fever dream: Downton Abbey on ecstasy, with some Satanism thrown in for good measure.

  1. Beethoven Symphony #7


  1. Mozart Symphony #41, “Jupiter”

Sounds simple, but if you look at the 4th movement along with the score, your mind will be blown by how complicated the fugue is!

  1. Bruckner Symphony #5

So Bruckner…so complex.

  1. Walton Symphony #1

The fragmented motifs, the iron-clad logic…every single movement makes me smile.

  1. Schubert Symphony #9, “The Great”

If this music doesn’t make you feel anything, you might want to check your pulse.

  1. Hovhaness Symphony #2, “Mysterious Mountain”

Subterranean caverns, glistening stalactites, corners with cobwebs, and sunlight glinting off giant broken geodes.

Image result for hang son doong

  1. Sibelius Symphony #4

Music that stares back at you, with a gaze “blank and pitiless as the sun”.

  1. Hovhaness Symphony #50, “Mt. St. Helens”

Mysterious Mountain on steroids, complete with a volcanic eruption unlike anything ever portrayed in symphonic form.

  1. Shostakovich Symphony #5

Even though it predates World War II, this is an invasion by Nazis, turned into music.

  1. Bruckner Symphony #9

Unrequited longing…unresolved harmonies…and then it—

  1. Sibelius Symphony #2

Has the greatest musical orgasm ever written.

  1. Beethoven Symphony #9

Encompasses all of human experience.

  1. Sibelius Symphony #5

The best symphony ever written.

  1. Sibelius Symphony #7

The best symphony ever written [stet].

Image result for sibelius 7th symphony

[Note: after having written all this, I realize there are some good ones I’ve forgotten: Strauss’ Alpine Symphony, Vaughn Williams’ Sea Symphony, Rimsky Korsakov’s Scheherazade, Saint-Saëns’ Carnival of the Animals.  I could probably justify not calling any of these symphonies per se (even the Sea Symphony sounds more like a cantata to me) but I’ll instead just call these honorable mentions.  Having said that, they’re all very good, and if I wanted to spend another hour or so they’d bump Bruckner’s Symphony #1, Schumann’s Symphony #4, Beethoven’s Symphony #6, and Tchaikovsky’s Symphony #1 out of the top 100.]

[Note added 2-20-17: Since writing this piece I’ve been listening to symphonies I wasn’t familiar with before.  Of these, I’ve really enjoyed Vaughn Williams’ 2nd and 3rd symphonies.  The former (“London”) is notable for having the Phantom of the Opera theme embedded in it, 72 years before its time.  The latter (“Pastoral”) is also good.]

Read Full Post »

Consider every symphony named Symphony #X, where X is an integer.  For what value of X is the set of Symphonies #X the greatest?

For example, let X = 9.  There are some incredible 9th symphonies: Beethoven’s, of course, but Mahler’s, Bruckner’s, and Schubert’s 9th all come to mind as well.  Is there a value of X which exceeds this collection?

This question is, obviously, absurdly subjective.  Whatever results I get will surely not coincide with yours.  Nevertheless, the question is entertaining, which (in my view) is reason enough to think about it.

First, some ground rules.  Symphonies without numbers are hereby excluded.  So, Berlioz’s Symphonie fantastique is out (rightly or wrongly), as is Tchaikovsky’s Manfred Symphony and d’Indy’s Symphony on a French Mountain Air.  That’s a shame, really, since all three of these works are awesome.  But, I didn’t make the rules.  (Oh wait, I did.  Never mind.)

Symphonies which are incomplete are fair game, however, such as Bruckner’s 9th, Mahler’s 10th, or Schubert’s 8th.  I’ll always remember the first time I heard Bruckner’s 9th: lying down, in the dark, with Walkman headphones.  I had no idea that the symphony was unfinished; no idea that the 3rd movement was not meant to be the finale.  I thought that the unresolved harmonies, the unfulfilled longing, was a magical way to end a piece…

Image result for sibelius symphony manuscript score

Brahms #4

Since the question is so subjective, let’s be as objective as possible with scoring.  I will go through integers X = 1 through 9, listing and discussing my top ten symphonies with that X value.  (Sorry, X = 0.  Although I enjoy Bruckner’s Symphony #0, that’s not enough.)  Beyond X = 9, the pickings are sparse.  You’re basically just looking at Haydn, Mozart, Shostakovich, and Hovhaness.  Each of my top ten will get a score (from 60-100, roughly equivalent to a letter grade) and the results for each X will be averaged.  Thus, each X will have a maximum possible score of 100.

