Pianissimo for pianists: Threshold Expansion Exercises

While teaching piano last summer, I developed some exercises to assist in learning a difficult element of piano technique, pianissimo. I describe them briefly here, along with some trivia related to them. I call these Threshold Expansion Exercises.


The introductory exercise:
Play multi-octave, hands-separate scales, but calibrate your touch so that only half of the notes sound. Try to make each note sound the same, with only a gradual recalibration if too many or too few notes are sounding. Do not allow the same fingers to not sound every time. Make sure each finger does not sound occasionally.

Once this is mastered, there are three key developmental exercises, varying the number of notes sounded:
1) Make only two notes sound per octave.
2) Make only two notes not sound per octave.
3) Make all notes sound. Alternate this exercise with Exercise 2, making them sound as alike as possible.

Supporting Physics

The perceived volume of a note increases logarithmically with its sound energy, while the sound energy of a piano note increases approximately linearly with the key velocity. This happily makes it easy to create perceptibly expressive dynamics. It means that we ordinarily do not need to train our fingers to produce very fine gradations of key velocity. Training for logarithmic differences is all that is required.

Unfortunately, this creates problems when playing pianissimo. The velocity threshold where keys no longer sound is right there next to where we would like to be playing. And we haven't trained our fingers in hyper-fine velocity gradations. So we play louder than we need to for safety. We would like to play softer, but we fail to sound when we try to.

Tthe key velocity of any note being attempted is the intended velocity plus some error term. The errors for some large number of notes might form a normal distribution around the intended velocity (a different distribution would not change the following argument). The coarse-grained logarithmic training that typically occurs when learning dynamics means that the standard deviation is much larger than we would like. The range of velocities produced thus needs to be kept safely away from the sounding threshold, as shown in Figure 1.

Notice what the introductory exercise does. When we make half the notes sound, our intended velocity is the threshold velocity. Since we are trying to "play" exactly at threshold, only the error term determines whether the note sounds or not. We immediately sort the positive from the negative error terms, with aural feedback on every note (Figure 2). This feedback is the quickest way to bring the standard deviation caused by the error term down to a range where we can begin to imagine moving our intended velocity down closer to threshold.

When this has been accomplished to a reasonable extent, it is useful to train our fingers in linear gradations. Different pianos have different thresholds, so you need to be able to adjust quickly to a different instrument. You also need to be able to determine if your problems on a different piano are caused by a different threshold or by improper regulation, which would produce noticeably different thresholds for different keys. The total set of four exercises correspond to the linear gradations shown in Figure 3.

Morrre bow!

I might have some more to say about the terrific opening UISO concert later. But first one comment about my annual start-of-season question.

I'm much happier than last year with the freshmen. We got some peeps from top string programs, and some of the others look good as well. Using my rule-of-thumb of bowing facility, Rebecca DuVall and Caitlin Secousse would be two to watch for, and I'm not including two others only because I am only 90% sure who they are. However, if you were a freshman in the firsts, and your name is not on this list, use more bow, please.

Actually, I learned a transformational lesson about that this last year. It began by finding my favorite violinist teaching the piece with which he hooked me on the violin. Listen to a couple minutes of this clip, through about where the student (Robert Witte) finally makes it through the rondo subject:

It had never so vividly struck me before what the effect of using more bow in very fast passages would be. It takes so much extra effort. It can seem to be a waste of resources, maybe dangerous. But WOW!

Later, he improves another lightning passage with the same prescription:

And another:

So I was looking for chances to see this in practice some more, to calibrate its effectiveness. Then soon after (God likes to pull off these little coincidences), I heard this:

I know. Just take some deep breaths. When you calm down, listen one more time, and listen for the differences in the sixteenth notes. Go ahead. I'll wait.

And he even told you how to do it. :-) (Minus the reframing a perpetuum mobile as a life-and-death adventure part. You'll have to come up with that on your own, although this performance also implicitly says to anyone who will listen, "It's ALWAYS there.")

But as for understanding the technical substrate of the interpretation, you've got that now. :-)

For Easter, a blog resurrection...

OK, I promised I would write something...

