Well, I’ve just returned from an excellent concert at Frank Gehry’s wonderful Walt Disney Concert Hall (photo at left by Tom Bonner). The Los Angeles Philharmonic (the Hall has been its home since it opened in Fall 2003) had as guest conductor Andras Schiff, who is one of those marvellous people who can direct from the piano while playing remarkably complex material. It was a program of Mendelssohn (String Symphony No. 10 in B minor), Schumann (Introduction and Allegro appasionato, Op. 92), Haydn (Piano Concerto in D major, Hob. XVIII: 11) and closing with Schumann again (Symphony No. 1 in B flat major, Op. 38 -Spring).
Schiff was just fantastic, and the orchestra was really solid, as usual. He played the Haydn with delight and a level of electricity that I’ve not seen for a while brought out of that material, even though its brightness is quite conducive to that sort of treatment.
So much about watching an orchestra while listening to it fascinates me, and I love having seats that get me as close as possible to watch what is going on. Different things fascinate me on different evenings, depending upon my mood. One thing that was particularly interesting in both Schumann pieces, even though separated in time quite a bit, was how the composer splits some of the lines across the instrumentation, starting a lot with french horns but then breaking it across to trumpets and some interesting doubling with flutes and oboe. I’ve not noticed it quite so clearly before in this work. Part of this may have been my mood, and part of it may be the fact that the acoustics in the Disney Hall are so amazing that I’ve (re)discovered aspects of several pieces that I thought were familiar by listening to them in that place. Something about the careful design of the space has produced the remarkable ability to separate out every instrument in the orchestra -even when at full size (which is was not this evening)- and allow you to hear them clearly.
The other thing that catches my attention a lot are the musicians who are not doing something the whole time. This can be interesting for a host of reasons, and not just the obvious, which is your curiosity about what they must be thinking about while waiting, and when are they going to come in. This is often the timpanist, but it is quite easy to work out when they are going to be needed most of the time. But tonight was a special treat for me. They had a triangle guy on the last piece! If you don’t know the piece very well -and I did not- it is not clear when he’s going to come in, and so you can sit and try to anticipate depending upon how the music is developing. The piece’s popular title is “Spring” so there’s clearly going to be some need in several places for bright sparkly springy bits in both quiet and loud places. Challenge to get into the mind of the composer there and see if you can anticipate. The other thing that was notable was that Mr. Triangle had not one but two chairs. He had one in which he sat in a state of readiness for the majority of the piece, but eventually he did stir himself, and pick up his triangle and one of his two tiny metal traingle-beater-sticks (do you “beat” a triangle or “tickle” it? And why do you need two sticks?) he had carefully laid out. He did his thing for a short while and then he sat in the taller chair, as he was to play soon after. I think of that second chair as his chair of preparedness - in the other chair he’s merely in readiness - or is it the other way around? I’ve enlarged the picture of the orchestra that I snapped secretly (no flash or noise of course) to show you the triangle guy, his chairs, and his equipment.
Well, while I was watching and listening to him in action, I began to wonder: Why is a triangle a triangle? Would a square sound as good? Or a pentagon or other polygon? Are triangles equilateral ones or isosceles? I think the latter, but I’m not sure. And was there a reason for his having two ticklers/beaters? (He did swop from one to another at one point, and I listened for a tone difference but was not sure if I heard it.) There’s got to be some interesting physics in the vibrations of such shapes….is the triangle shape just a traditional one or is there some experimental reason behind the preference for that shape?
Well, I’ll go to bed with these important questions on my mind, along with the pressing puzzle of what on earth to wear to tomorrow night’s Hallowe’en party in West Hollywood. Apparently it’s a 70s disco theme. I’ve no clothes for that….can’t I just go as a scary Physicist from the 21st Century, i.e., me? At parties, women (and men) already run screaming when I tell them what I do anyway, at any time of year, so I don’t need a costume.