[Note: a score of 60, which I would call a D-, doesn’t mean that I think the symphony sucks.  Far from it: any score of 60 or greater I would give a positive review for, much like a Tomatometer rating on Rotten Tomatoes.  Remember that there are 90 symphonies here, and that I’m comparing them against one another.]

Let the games begin!

X = 1

Beethoven Symphony #1

It’s hard to like early Beethoven symphonies.  I admire them in the abstract; they’re transitional Classical pieces before Beethoven took off the gloves and became a Romantic.  But really, who wouldn’t rather listen to Mozart’s 41st symphony than this thing?  Score: 68

Brahms Symphony #1

This one’s a giant.  All the movements are solid, but the sunlight pouring in from the door in the middle of the finale, when that Melody comes in, is incomparable.  Score: 92

Brian Symphony #1, “Gothic”

This one’s a giant for a different reason: a performance lasts almost two hours.  There are lots of interesting bits in there, but the whole thing is rather murky.  The youtube link for this symphony has pictures of Gothic cathedrals, which is appropriate: the symphony is stodgy, contrived, yet beautiful.  Score: 81

Image result for gothic cathedrals

Bruckner Symphony #1

I’ve always liked Bruckner, but this is one of his average efforts.  It’s as if he hadn’t learned subtlety yet.  Yet the Brucknerian chordal progressions are there…you can tell there’s greater stuff yet to be written.  Score: 75

Mahler Symphony #1

This is good, I suppose; I like most of it.  As Aladdin said, it’s like a whole new world.  But the Frère Jacques thing in the slow movement puts me off.  Score: 80

Prokofiev Symphony #1, “Classical”

You don’t like 20th century atonalism?  Then try this.  I can hear Prokofiev saying, “Hey?  Whadda ya want from me?”  It’s funny how Prokofiev imitating Haydn sounds a bit like cheerful Shostakovich.  Still, it’s catchy.  Score: 84

Shostakovich Symphony #1

Speaking of Shostakovich, this one ain’t cheerful at all.  It’s warped: it’s like a stroll through a museum of artworks by mental patients.  Near the end of the 2nd movement, the shoe drops.  Am I the only one who hears the Imperial (Death Star) march in there?  Score: 86

Sibelius Symphony #1

No one wrote symphonies more consistently than Sibelius.  Unlike Beethoven or Bruckner, I actually choose to listen to Sibelius #1 on occasion.  The theme of the 1st movement is great; the Andante is relaxing; the finale is hardy and (like much of Sibelius) somehow Arctic. Score: 83

Tchaikovsky Symphony #1, “Winter Dreams”

Most people don’t think of Tchaikovsky as a symphonist, except for maybe his 6th.  But many of his other symphonies are worth a listen.  His 1st is sprightly, Mendelssohnesque, but indisputably Tchaikovsky.  The triumphant ending is worth the price of admission.  Score: 76

Walton Symphony #1

It makes me sad that Sibelius never gave us an 8th symphony (the sketches that survive don’t count).  Walton’s 1st symphony is a consolation, though.  The influence of Sibelius is obvious: the fragmented motifs, the iron-clad logic.  Every single movement makes me smile.  And the ending is so optimistic!  Score: 95


