Polyrhythms and Introducing labs.seanchenpiano.com

Today we’re going to be looking at figuring out how to calculate the execution of polyrhythms. It can seem difficult trying to figure out how to divide a beat into different numbers evenly, especially if they’re odd or prime numbers. But all it is is simple math, and once you have the system down, it’s pretty automatic and you can even find patterns that are even more helpful (and you probably learned those in music school if you went).

Before we start with that, I also want to introduce a new subsection of the website: labs.seanchenpiano.com. I have a lot of programming projects that I’ve worked on throughout the years, and I’m going to try to finish them up and put them on. They won’t be super polished at first, and will receive many updates after publication. Right now, there’s only one thing on there, and that is a polyrhythm metronome app. It should work on most browsers and devices, but let me know in the comments if anything is buggy, or any feature requests!

Preface

Polyrhythms are usually not meant to be performed exactly mathematically correct. Oftentimes it is just a composer trying to fit more notes into a beat, or maybe the composer wants the de-synchronization as part of an affect or expression, and not necessarily the precise division. But just like with many expressive techniques, I think it is important to know what the baseline is — what it should precisely be — before you add in rubato or other personal touches. So, just to be clear, I’m not advocating for metronomic or robotic execution of polyrhythms.

Definition

So what are polyrhythms? It happens when you have two or more voices going, and each of them are dividing a beat into different tuples. Tuples are just a subdivision of beats: duples, triplets, quadruplets, etc. The most common of polyrhythms is 3 against 2 or 2 against 3, written 3:2 or 2:3, and most musicians learn how to execute those early on. I’m not aware of any tradition or logic behind what number goes where; for me, as a pianist, it seems that the first number corresponds to the right hand and the second to the left hand, though I can see it being interpreted as the second number being the general beat of the passage, and the first number being the “ornament” or deviation.

9:5 Polyrhythm from Scriabin’s Etude Op. 42 No. 1. The actual meter is 3/4

The Problem

We want to find a method so that we can be 100% sure of where the micro-beats should lie. Let’s do a pie analogy:

  1. We have a whole pie.
  2. We want everyone at the dinner to get the same amount of pie with no leftovers
  3. We know we are going to have either 2 or 3 people at the dinner.
  4. How can we divide up the pie so that regardless of whether 2 or 3 people show up, we can divide the pie evenly?

The question then becomes, what number of slices divides into both 2 and 3 without remainder? The answer lies in something you learned in elementary school, but probably didn’t care to remember how to calculate it: the Least (Lowest) Common Multiple (LCM). But wait, there’s more! In order to calculate the LCM, you need to know the Greatest Common Divisor (GCD) of the two numbers. Yay! Math! Fun!

Keep in mind, this proof is very non-rigorous, and probably has many holes and unwritten assumptions. But I hope it’ll make it logical how to find the LCM.

Numbers

A couple of terminology clarifications.

I’ll be saying “number” a lot, but what we really care about are only the natural (or counting) numbers: 1, 2, 3, .... So, you can replace any “number” with “natural number” or “positive integer“.

In this set of numbers, we call one number divisible by another if the remainder is exactly 0. You might say, “3 IS divisible by 2; you get 1.5!” Again, we are dealing with the set of natural numbers, and 1.5 is not in this set, so 3 is not divisible by 2.

A factor or divisor of a number divides that number, i.e. 2 is a factor 6, but 5 is not a factor of 6.

A Common Multiple

Most of you might recall that to find the LCM of two numbers, you should just multiply the two numbers together… or something. But let’s reason this out:

  1. A number x is always at least divisible by 1 and itself; there can be other factors, but the number itself and 1 must always be factors. (Think prime numbers: they are the least divisible numbers, besides 1, and even they are divisible by one and themselves.)
  2. The easiest way to make any number into a multiple of another number n is to multiply by n.

Fine, so we have a number x, and its factors include at least 1 and x. If we want to make that number also a multiple of y, then we multiply the two together. Algebraically, the fact that this makes the resulting number a common multiple (ACM — my abbreviation) is obvious. (Note for people who don’t know algebra, when we write two variables right next to each other, we mean that they should be multiplied):

\(\)Given positive integers \(x\) and \(y\):  \(acm(x, y) = xy\), since the numbers \(x\) and \(y\) are \textit{literally} in the product.

You can divide xy by x and get y and vice versa. And we can be sure that there is no remainder, because by definition, x and y are whole numbers.

Let’s call this xy product officially the ACM.

The Least Common Multiple?