Kelsey Schmidt's Junior Chamber Music Recital tonight had the most creative programming I can remember here in more than twenty years. Have you ever heard on one program:

A number by a vocal jazz quartet
Misty, by our abovementioned jazz soprano
Mozart Sinfonia Concertante, with Kelsey on viola
Bach Concerto for Two Violins
Brahms Piano Quintet (Allegro)
von Webern Langsamer Satz (for string quartet)
Shostakovich Quartet #8 (three movements)

WHAT?!? This was my first reaction.

Vocal jazz quartets can be really effective - there are few enough people that you can lock intonation for marvelous consonances and dissonances, which was captivating when it happened. When it didn't, the person responsible would almost always correct, which kept the train of striking moments flowing.

Kelsey got more into her torch singer role midway through Misty. The musical problem it set was that here she was singing to all her friends and family this very personal declaration of love. She made eye contact all around, which is excellent stagecraft per se, but since Kelsey is all about committing to the music, I wonder what would have happened if she could have sung to her invisible love standing off to the side. Declarations of love addressed by females directly to their beloved are inherently intimate, and that would have freed her from the "There's Dad, there's Raul, there's Jan..." TAKE ME, I'M YOURS! conflict. The intimacy was there vocally, though, so if she ever breaks a C string in a recital, she can just put down the viola, lean back against the piano, tell the pianist to start Misty, pick out a guy in the audience...

High school flashback time for Bill! We played both Sinfonia Concertante and the Bach Double Concerto at Moline, and I once knew the accompaniments for both of them. Mozart really shows his love of the viola here, and Kelsey made it clear why. She kind of took the stylistic lead, an unusual position for a violist to be in.

I had run into Kelsey when she was putting this recital together and was looking for someone to play the Back Double with.


Kelsey's face lit up, so I knew she understood what I was talking about. Tonight everyone did. Just to keep this most touching of all Bach Double Concerto performances human, there were a few spots in the fast movements where someone came in a measure off. But Bach had their back! (As you musicians can imagine.) It sounded more like, "Hey, that's cool!" Nobody even changed expression and suddenly they were together again, which was pretty much as impressive as simply playing it perfectly.

Of the three quartet pieces, the von Webern was most interesting because it was hyper-romantic. Right... I liked how you could sorta listen to this piece and tell about von Webern, "OK, this guy is gonna go off the deep end any day now."


Unforgettable recital - you rock, Kelsey!

All-Music Saturday: The Grads Take Over

After Hillary and Sara finished, Özgül's DMA recital was at intermission. The good news: Jennifer Garrett was accompanying her. Jennifer was now passing 3-1/2 hours of performance today, having accompanying our rehearsal this morning. The bad news: All that was left was Bartok #2. Oh, well.

Özgül is accurate with good sound and intonation. Musically, she was playing one of the less accessible Bartok pieces, so there was no intelligible emotional program, but it wasn't necessarily her fault.

Karen Copeland is as good as I hoped she was. After the first piece, the Gluck Menuet and Dance of the Blessed Spirits, I was wishing I had made friends with some of the flutes so I could say, "See what happens when you practice your long tones?" Wonderful phrases that went on forever, seemingly effortless. She gave us not one, but two concertos, Ibert (so I DID get to hear the part I remembered) and Mozart G major. Mozart can apologize to Karen now, for what he said. Plus, I got to hear the new freshman orchestra bassoon, Andrew Brown, in a wind quintet. Competent player. Plus wonderful Bach with Casey Robards. Only the best accompanists for All-Music Saturday.

On my way to Krannert from there, in front of the La Casa Latina, a delivery car backed loudly into another car. When I looked up, he sized up the situation - and fled like a bandit. I ran after him to try to get the license plate, but he got around the corner before I could. When I looked back, the wind quintet folks were looking at the car, so I hope it wasn't one of theirs. I almost made the rounds of the fast food joints to find this upstanding citizen. I hope it wasn't Nick or Lesley or Laura or Andrew or Karen's car.

I had an hour to get a shower and get to Bohemé. But I ran out of gas shy of the first down.

You know, like Ohio State.
  • Current Music
    Ibert, twice! (Um, one and two-thirds?)

Live-blogging All-Music Saturday

All-music Saturday started at 10AM, with a rehearsal of Messias for the December C-U Symphony concert. That is Messiah, as adapted by Mozart into GERMAN. This has significant consequences.