X = 2

Sibelius Symphony #2

Speaking of Sibelius, with only his 2nd symphony, you’re already in rarefied territory.  I have probably listened to this symphony more than any other piece of music written, with the possible exception of Bartók’s Concerto for Orchestra.  Sibelius #2 transports me to some remote part of Finland, maybe Helvetinjärvi National Park.  I like how the entire symphony builds inexorably to the finale, maybe one of the greatest musical exhalations ever written.  Score: 98

sibelius 2.jpg

Borodin Symphony #2

My opinion of this piece depends upon my mood.  Sometimes I love it.  Other times it’s meh.  The opening movement is dark and energetic, but seems like a prologue.  The 2nd movement is fast yet forgettable.  The 3rd movement is the best: a faultless, serene melody.  The finale is vigorous, rhythmically interesting, complex, yet hollow.  Score:  77

Hovhaness Symphony #2, “Mysterious Mountain”

One of the few symphonies whose nickname adds something to the listening experience.  Picture a mountain, shrouded in mists.  The music takes you onto the mountain, but also underneath it: there are subterranean caverns, glistening stalactites, corners with cobwebs, and sunlight glinting off giant broken geodes.  Listen to it in the dark.  It never gets old.  Score: 96

Mahler Symphony #2, “Resurrection”

One of Mahler’s epic choral symphonies.  I consider this one superior to the more unfocused 8th.  There’s a journey here: from life to death to life.  Heady stuff, and emotional.  Score: 90

Rachmaninoff Symphony #2

Rachmaninoff knew how to write for the piano (his 2nd Piano Concerto would get a score of 100 if it were a symphony).  There’s no piano here, but it’s still sublime.  No real melodies to hang onto, just gorgeous sonorities, key changes, textures, a harmonic mosaic that somehow conveys poignancy, joy, and sadness at the same time.   Score: 88

Shostakovich Symphony #2, “October”

This one’s very experimental.  The music is layered on chaotically, almost randomly.  And the chorus at the end sounds like it is singing on pain of death.  But…there’s energy here, and life.  Score: 80

Beethoven Symphony #2

See comments about Beethoven’s 1st symphony.  I’ll only add that the 2nd has a better, more vigorous opening movement.  But the slow movement is dull, and the final movement starts…and stops…too much…for my taste.  The “melody” of the finale is strange to say the least.  Score: 70

Tchaikovsky Symphony #2, “Little Russian”

This C minor effort is, like the 1st, obviously Tchaikovsky.  The tone is more “serious” than the 1st, though: it’s rousing and Russian in a sort of stereotypical way.  There’s also another triumphant ending.  Tchaikovsky really knew how to end things with a bang.  Score: 79

Schubert Symphony #2

One gets the feeling this is a continuation of Mozart or Haydn, with hints of Romanticism lurking around the edges.  In a way, it’s like Beethoven #1…but more elegant; more melodic; happier. Score: 72

Brahms Symphony #2

Brahms wasn’t able to match his 1st symphony with this attempt.  Still, it’s well-made: bucolic, relaxing; serene.  A little dry. Score: 74



Górecki Symphony  #3, “Symphony of Sorrowful Songs”

This may be the strangest of the symphonies on this list.  The first movement is a minimalist canon (with strings only) that gradually reaches apotheosis with a soprano, singing laments in Polish.  It’s sad; the other movements are even sadder.  The music might seem clichéd, but that’s only because of over-exposure (the CD from 1992 sold over a million copies). This music never fails to move.  Score: 89

Saint-Saëns Symphony #3, “Organ Symphony”

Monumental but put together with exquisite craftsmanship, the organ symphony is one of those works that will make you stop whatever you’re doing and listen.  The organ’s entry in the finale is spectacular.  And is that a fugue?  Too bad they used the music in the pig-movie Babe.  Score: 92

Sibelius Symphony #3

Sibelius can do no wrong, yo?  Leaner and more focused than #1 and #2, Sibelius #3 looks toward the 20th century with optimism, almost naively missing World War I on the horizon (which will descend 7 years later).  But I can’t help but feeling Sibelius is saying more here than I realize.  Score: 84

Beethoven Symphony #3, “Eroica”

Beethoven symphonies improved almost linearly.  His third effort is the first, in my mind, that might make you say, “hmm, this guy’s got some talent”.  The funeral march is boring, but the other three movements are masterful examples of early Romanticism.  Score: 79

Bruckner, Symphony #3, “Wagner Symphony”