How can we be sure it’s the least common multiple? And if it isn’t, how can we make it the least?

Let’s assume for now that this ACM xy is not the LCM, and that there is a whole number d>1 that you can divide the ACM by to get the LCM. That means:

     \[lcm(x, y) \stackrel{?}{=} \dfrac{acm(x,y)}{d}= \dfrac{xy}{d}\]

Fine! So if this new fraction is indeed the LCM, we can then still divide by each of the original numbers (and get 0 remainder). Let’s see what we get if we do that:

     \[\dfrac{xy}{d} / x = \dfrac{y}{d} \text{ and } \dfrac{xy}{d} / y = \dfrac{x}{d}\]

So, since the remainder must be zero, that means that \dfrac{y}{d} \text{ and } \dfrac{x}{d} are both whole numbers, and thus d must be a divisor/factor of both x and y. We now divide the ACM by d to get a new common multiple. If this new common multiple is not the least, then we should be able to find another common divisor of x and y. Rinse and repeat until there are no more common divisors, in which case, we have found THE least common multiple.

So all we have to do to go from ACM-> LCM is to continually divide by common divisors until there are no more common divisors besides 1 (since dividing by 1 doesn’t change anything).

Example:

  Find the gcd of 24 and 30.  Common divisors of 24 and 30 are 1, 2, and 3. First we multiply 24 and 30 to get 720, then divide by 2 to get 360, then divide by 3 to get 120. gcd(24, 30) = 120.

An easier way than dividing sequentially through all common divisors is just to find the greatest common divisor, and divide our ACM by it. Almost there.

Greatest Common Divisor

The GCD of two numbers is the largest whole number that divides both numbers without remainder. For example, \(gcd(6, 3) = 3\) and \(gcd(7, 9) = 1\). You can check for yourself using these examples that the gcd is the largest number that will divide evenly both numbers. Sidenote: numbers that have a GCD of 1 are called coprime numbers.

There are many methods for finding GCD, including the Euclidean Algorithm. For our purposes (since polyrhythms don’t tend to get that high in number), we can just try every number from smaller of the two numbers (whose GCD we are calculating) down to 1. If you get to one and haven’t found a number that divides into both, then the GCD is 1, and the numbers are coprime, in which case the ACM we calculated is equal to the LCM. Otherwise, you divide the ACM by the GCD to get the LCM.

The Least Common Multiple!

Let’s summarize the equation for finding the least common multiple:

lcm(x,y) = \dfrac{xy}{gcd(x,y)}

So what do we do with this?

Method 1

Again, let’s do any easy example: 3:2 polyrhythm. First, we write down all the numbers:

 \begin{tabular}{c c c c c c} 1 & 2 & 3 & 4 & 5 & 6 \\ \end{tabular}

Then, on the bottom, we want to ask ourselves, if two people showed up to our pie party, how many slices would each one get? \dfrac{6}{2}=3. So on the bottom row, let’s write two groups of “123”

 \begin{tabular}{c c c c c c} 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 2 & 3 & 1 & 2 & 3 \\ \end{tabular}

Now, let’s put an X on the first of each group, and erase the rest:

Then you

 \begin{tabular}{c c c c c c} 1 & 2 & 3 & 4 & 5 & 6 \\ \hline X &  &  & X &  & \\ \end{tabular}

The X’s are where the notes are going to be played. Do the same sort of thing for the top, except now it’s three groups of two (the pie divided among three people):

 \begin{tabular}{c c c c c c} 1 & 2 & 1 & 2 & 1 & 2 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 \\ \hline X & & & X & & \\ \end{tabular}

And then change the first of each groupinto X’s

 \begin{tabular}{c c c c c c} X & & X & & X & \\ \hline 1 & 2 & 3 & 4 & 5 & 6 \\ \hline X & & & X & & \\ \end{tabular}

To read this chart, we count to 6, and on one hand we tap the top line, and the other the bottom. Now you have one way of thinking about 3:2 accurately – subdivide the beat into 6, and play the notes on their respective microbeats.

But, when the polyrhythms get more complex, it can result in a high LCM, and we don’t want to have to count to that high of a number. There’s a cyclical way to think about this chart, and we will do it with the same polyrhythm.