-cvj
October 29th, 2005 at 6:28 am
The triangle of course. It is a legend at least in the German speaking community, ever since this song by the Austrian cabaret artist/singer Georg Kreisler. You can find the text here.
http://www.astro.uni-bonn.de/~kilbinge/kreisler/kreisler.shtml#triangel
I did not find an English translation, and I am too lazy to do it myself. It’s the lamento of a triangle player who sits in the orchestra and … waits for his action. He knows all the pieces by heart, he even was a hopeful piano player once, but now he only sits in the orchestra and … waits for his action.
October 29th, 2005 at 11:29 am
The question about the shape of the triangle seems related to the shape of brass instruments. They are bent simply because the long tubes required would be unmanageable if they were one (or several) long tube(s). Whether or not this affects the sound is a good question. My guess is “not noticeably”.
And it does seem odd that they have someone dedicated to the triangle. Usually it’s just one of the percussionists.
October 29th, 2005 at 12:11 pm
Hmmm, well, the various valved brass instruments which are blown have quite different timbres depending upon the shapes and tubing….. but a triangle is not blown, but struck…so who knows? There’s probably some analysis to be done.
As a theoretical physicist, I’d probably start by analyzing the two special cases:
(a) Infinitely long triangle.
(b) Circular triangle.
Maybe get a clever exact solution for one of the cases named after me.
Then spend the rest of my career studying the case of polygons…. Or if I’m really smart, kick off an entire field within physics dedicated to studying this…. thousands of papers written by an entire generation with titles like (”A twistor proof that the triangle is not in the same acoustic universality class as the hexagon”) …with all sorts of wonderful connections to various branches of mathematics, applications to making better electronic devices, etc…. but after 60 years…..still no solution of the triangle problem…..
-cvj
October 29th, 2005 at 12:18 pm
Woohoo! I get to de-lurk for the moment… In my youth, I was a percussionist in both bands and orchestras (and now I’m just a physics grad student), so I’ll say what I know. When I play timpani and I have to rest/tacet for quite sometime, I usually try to get a feel for what the orchestra (or whatever) is doing, so that when I come in, I sound appropriate. I also (at least at the beginning of movements and right before I come in) think about whether or not I’m in tune, and whether or not it’s possible to be more in tune. I also look for landmarks in the piece to make sure my counting is on track. My mindset while I’m playing the triangle is similar, but I’m more concerned with timbre (because if you hit a triangle in different places you get slightly different sounds, and the aim (usually) is for consistancy). The two different beaters (at least with the Schumann) probably have more to do with the ease of acheiving different dynamics (loud, soft) on the triangle than acheiving different tones. There are times when you want different tones, like in Bartok’s Sonata for Two Pianos and Percussion, but those are rarer. I always thought that the reason a triangle was shaped the way it is because it’s easier to play a triangle than it is to play a metal rod. Plus, it looks better. Just my $0.02.
October 29th, 2005 at 12:32 pm
Thanks Greg A!
Are they really called “beaters”? I did notice that when he wanted to go loud he changed to the other one, and he also did a rattling back and forth in a crescendo which would have been hard with a rod, but not with a square, say…. but higher polygons or a circle would make the rattling technique difficult. But of course composers probably wrote rattling bits because the triangle already existed. What would they have written for the decagon, one wonders?
Keep playing the music….being a physics grad student is no excuse to stop!
Cheers,
-cvj
October 29th, 2005 at 12:42 pm
This is a great question, I’ve often gazed curiously at the musicians patiently awaiting their turn. But I’m guessing that the shape of the triangle has a lot to do with timbre of the instrument — a long rod or a circle would have different overtones.
Now, why they don’t equip the plucky trianglist with a set of options including rods and circles, I don’t know.
October 29th, 2005 at 12:46 pm
Magdalena - Thanks. I sometimes feel like that triangle player you describe.
-cvj
October 29th, 2005 at 1:14 pm
I’m no TMBG fan, but reading this post I can’t get the lyrics “triangle man hates particle man” out of my head.