Bruckner also showed steady improvement in his symphonies over time.  This symphony is the first of Bruckner’s symphonies to sound fully Brucknerian: adult, ponderous, serious, incisive, and complex.  It feels to me like the soundtrack to a depressing tale from the Silmarillion, perhaps the fall of Gondolin.  And I mean that as a complement.  Score: 81

Image result for fall of gondolin

Ecthelion vs. Gothmog

Khachaturian Symphony #3

This is a very iconoclastic pick on my part.  The symphony (from 1947) is very obscure, but there’s something compelling about it.  It’s a single movement, dominated by an organ and 15 trumpets.  Wikipedia calls it “raw and strident” and I agree.  That’s why I like it.  Score: 87

Mahler Symphony #3

I want to like this symphony.  Most of the time, I do.  It’s Mahler’s most epic symphony:  it clocks in at an hour and a half.    Depending on your mood, that might be a good thing, or it might seem a tad bit prolix.  There’s definitely some interesting stuff scattered in there.  But then: that weird song an hour in.  WTF?  Then there are some elves singing a Christmas song.  Um, OK… Score: 80

Mendelssohn Symphony #3, “Scottish”

No elves here; just early Romantic stuff disguised as faux-Mozart.  There’s nothing to complain about, but also nothing much to remember.  Score:  73

Glass Symphony #3

Not the best work of Philip Glass, but then, he’s better with opera (The Photographer) and movie scores (Koyaanisqatsi). Still, there aren’t many “Symphony #3”’s to pick from, so Glass makes the cut.  And this is an interesting fusion of Glassian minimalism and traditional symphonic form.  Score: 84

Schubert Symphony #3

The musical equivalent to crème brulee.  There is a Mozartian perfection here, but with hints of Romanticism.  After a stately “French overture”-type intro, the orchestra and a lone clarinet get into a good-natured pillow fight.  Melodic.  Reassuring.  Only the Grinch would dislike this.  Score: 87


X = 4

Mendelssohn Symphony  #4, “Italian”

This symphony covers the same happy ground as the Schubert #3, and much of it is ingenious, but there’s something indefinably missing.  It’s like crème brulee that’s been sitting out for an hour or so.  While listening to this, I daydream about Mendelssohn’s Midsummer Night’s Dream, which is superior.  Score: 84

Tchaikovsky Symphony #4

One reviewer called this a “Sleigh Ride Through Siberia”.  Another said “the composer’s twaddle disturbed my mood”.  I agree somewhat, but rather like this symphony anyway.  Tchaikovsky symphonies, like Bruckner’s, got better as he went.  Score: 82

Brahms Symphony #4

Finally Brahms matches his 1st symphony!  The lilting melody at the opening is sublime.  And the finale—a passacaglia (theme and variations), based on a Bach cantata!—proves that rigid structure and control can still yield immense beauty.  Score: 92

Beethoven Symphony #4

The most underrated Beethoven symphony.  Everybody talks about the odd-numbered ones (3,5,7,9) but this one is right up there.  The ambiguous tonality of the opening reminds me of the great Beethoven overtures like Lenore III or Fidelio.  Score: 87

Sibelius Symphony #4

Not for the faint of heart, this symphony is the bleakest music ever composed.  And I don’t mean pathos; for that, take Barber’s Adagio for Strings if you like, or Ravel’s Pavane for a Dead Princess.  No, the Sibelius #4 is music that stares back at you, with a gaze “blank and pitiless as the sun”.  The universe isn’t a sad place, it’s just indifferent.  Score: 96

Bruckner Symphony #4, “Romantic”

With the 4th Bruckner is really hitting his stride.  I’ve heard it said that the movements depict scenes from Medieval Europe.  There’s certainly a lot of French horn calls in there: Tallyho, and all that.  The Scherzo is great.  Score: 85

Nielsen Symphony #4, “The Inextinguishable”

Composed during World War I, this symphony might have the most dramatic opening of any symphony.  The rest of the piece is eclectic, disturbing, psychological.  Be sure to stick around for the timpani battle. Score: 87