Method 2

For this method, you will choose one of the divisions to be the main “pulse.” In this case, since the duple is on the bottom, that will be the main pulse. We’re going start by doing the same thing as the previous method:

 \begin{tabular}{c c c c c c} 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 2 & 3 & 1 & 2 & 3 \\ \end{tabular}

Now copy the bottom line to the middle line, and then put X’s on the bottom line first micro-beats, like so:

 \begin{tabular}{c c c c c c} 1 & 2 & 3 & 1 & 2 & 3 \\ \hline X & & & X & & \\ \end{tabular}

Next, let’s put our 3 groups of two on the top line:

 \begin{tabular}{c c c c c c} 1 & 2 & 1 & 2 & 1 & 2 \\ \hline 1 & 2 & 3 & 1 & 2 & 3 \\ \hline X & & & X & & \\ \end{tabular}

And then turn them into X’s:

 \begin{tabular}{c c c c c c} X & & X & & X & \\ \hline 1 & 2 & 3 & 1 & 2 & 3 \\ \hline X & & & X & & \\ \end{tabular}

Last step, for each top X, copy the number directly under it and overwrite the X:

 \begin{tabular}{c c c c c c} 1 & & 3 & & 2 & \\ \hline 1 & 2 & 3 & 1 & 2 & 3 \\ \hline X & & & X & & \\ \end{tabular}

Though in writing this seems like a lot of steps, in practicality, you don’t need a lot of the intermediate steps once you know what’s going on.

To perform this, you tap or clap the bottom line, then you start saying the middle line quietly (or thinking it), and then once you get a good groove, you start accenting the numbers that fall on the top line. In graphical form, you would be doing something like this: 1 2 3 1 2 3, where the gray numbers you don’t say out loud, the magenta ones you do, and you clap on “1”.

This way of thinking about polyrhythms is how some conservatories teach you. Again, that is to clap the bottom line, think the middle line, and say the top line:

 \begin{tabular}{l | c c c c c c} say & 1 & & 3 & & 2 & \\ \hline think (or whisper) & 1 & 2 & 3 & 1 & 2 & 3 \\ \hline clap & X & & & X & & \\ \end{tabular}

This table also gives you a visual aid to use if you want to tap, say, the right hand for the top line and left hand for the bottom line. You can see how things are supposed to line up.

Here’s one for 7:3 ( lcm(7,3)=21 ) in both table versions:

 \begin{tabu}{*{21}{c}} 1 & & & 4 & & & 7 & & & 10 & & & 13 & & & 16 & & & 19 & & \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21\\ \hline 1 & & & & & & & 8 & & & & & & & 15 & & & & & & \\ \end{tabu}

 \begin{tabu}{*{21}{c}} 1 & & & 4 & & & 7 & & & 3 & & & 6 & & & 2 & & & 5 & & \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline X & & & & & & & X & & & & & & & X & & & & & & \\ \end{tabu}

The second one is easier to count, right? (I mean, neither are particularly easy.)

Conclusion

Again, I want to make sure to emphasize that one should not be robotic about their performance of polyrhythms. However, knowing how it should mathematically work allows you to know what the baseline is. And with modern music, sometimes you have to do it precisely! I hope this and the tool on the labs will help you. Again, check out labs.seanchenpiano.com/polyrhythms! The default (non-verbose) mode on the metronome shows you the cyclical way of counting (method 2), and the verbose mode shows you everything!

Memorization Tip: Knowing the Rules


Featuring Chemistry and Chopin Etude Op. 25 No. 7

This post was originally going to be some extended analogy between science and music, about how knowing contrapuntal rules can help you memorize pieces better, just like how knowing various physical rules can help you derive formulas easier. In the end, I don’t think the connection was super interesting beyond the obvious. I’ll still write a bit about it, but it’s mostly so I can actually post these animations that took me forever to make.

The scientific rule I want to look at is from chemistry. Take a look (click the play button):

I think all good art follows some kind of rule (even chaos can be a rule), and we can use that rule to make sense of the piece not only for memorization, but also for interpretation.

I chose an example from Chopin because he studied and carefully internalized Bach’s works, mixing contrapuntal integrity with harmony, dance, and melodies to create a style that was distinctly his own. On the surface, many works seem to have a homophonic texture – melody with accompaniment. But, further analysis reveals the effortless way in which he incorporates counterpoint into his signature texture. These rules grant predictability to how the chords are voiced and how the accompaniment is arranged. This predictability is not bad. Rather, each note is in its perfect place; there is logic to it, such that Chopin could not have written it more perfectly.

Hope you enjoyed those little animations. They were made using https://greensock.com/gsap and https://mithril.js.org/. I also learned that it’s quite convoluted trying to add your own scripts and stylesheets to WordPress.