October 29th, 2005 at 2:03 pm
Yep. The mallets used in persussion essentially are triangle beaters, drum sticks, and a bunch of things where the form is like [instrument] mallets, like timpani mallets, chime mallets, xylophone mallets, etc. The rattling back and forth is a type of roll, called a triangle roll, which is the same idea as a drum roll, but on a triangle.
October 29th, 2005 at 2:08 pm
Wow! I guessed correctly!
I must try a triangle roll one day. I had a physics undergraduate friend when I was at university who was an excellent jazz drummer and he taught me how to do pretty good drum rolls…. this was after I got fascinated by drum rolls after going to see Buddy Rich -with another physics undergraduate friend- at Ronnie Scott’s not long before Rich died. We spent a lot of time doing drum rolls on random surfaces… I wonder what happened to those dear friends….and if they still drum roll?
Anyway……..
-cvj
October 29th, 2005 at 2:54 pm
Sorry Clifford, couldn’t help but think, hey, a guy has these kinds of observations, and all of a sudden , I get these crazy ideas.
October 29th, 2005 at 3:07 pm
in west hollywood, do the transvestites dress up as men on halloween?
October 29th, 2005 at 3:13 pm
Sam Gralla…. Not being acquainted with any -that I’m aware of- I can’t say. I’ll let you know if I find out.
-cvj
(Stop giggling.)
October 29th, 2005 at 4:04 pm
I enjoyed the posting, very descriptive; sounds like it was a wonderful concert. Makes me even more excited about the one I’m attending tomorrow.
As for the questions - what great experimental fun! Perhaps those musicians patiently awaiting their turn are wondering what physicists think about in coffee shops. ; )
The thoughts of the seemingly idle percussionist are probably less random than that of the seemingly idle physicist. : ) Part of the talent of playing percussion is quietly switching from instrument to instrument, all the while counting rests (beats), listening to the other players — without making any unnecessary movements or coming in early or late! Takes planning, and is physical and demanding, like a dance.
The triangle is a rod and not a tube, so the size and material, more than the shape, account for the sonority. Larger sizes, lower tones, easier to strike. Smaller sizes, brighter tones. I imagine the proximity of the sides of the triangle would allow for different sweet spots and for faster striking than that of a circle or a rod.
October 29th, 2005 at 4:29 pm
Hi Athena,
Yes…. as a trumpeter in an orchestra (a while back), I remember the counting. I would always get myself too anxious and then miss the cue because my embrochure had failed me due to nerves…..
Yes, I am beginning to think that a triangle is in fact optimum,… but a square might be interesting….
Any thoughts on whether equilateral vs other might matter?
-cvj
October 29th, 2005 at 5:35 pm
Don’t have the author at hand, but the series of 1950s/60s physics books created by the Physical Science Study Committee in the US has an excellent intro book about the physics of musical instruments (mainly horns). Fairly short, very readable, and laments the loss of acoustics as an endeavor of physics, as it apparently was replaced by modeling acoustical systems as RLC circuits since those were often easier to solve when such a model could be built.
Anyways, from my time as a music major, I seem to recall these being equilateral triangles (but not sure if that was the samples at hand or if it was a general characteristic). And the bending of the pipes in horns doesn’t really alter the tambre very much, the curvature is too small to really alter the wavelength through interactions with the walls — it’s much more like specular reflections a bunch of times, though of course that ignores dispersion of harmonics (not just the octaves, which is what most physicists mean when they say harmonics, ALL the overtones), it ignores non-linearities that very few people have really investigated (whether due to “triviality” or lack of grant money), absorption, etc. It also doesn’t account for any density-dependent effects which would show up, say, in the valves, where the cross section is noticeably different; the authors of the book presented an argument wherein these sorts of things were more like shifting around holes in a long tube with an open end, which changes its modes in interesting ways, but don’t say much more than that (also, as Greg A pointed out, the placement and method of excitement alters the spectrum of available harmonics as much as changing the “resonator” does). Nonetheless, very interesting reading.