Image result for famous world war 1 art

“The Tanks at Seicheprey” by H. T. Dunn


Ives Symphony #4

And speaking of eclectic and disturbing, the Ives #4 can be downright weird at times.  What’s that piano doing in there?  Is that a church choir?  This music sounds almost ethereal.  But then…it’s like a church service with goblins besieging the place.  Polystylistic in the extreme.  The 3rd movement is downright serene. Score: 89

Mahler Symphony #4

OK, OK, I know it’s Mahler.  By default, it’s good.  But…sleigh bells?  This is a kid’s symphony, like Mahler writes the soundtrack to a Harry Potter book.  Score: 70

Schumann Symphony #4

In the beginning of the Romantic period was Beethoven.  At the end, there was Brahms.  In between was…Schumann.  This is well-crafted and well-orchestrated stuff, but kinda forgettable.  Score: 76


X = 5

Beethoven Symphony #5

I’ve heard this so many times it’s clichéd—it’s hard to hear it “objectively”.  But there’s not a dull moment, and the transition from C minor to C major (going from the Scherzo to the Finale) is awe-inspiring.  The coda is a tad over-long (OK, we get it, we’re in C major now) but all is forgiven.  Score: 90

Shostakovich Symphony #5

When I first heard this, I had no expectations whatsoever.  I knew nothing about the piece.  It starts with a strange, jumping, disturbing melody, and seems agitated, almost anxious.  Then: holy shit, what just happened?  Dear lord, it sounds like Nazis have invaded.  Just writing this, I have to listen to the symphony again.  Score: 96

Sibelius Symphony #5

Best symphony ever written.  The final movement gives me hope for humanity.  Nothing more needs to be said.  [Note: make sure you listen to Vänskä’s version.]  Score: 100

Bruckner Symphony #5

There’s so much going on here, I don’t know what to say.  So Bruckner.  So complex.  The finale takes every theme of the symphony, and creates a sonata-like movement, or is it a fugue?  Or something else?  Score: 94

Tchaikovsky Symphony #5 “Fate”

Tchaikovsky just gets better and better.  Despair, ultimately, gives way to triumph.  Score: 86

Mahler Symphony #5

For people familiar with the Adagietto from the 5th, this symphony has a lot more to offer.  Sure, the Adagietto is beautiful and achingly poignant, but the rest of the symphony is epic.  Like most Mahler, however, he makes Bruckner look laconic.  Score: 84

Image result for melancholy flowers

Nielsen Symphony #5

I like this Nielsen symphony even more than his more famous 4th.  It continues on the World War I theme.  This time, the snare drum tries to destroy the orchestra.  Eventually, the orchestra (barely) wins.  Score: 88

Schubert Symphony #5

Schubert continues to channel Mozart well into the Romantic period.  But this is late Mozart, with some heft and substance to it: if you said this was Mozart’s 42nd symphony I wouldn’t be surprised. Score: 86

Vaughn Williams Symphony #5

I suppose I’m fond of this because of the Sibeliusian influence.  The symphony was, after all, dedicated to Sibelius.  It’s very pastoral; it reminds me of the Shire.  See the hobbits, walking over there?  Score: 84

Prokofiev Symphony #5

There aren’t as many 5th symphonies as I thought.  I decided to round-out the 5’s with this effort of Prokofiev.  It’s got many of the qualities (novel orchestrations, percussive melodies, dramatic fortes) that drew me to, say, Romeo and Juliet.  Score: 75


X = 6

Beethoven Symphony #6, “Pastoral”

Many people rank this as Beethoven’s best symphony, but it’s too cheerful for me.  Maybe I can’t get the image of the horny centaurs from Fantasia out of my head.  But if you want cheerful, this is it.  It’s hard to believe the guy who wrote this was a grumpy middle-aged man going deaf.  Score: 76

Tchaikovsky Symphony #6, “Pathetique”

And we come to Tchaikovsky’s best symphony, the 6th.  That wistful melody from the opening… The dance movement in 5/4 time… The weirdly addictive scherzo march theme… The finale: is it sadness, or resignation?  Score: 89

Mahler Symphony #6, “Tragic”

Unlike Sibelius or even Bruckner, many of Mahler’s symphonies kind of blur together in my mind into a sort of Mahlerian mush.  This is the one with the hammer blows, I think.  I know that I enjoy this one; it’s suitably epic and dramatic.  But as for the details, well, I’m not in the mood right now to listen to this for an hour and a half.  Score: 84 (?)