In fast German choral music, unfortunately, us lazy American speakers are not even in the game. As Stolzfus explained, "Without the final consonant, a German word is unfinished." Try singing the fast, "He is the King of glory" chorus to the words "Er ist der König der Ehren" with the required loud final consonants. No, you forgot to clearly enunciate the T.

Several tricks save me; I am the unofficial #2 consonant guy in the basses.

  • You have to accept the unfamiliar feeling of your mouth and tongue being athletic really at the competitive level.
  • Things that just cannot be enunciated by an American are nicely mimicked by adding a throwaway uh to the end; "Er is-tuh der..."
  • With that trick, sometimes I physically rewrite an eighth note as two sixteenths: "Lasst" to "Lass-tuh".
  • The two different ch sounds, no one ever has enough breath to add when in fast lines or at the end of phrases, even if we had the skill to pronounce them. Since I got used to diaphragm-breathing, not only do I have the air, my diaphragm is low enough at the end of the word to force out the consonant clearly. But after the consonant-heavy choruses, I'm pretty dizzy. :-) THONK!

Oh, and it helps to have credit for four years of high-school German. :-)

Done at twelve-thirty; lunch; then to hear the flutes at 2PM.

Regardless of how controversial the other Hillary is; our Hillary is much more unanimously acclaimed as qualified in her area. I actually had high expectations for Sara Kohnke, just based on Hillary's last duo-recital, the duo of the hyphenated flutes.

And I was not disappointed. They add something moving, emotional, and original to about a third of their playing, a very high student standard, moving into the realm where people will pay to hear them. Since they already can conceive these effects, and since neither is very limited technically, I would like to see them spending more time away from the flute, just thinking about what they want each phrase to say, and then not resting until it does, in their practice. Hope to hear them both again.

Sara played my favorite Bach (C major) that Jenny Swanson played and the Night Soliloquy that Jen Nelson played with string-like articulation her freshman year. Hillary played the first two movements of the Ibert concerto in reverse order, which confused me because I know it enough to remember the last movement exposition, but not enough to remember where it occurs, so when the piece finished, "OK, where's the part I remember?!?" (Sara explained this to me after the recital.)

Gotta go...Karen Copeland in a half-hour...

Hear them now before the tickets get expensive

The pairing of Rebecca Johnson, flute, and Jennifer Garrett, piano, is the clear high point of my adventures in branching away from listening to strings here. If you've only heard one of them, just imagine if she had learned the other instrument; that's what the other one sounds like.

My exchange with Keeble afterward sums up their recital today:

"You should review this recording to see if there's anything that can be submitted to Performance Today."

"That's a good idea. That was really beautiful playing."

When we walked in, SMR was unlighted except for a fake candle on the piano. I was afraid baroque performance practice now encompassed period lighting. But they were just creating a salon effect; they kept the audience unlighted throughout the recital.

The two baroque pieces had an eclectic and balanced blend of baroque practice and affecting musicality, with well-ornamented and mostly restrained micro-phrasing, but larger-scale dynamics and a low-key but differentiated vibrato.

Both halves of the recital ended with showpieces. The Gaubert Nocturne et Allegro Scherzando had these just-WOW long runs of two-slurred, two-staccato 16th notes. I mean, she was just showing off... :-)

The Reinecke Sonata might be their signature piece, however. Constantly surprising landscapes - weave together most all (19th-century) combinations of texture, dynamics, and tempo and you cover a lot of ground emotionally.

They have what I call a fractal balance of expression. Fractals are shapes whose structures are similar at every scale. Magnify one a thousandfold and it looks pretty much like it did before. So is there a carefully thought-out highlight to most every movement, section, phrase, measure, and note in their playing.

OK, so now I'm gonna be a jerk and talk about the WORST FOUR SECONDS OF THE ENTIRE RECITAL!

I've always wanted to put together a course on intonation. And talk someone who knows what they're doing into teaching it here. If you think you understand intonation, I have a few questions to make sure we're on the same page. Is a string in tune with itself - why or why not? What are some of the differences between harmonic and melodic intonation? Discuss the compromises available to a string quartet regarding intonation.