The two chairs were likely to keep the percussionist “out of the way”, mentally as much as physically, when he was not playing anything, as if done with page turners for someone playing the piano in recital.
October 29th, 2005 at 6:21 pm
Hi Clifford!
Nerves, yes, those will get you! Had a minor case of those last week during a performance — ugh. I naturally have a loud singing voice, and rather than cooing, I blared the opening line of a ballad, a bit louder than planned. Thank goodness for monitors.
As for equilateral vs. other triangle types (I think that’s what you mean), it’s an interesting thought. From its prevalence, I would suppose the equilateral to be most versatile, but I think the shapes in this case affects the ergonomics more than the acoustics. Seems that keeping a steady rhythmn would be easier to maintain with equal angles between sides; the travel time from side to side, so to speak, when striking the center of each side, would be the same, given that the movement had consistent speed and the center of the sides were reached each strike. The angle of the strikes in relation to the sides of the triangle would be the same as well, delivering similar tones. With other triangle types, depending on the lengths of the sides and the angles, you may have to adjust for the differences while you were playing if you didn’t want those effects.
October 29th, 2005 at 6:42 pm
Well, I’d imagine it would be fine to have just two sides the same (isosceles) to meet those criteria. The vertical would be the symmetry axis, right? And then you’d have the same travel time on each side when triangle tinkling/rolling. (He did not seem to use the vertex near his hand for this technique; I presume this is because of damping…..)
Seems to me it would be more fun (if it did not affect the sound) to have scalene triangles. Very cool. Everyone will be doing it one day… just watch.
Well, I have to go find an outift for the 70s Monster Mash party now.
-cvj
October 29th, 2005 at 7:22 pm
Damnit. This is why I don’t like to read blogs by physicists. I always end up second-guessing their throwaway comments and spending ages modelling ridiculous ideas. Such as the difference between the acoustic spectra of isosceles and equilateral triangles. I’ll have a go at this problem after I finish preparing a couple of supervisions for next week, undoubtedly beginning with an R1 “triangle” and then an S1. The transition to piecewise R1 should be interesting….
On a different note (groan) the triangle in the picture definitely looks like an equilateral. Bizarrely, when I was at the Festspiele in Bayreuth over the summer I saw a triangle player (a trianglist?) who had three different triangles: an isosceles, an equilateral, and a curious one that seemed to be a strip of cold-rolled steel with holes punched in it. I don’t know what’s more difficult to figure out, the different types of shape or exactly where a triangle belongs in a performance of Parsifal.
October 29th, 2005 at 9:06 pm
Clifford, you should get some zombie makeup and a lab coat, then go as a zombie theoretical physicist. “BRAAAAAAANES. BRAAAAAANES.”
October 29th, 2005 at 10:11 pm
Thanks Schwaumlaut, I thought of that, but it was not 70s enough. My hosts were quite specifc, and its a crowd who are professionals in the business of dressing up and impersonating, so I have a high standard set for me. Just got back from hunting for custume items…..successfully! More later.
-cvj
October 30th, 2005 at 6:40 am
Perhaps it would be a good idea to pay homage to the Fast Show and go as Professor Denzil Dexter?
October 30th, 2005 at 1:52 pm
So what did you wear to the party?
Inquiring minds need to know!
October 30th, 2005 at 2:11 pm
erc: Thanks for asking. Will blog it. Can’t blog now…must work on some physics a while longer this morning (and continue recuperation from party’s effects).
…..must…have….more……………coffee…..
Later.
-cvj
October 30th, 2005 at 2:36 pm
If there are after-effects it must have been a good party…
Hhmmm…coffee sounds like a good idea….
October 30th, 2005 at 6:24 pm
Halloween costume has always been … drumroll (triangle trill ?) … Schrodinger’s cat. (Where again do you find diacritical marks that can be used here? Anyway, assume the umlaut.)