Bruckner Symphony #6

Even Bruckner fans often diss the 6th, but it sounds good to me: more contained, more modest than the 5th, but still full of organ-like pedal-point harmonies and the “Bruckner rhythm” of two quarter notes followed by a triplet.  It’s like Bruckner’s 5th on Xanax.  Score:  85

Sibelius Symphony #6

A great symphony, but it’s overshadowed in my mind by the 5th and 7th which bookend it.  Snowy harmonies, and a mixture of serene contentment and vague unease.  It’s like waking up to a foggy dawn in the Smokies, to discover autumn’s first frost.   Score: 86

Image result for frost in the great smoky mountains

Shostakovich Symphony #6

And just like that, I’ve run out of 6’s which come to mind instantly.  I’m not that familiar with the Shostakovich #6, but have heard it a few times, and the impression I’ve always had was that the movements, although good individually, don’t quite jive.  The first movement is the best: depression and despair.  Nobody does despair and oppression quite like Shostakovich.  The other two movements are jolly, and good in a “Festival Overture” sort of way, but don’t quite mesh with the opening.  Score: 74

Dvorak Symphony #6

This is a standard late-Romantic symphony.  Brahmsian.  It’s a good effort: good enough to pay the bills, at any rate.  Score: 71

Vaughn Williams Symphony #6

Oh wait: I forgot about the Vaughn Williams #6.  This is good shit: we have the utter chaos of World War II giving rise to an austere nuclear wasteland.  You have to turn the volume up to 11 in the final movement just to hear anything.  Crap, now I’m depressed.  Score: 84

Schubert Symphony #6, “Little”

This is a transitional piece.  It’s as if Schubert was tired of being a faux-Mozart and wanted to go in a new direction.  That new direction was to be a faux-Beethoven.  Still, the melodies are superb.   Score: 80

Bax Symphony #6

The last of the 6’s is Bax’s 6th, which almost sounds like the soundtrack to a Conan movie.  That’s not meant to be derogatory; the music is muscular, modal.  There’s meat on these bones.  And gristle.  Score: 81


X = 7

Beethoven Symphony #7

Not much can be said about the 7th that hasn’t already been said.  For a while, I was obsessed with the slow movement—maybe the best Romantic slow movement ever written.  (Speaking of which, why are Classical slow movements, like Mozart’s, so boring?)  The finale is vigorous.  Score: 93

Sibelius Symphony #7

Forget what I said about Sibelius #5.  This is the best symphony ever written.  I could listen to the opening 7 minutes on infinite loop, no joke.  And the mysterious, abrupt ending makes a transition to C major seem (somehow) like a defeat!  Note that some conductors wimp out and change the ending, which I consider heresy.  Stick to Vänskä’s interpretation.  Score: 100

Mahler Symphony #7

The Mahler #7 is not part of the Mahlerian mush: I recall this one in more detail.  It’s strange, bleak, demonic.  It makes me think of the movie The Descent.  The ending always strikes me as a tad absurd, though.  There’s a dawn-like triumph into C major.  The entire work is good, but rather incoherent and naïve.  Score: 85

Bruckner Symphony #7

Bruckner’s just plodding along, cranking out solid Brucknerian symphonies.  The 7th is memorable (to me) for its wonderful Adagio.  Hitler is said to have liked the 7th, but fuck it, I like it too.  Score: 86

Shostakovich Symphony #7, “Leningrad”

I didn’t understand this when I first heard it.  But then repeated listening have carved out a channel in my brain where this symphony resides.  The first movement dominates: the “invasion” theme is ridiculous, almost a joke, but then it gets repeated over and over, louder and louder, until it’s scary and threatens to take over the world.  This is Trump’s ascension, portrayed in music.  The good news is that in the 7th, at least, good triumphs, and all is restored by the end. Score: 90

Image result for Siege of Leningrad. Diorama at the Museum of the Great Patriotic War of St. Petersburg.