So Rebecca started the first piece and Jennifer came in, and for a couple seconds it sounded like Middle School Saturday, and then everything was fine for 90 minutes. So did Rebecca start out-of-tune?

Probably Rebecca did not play out-of-tune enough to match the piano at first. The euphemism Well-Tempered actually means, in ensemble, out-of-tune in any conceivable key. A phrase that is perfect and lovely solo can be expired milk with a piano. You simply have to play out-of-tune like the piano, but in-tune with the (tempered-intonation, octave-stretched) piano, in ensemble phrases. Later in the recital, I noticed Rebecca (the only one who can adjust) paying careful attention to tuning before movements, so given her impeccable intonation, don't expect to hear this problem recur from her. But I expect to hear it recur a lot, and in that very same room.

By the way, if you support the tempered-tuning compromise, just remember that it is the foundational logic of tone rows. "Since we're so out-of-tune that we're not in any particular key, why not just play anything as long as we never repeat! Repeating a note too soon must be what makes music uninteresting."

Back to talking about the other 90 minutes! I suggested to Rebecca, and will suggest to Jennifer, that they do a CD. After grad school, Rebecca will have a hard time finding another Jennifer, and Jennifer will have a hard time finding another Rebecca. Seize the moment.

I might add, we are really in a Golden Age of accompanists here, with Jennifer and Casey Robards here at the same time.

After the recital, I heard the end of Maid of Orleans (in more than one sense) by Tschaikovsky on WILL. Why is this opera forgotten?
  • Current Music

No Good Deed Ever Goes Unpunished

The International Music Score Library Project (IMSLP) has since its creation, grown to be the primary source for public domain music on the Internet. Nineteenth-century masterworks, the complete works of Bach or Chopin, thousands of obscure works by obscure composers; it was a world treasure trove for classical musicians. They had a vigorous copyright review team among their rafts of volunteers. If you wanted to play through the Vieuxtemps Second Concerto, this was the place to go.

Because of their proactive copyright enforcement and vast collection, it was the leading legitimate site, and as such had been recommended by a host of university and conservatory libraries, including use in MIT's OpenCourseWare courses. This was even more remarkable, considering that it was founded and directed by a Canadian college student in his spare time.

Yesterday, October 19, 2007, it announced its shutdown following a Cease-and-Desist demand from Universal Editions in Vienna. Universal publishes works by Mahler, Bartok, Shostokovich, Milhaud - well, all these people and more. Although IMSLP's copyright review team enforces the Canadian copyright term of 50 years post-mortem, Universal Editions threatens to hold Feldmahler, the owner, personally liable for international downloads from any parts of the world where copyright terms are 70 years post-mortem (The U.S. Mickey Mouse Protection Act and the EU). Presumably, he would also be held liable for the costs of ascertaining the damages ("We need your server indefinitely."), and their legal fees as well. ("Quit now or we will ruin you, kid.")

There are lots of things you can do:

  • Contact Universal Editions to let them know how you feel as a customer (or observer). Use whatever language you happen to speak best; I'm confident that my audience will be able to make their feelings on this topic clear despite any language barrier. Note the separate contacts for the main firm and their PR department, who would certainly be interested in the grave damage to their reputation.

  • Head over to the IMSLP Forums, register, watch for developments, and rally the troops. Contribute in any way you feel led.

  • Let people know about what's going on. Especially public people, with loud voices. Remember all those composers they publish? Wonder if they know...

There are other things you can do, and I'm almost mad enough to suggest them. But don't, because the point of IMSLP is that THEY PLAY BY THE RULES.
  • Current Music
    Not Mahler, for a while

Renee Fleming Sings Brünnhilde

Well, I'm certainly more sanguine about our winds after that concert, um, our woodwinds. All other winds (of the metallic persuasion) should follow this simple two-step procedure:

  1. Listen to Gerry Wood.

  2. Do that.

But Jamie, Erin, Katie, et al. gave us some very beautiful moments last night. Jamie even got a rather poignant hug out of it from Schleicher, who waded through the orchestra to award it for her prismatically-toned variation in the Brahms Fourth. Yay, hugs for Jamie!