I play classical piano and have performed in public just once. It can be pretty nerve-racking! On TV I’ve seen Andre’ Previn conduct from the piano while playing Mozart’s piano concerto # 9 in E flat (my favorite!). I’ve always admired the kind of coordination and reflexes required for this effort. Does that ability make one a Superconductor?
I don’t mean this to sound patronizing, but is there a lot of competition to be a percussionist for an orchestra? Again, pardon my curiosity, but what special skills are needed for this job above and beyond a good ear and quick physical reflexes?
October 30th, 2005 at 6:25 pm
My Halloween costume has always been … drumroll (triangle trill ?) … Schrodinger’s cat. (Where again do you find diacritical marks that can be used here? Anyway, assume the umlaut.)
I play classical piano and have performed in public just once. It can be pretty nerve-racking! On TV I’ve seen Andre’ Previn conduct from the piano while playing Mozart’s piano concerto # 9 in E flat (my favorite!). I’ve always admired the kind of coordination and reflexes required for this effort. Does that ability make one a Superconductor?
I don’t mean this to sound patronizing, but is there a lot of competition to be a percussionist for an orchestra? Again, pardon my curiosity, but what special skills are needed for this job above and beyond a good ear and quick physical reflexes?
October 30th, 2005 at 7:04 pm
A concerted effort can be seen in the gravity of the situation?
October 30th, 2005 at 7:46 pm
citrine, have you been quantum xeroxed?!! Oh, wait, that’s impossible.
-cvj
P.S. I used to like Andre Previn until I learned that he married Anne-Sophie Mutter. I’m very annoyed at him indeed. The younger me fell in love with her in 1985 upon hearing her play the Brahms Violin concerto (the first time I heard it) at the BBC Proms over Radio 3. (Yes, the radio….I had no idea what she looked like…..it was her playing that got me.) I still have the recording, and it’s fantastic. Hmmm…maybe it’s Brahms I was in love with.
October 30th, 2005 at 7:55 pm
WHAAAAAAATTTTTTT?
I’m a straight female but I’m dazzled by the stunning beauty of Anne-Sophie Mutter. I haven’t heard any of her recordings but judging from all the CDs she seems world-class. With THAT combo going for her she could have had any guy in the world, and she married Previn?
October 30th, 2005 at 7:59 pm
I see….. you’re just as outraged as I am….. Excellent.
Oh well…I just tried to get over it and move on down the list… I’m doing ok with my recovery.
-cvj
October 30th, 2005 at 8:05 pm
I guess it only goes to show that if you’re a Superconductor (like Previn) you can do extraordinary things….! ..
-cvj
October 30th, 2005 at 8:46 pm
Anne-sophie Mutter… meh. Change the M to an O, however, and you have some seriously dazzling beauty (of voice). Combine her with Barbara Bonney, who happens to seriously dazzle with voice AND face, and you have–yes, it’s better than sex–the beginning of act II on this dvd.
http://www.amazon.com/gp/product/B000056JSS/102-2145595-8187327?v=glance&n=130&v=glance
Not sure if there are any triangles in this one, but you can be sure that the next time I watch Parsifal I’ll be listening…
October 30th, 2005 at 11:52 pm
Mmm, violinists. How about Hilary Hahn?
October 31st, 2005 at 6:09 pm
AthenaThe angle of the strikes in relation to the sides of the triangle would be the same as well, delivering similar tones. With other triangle types, depending on the lengths of the sides and the angles, you may have to adjust for the differences while you were playing if you didn’t want those effects.
While one might think of the triangle of consideration, it would not be to hard to figure that architectural features would have also been harnessed? Similar respective examples of solutions from angled to parallel lines, leads to hyperspherical “inner” solutions of the dome, as a consequence of dimensional shape exploitation?:)
March 12th, 2006 at 8:09 am
From A layman who struggles.
Those that do not follow string theory might have been less inclined to believe in it’s history?
That the singing bowls might by analogy lead to “another thought” when clicked on?
A linked paragraph to some greater kernel of truth,or some “orchestration” in the value of sound?