Dvorak Symphony #7

OK, it’s not just Mahler; the Dvorak symphonies aren’t too distinct in my mind, either.  I just know that the 7th is my favorite other than the 9th.  (Come to think of it, that’s like Beethoven.)  Score: 89

Prokofiev Symphony #7

I’m floundering to get a total of ten 7’s.  This one’s pretty good: quite melancholy, with echoes of Shostakovich.  The Prokofiev flair for drama and violence is there, too.  Score: 83

Bax Symphony #7

The Bax #7 is theatrical, and galactic in ambition.  Think: Star Trek.  It almost wants to be a sequel to Holst’s The Planets.  It’s only moderately successful in that ambition.  Score: 79

Piston Symphony #7

Walter Piston’s #7 is, like Bax #7, very cinematic.  But this one owes more to Copeland than Holst.  I don’t know which #7 I prefer.  Score: 79

Haydn Symphony #7, “Le Midi”

A total throwaway; it’s fine, such as it is, but not even in Haydn’s top 10.  Still, there aren’t that many Symphony #7’s to choose from.  Score: 65


X = 8

Dvorak Symphony #8

I’m listening to this right now.  It’s like a happier version of the 7th.  It’s mature.  It’s like a hike for grown-ups. Score: 82

Bruckner Symphony #8

Some call this “The Apocalyptic”.  Seems a fitting description.  It’s one of my “go-to” selections, matching any mood I feel.  I especially enjoy the timpani in the Scherzo, and the finale has gravitas.  Score:  92

Image result for apocalypse

Mahler Symphony #8

Mahler’s attempt at a gargantuan choral symphony, a la Beethoven’s 9th.  It starts right up in there (no beating around the bush; the chorus is rarin’ to go!) but it all eventually bogs down.  Score: 81

Schubert Symphony #8, “Unfinished”

Pristine; maybe even flawless.  The first movement is rich, lyrical, pretty, and almost menacing…like an elf who stabs you in the kidney.  The second movement is all peace and kittens.  Score: 86

Shostakovich Symphony #8

A tragic symphony from Shostakovich (surprise, surprise).  It’s heavy, oppressive.  When you’re done listening, you feel like you spent a vacation in East Germany.  The muted triumph at the end feels like walking across Checkpoint Charlie into safety.  Score: 87

Beethoven Symphony #8  

I’ll take the word of experts and say this is “good”.  But I don’t really enjoy it.  It’s hard to like.  Did Louie forget he even wrote the 5th and the 7th?  Score: 71

Vaughn Williams Symphony #8

Here is music for the Elohim, those of Donaldson’s The One Tree.  I want to use Donaldson words to describe the symphony: “…as edifying as crystal, as clinquant as faery promises…but obdurate, uncompromising.  [Full of] whorled and skirling shapes…”  Vaughn Williams is channeling both Copeland and Hovhaness here; the orchestration is inventive.  But that ending is Who’s in Whoville!  Score: 84

Glass Symphony #8

The rest of the 8’s are reaches, to be sure.  This one’s typical Philip Glass, which is all you need to know.  It’s interesting, but not much of a “symphony”.  Score: 72

Kabeláč Symphony #8, “Antiphonies”

Pretty obscure, I know.  Basically, a half hour of horror music, written by a madman.  Score: 71

Brian Symphony #8

Another shout-out to Havergal Brian, who wrote so many symphonies he needs to be on the list twice.  This one is decent enough.  Score: 74


X = 9

Beethoven Symphony #9

At various times in my life, this has been my favorite symphony.  It encompasses all of human experience.  If you’re only familiar with the Ode to Joy, listen to the rest.  There’s an hour of great music in there before the people start singing.  My only (minor) complaint is that the finale goes on maybe 5 minutes too long.  Score: 98

Bruckner Symphony #9

Perhaps the symphony I connect to the most on an emotional level.  The opening movement’s great, and the scherzo is sinister and delicate at the same time.  But it’s the unresolved harmonies of the “finale” that choke me up.  Score: 97