When I saw the Mahleresque orchestration for the Elgar Bach, I anticipated, a little too cheerfully, all the Whining Strings Purists who would have to endure what I have to put up with from their performances - entirely uncongenial musical graffiti spray-painted over a beloved masterpiece. This is Bach with the traditional:

  • Bass clarinet

  • Contrabassoon

  • Tambourine

  • Cymbals

  • (2) Harps

...adding horsepower to a full orchestra. I was expecting a Stowkoski arrangement, with one-third fewer cymbal crashes.

It was surprising, then, when Elgar's sensitivity and ear for beauty spoke early and often - think his Cello Concerto rather than Pomp and Circumstance. There was the occasional jarring tambourine roll, which I enjoyed for reasons mentioned above. Plus the sight of the Bach bass clarinet being carried offstage to prepare for the less colorful Rachmaninoff!

Next was the tragic Rhapsody on a Theme of Paganini. It was tragic because she should have played the Grieg Concerto. The soloist is an immensely talented young lady. Her articulation and fluency were a brilliant combination, and in the softer passages, she had touching and masterful dynamic expression.

But it was mostly in vain. The couple speaking Russian to each other behind me delivered the verdict when the applause had died down, "Boring." There are just too many ways Rachmaninoff can ruin you. In this case, it only took two missing ingredients to leave the entire performance flat - metronomic rather than rhapsodiac rhythm and lack of a fortissimo. In fact, the Rachmaninoff was so mundane without those that I at first underestimated her musicality. But in the few places that she wasn't being swamped by the orchestra or delivering her monotone love poem, I noticed her mercurial dynamics when in quieter passages. Wait a minute! More involved listening followed, producing the lament before you.

And it was entirely avoidable. Mitsuko Uchida Plays Hindemith. If she had concentrated her incredible crispness, fluency, and dynamic coloration on the Grieg, she might have gotten a huge ovation. I hope to hear her in that someday.

As a side note, you sometimes are called on to be heard over a hundred-odd collegues sawing and puffing away unrestrainedly. Fortunately for violists, bassoonists, and small pianists, this requires as much sleight-of-hand as it does power. When you have inadequate power at your disposal, the trick is timing. There are three principles for this:

  • Identify the shape of your phrase. Only the highlights and key notes should soar over and return into the din via the following tricks.

  • If it is brilliant and major, advance your beat ahead of the orchestra. Verve.

  • If it is dramatic and minor, retard your beat behind the orchestra. Struggle.

The "Hello, World!" version of this can be heard on any concerto recording, where the soloist plays the last note a 32nd-note before the orchestra.

And Brahms. I never sufficiently prepare myself for the wonder that is a Schleicher orchestra playing a warhorse. It is always powerfully architected, with a full range of glades and storms and frolics and burlesques.

I learned something very useful that I will probably also put up on violinist.com. What to do when a section string has a catastrophe of some sort, a broken string, a sprain, or disintegrated bow (until the end of the movement, when you can leave to address it). Usually people just sit calmly, which is a perfectly reasonable first reaction.

The problem with that is that you are now the center of attention, based on the drama of your situation. The audience is watching you. There is no way to fix that. Your situation is way more dramatic than the music. Embarrasing, volatile, and unresolved. Composers would give their left eardrum to create that kind of drama. Someone I know collapsed once during a concert. Will you collapse or fix your bow or WHAT? You're the wounded soldier waiting for a medic in combat.

I was glancing around the orchestra and I noticed that Chih-Ming was sitting with his violin in his lap while everyone else was playing. Did he injure himself playing? Then I noticed the horsehair splayed across his lap. Bow.

Then he did an inspired thing. He put the broken bow on the floor. He brought his violin up and began playing the left hand of his part. He was back in the music. There was no longer any reason to empathize with the poor guy, sitting uselessly in the middle of the music. He was back as completely as he could be. From much of the audience, when you glanced by his section, it would be difficult to even tell he wasn't bowing.

Since he had gone back to Brahms, so did we.
  • Current Music
    Grieg, I hope

White and Nerdy

Next Friday, you can hear the Prairie Ensemble play a Mahler symphony arranged for one soprano and chamber orchestra.

Or at the Assembly Hall, you can hear Weird Al Yankovic.

Somehow, it sounds like they are competing for the same audience.
  • Current Music
    Pretty Fly for a Rabbi