Dvorak Symphony #9, “From the New World”

Might be the most rousing, and “catchiest”, of the symphonies.  I can hum the theme of every movement.  Sing along to the Largo: “Crisp and clean, no caffeine, cool refreshing beverage…”  And it ends with Jaws.  Score: 91

Image result for zion national park

Mahler Symphony #9

My second-favorite Mahler symphony, this is Mahler’s farewell to life.  Good times.  The finale reminiscent of Bruckner’s 9th.  Score: 89

Schubert Symphony #9, “The Great”

It’s the first movement that you’ll remember, which takes its time to build to one of the most triumphant expositions in the symphonic canon.  I can’t get the pulsing sextuplets out of my brain!  If this music doesn’t make you feel anything, you might want to check your pulse.  Score: 95

Shostakovich Symphony #9

A cheeky symphony.  It’s like Shostakovich smoked some weed, got high, and tried to emulate Mozart.  Does the 1st movement come across as goofy, or sinister?  Maybe it’s a little of both.    Then, WTF?  The rest of the symphony is different in tone: more serious.  The ending is vigorous and off-putting.  I have no idea what’s going on here.  But I like it.  Score: 85

Vaughn Williams Symphony #9 

Speaking of not knowing what’s going on here…  There is undefinable strangeness in this symphony.  But also lyricism.  Is this a battle of modalism vs. melody?  I have no idea.  Score: 73

Glass Symphony #9

We’re running out of 9’s… So… How about Glass #9?  It’s better than the 8th.   It’s qloomy, but not as minimalist as most other Glass works.  I want to say it even starts channeling Bruckner and Sibelius later in.  Score: 80

Haydn Symphony #9

A total throwaway.  Yet there’s a paucity of Symphony #9’s, so Haydn makes the list.  You really want to listen to a Haydn symphony, try #26, or #39, or #49, or #82, or #88.  Score: 60

Hovhaness Symphony #9, “St. Vartan”

Another throw-away.  You really want to listen to a Hovhaness symphony, try #2, or #22, or #50, or #63.  Score: 67


Before we tabulate the results, here are some honorable mentions with higher X-numbers:

X = 10

Mahler Symphony #10 [unfinished]

Shostakovich Symphony #10

X = 11

Shostakovich Symphony #11, “The Year 1905”

X = 12

Shostakovich Symphony #12, “The Year 1917”

X = 15

Shostakovich Symphony #15

X = 25

Mozart Symphony #25 in G minor

X = 26

Haydn Symphony #26, “Lamentatione”

X = 29

Mozart Symphony #29 in A major

X = 35

Mozart Symphony #35, “Haffner”

X = 38

Mozart Symphony #38, “Prague”

X = 39

Mozart Symphony #39 in E flat major

X = 40

Mozart Symphony #40 in G minor

X = 41

Mozart Symphony #41, “Jupiter”

X = 49

Haydn Symphony #49, “La Passione”

X = 50

Hovhaness Symphony #50, “Mt. St. Helens”

X = 88

Haydn Symphony #88 in G major


Here, then, are the average scores for the ten symphonies in each X-number:

#1: Average score: 82

#2: Average score: 82.4

#3: Average score: 83.6

#4: Average score: 84.8

#5: Average score: 88.3 The Winner!

#6: Average score: 81

#7: Average score: 84.9

#8: Average score: 80

#9: Average score: 83.5


The gold medal goes, without a doubt, to X=5.  The silver goes to X=7, and the bronze to (surprisingly) X=4.

Notice how scores go up steadily, as composers perfect their craft.  There’s a drop-off after 5, I think, because fewer and fewer composers write that many symphonies in their careers.

One final note: three composers had every one of their symphonies make my list: Sibelius, Beethoven, and Mahler.  In terms of average score, Sibelius (92.4) beats Mahler (82.6) who beats Beethoven (81.3).  Bruckner misses out because I didn’t include his 2nd; Tchaikovsky misses out because I didn’t include his 3rd.  C’est la vie.

Read Full Post »

« Newer Posts - Older Posts »