Web Technologies for Musicians

or, From Score to Performance for Programmers

In this post I hope to give musicians (or anyone with a musical background) an easy insight into how a web page gets from the “internet” onto your browser. You won’t learn how to program, or even get a remotely detailed look at it, since this will be a high-level overview. But hopefully, it will allow you to be able to communicate more clearly with someone who is a programmer (especially if they’re working on or maintaining your site). And besides, we live in a world now where everything is basically a website; even many of the “apps” on your phone are just basically running a web browser.

For programmers who are interested in the behind-the-scenes for musicians and performers, this is just as simplified (and agenda-ified) a view of musicians as it is of web rendering, but hopefully it inspires you to read more into it.

Scenario: musician

Okay, so let’s say you’re a pianist – you’ve gone through years of school, learned how to interpret the score and make stylistically informed performances. Your teachers have put good habits into your practice and your playing, and you’re out on your own now.

You get a request one day to perform this cool Cage piece. Since you don’t have a copy of this piece, you have to get one from the library. You look up the phone number of the library, (123) 456-789 and call them, because you’re too lazy to go there physically. You ask the librarian if you can borrow the cool Cage piece. She checks her computer for a bit, and then puts you on hold. Moments later, she returns and says, “I’ve found the piece you wanted.” You’ll get it in a few days.

Few days later, the score comes in the mail. You take a quick look at the score. There’s a note in the first page that says that there are two inserts necessary to perform the piece. Confused, you call the library back, and ask the librarian about the inserts. “Ah,” she says, and puts you on hold again. She returns and says, “I’ve found the two inserts. One of them has some extra dynamics and articulations that either aren’t in the score or are corrections, listed by measure and beat numbers; the second insert has some complicated performance directions. We’ll send it over.”

A few more days pass, and now you have all the parts and begin learning the piece.

As you read through the piece, you realize that the first insert (of dynamics and articulations) has two options. One of them is meant for performances in large halls, the other for small halls. Furthermore, there is a small addendum in case the performer does not have access to electronic amplification.

The second insert is more involved. You have to roll dice to get random numbers, rearrange parts of the score, repeat some sections, etc. This is some serious business!

The day comes for your performance, and after all of your work reading the score, incorporating the right option in the first insert (you didn’t know how big the hall was, or if they could provide amplification, so you were pretty stressed out), and following all of the instructions in the second insert to a tee, you’re met with thunderous applause and standing ovation perplexed faces, furrowed eyebrows, and noncommittal applause, because modern music.

Scenario 2: Web Client (browser)

Okay, so let’s say you’re a browser, maybe Google Chrome – you’ve been programmed by thousands of programmers, learned how to read HTML, and render it onto the screen according to all of the specifications. Your programmers made sure you followed all the rules before they released you, and you’re now installed onto some bozo’s computer.

One day, the bozo opens you up, and directs you to go to a website. Since you don’t have this website in your cache, you have to call its host and get a copy. You look up the IP number of the library, 123.456.789.012, and call them, because you’re a browser, and you can’t go anywhere. You ask the host if you can get that HTML page that the bozo wants. She checks herself (because she IS the server) for a bit, and then puts you on hold. Milliseconds later, she returns and says, “I’ve found the HTML page you wanted.” You’ll get it in a few milliseconds.

Few milliseconds later, the HTML comes in through HTTP. You take a quick look at the page. There’s a note in the header that says that there are two inserts necessary to render the page. Confused, you call the host back, and ask it about the inserts. “Ah,” she says, and puts you on hold again. She returns and says, “I’ve found the two inserts. One of them is a CSS that has some extra styles that aren’t in the HTML, or are corrections, listed by element class or ID; the second insert is a JavaScript file. We’ll send it over.”

A few more milliseconds pass, and now you have all of the assets and begin rendering the page.

As you parse the HTML, CSS, and scripts, you realize that the CSS has two options. One of them is meant for large screens, the other for small ones like smart phones. Furthermore, there is a small addendum in case the browser does not support modern CSS grid-based layout.

The second insert, the script is more involved. You have to generate random numbers, rearrange parts of the DOM, repeat some elements, etc. This is some serious business!

The time comes for your rendering, and after all of your work parsing the HTML, incorporating the right option in the CSS, and following all of the JavaScript instructions to a tee, you’re met with gratitude and praise from the bozo complaints that it took too long to render, and questions of why the scrolling is so laggy.

The Components

HTML <-> Score

HTML stands for HyperText Markup Language. Hypertext just means text that can contain hyperlinks (which are links to other webpages). The important thing is that it’s a markup language which is a way to create documents or pages that describes not only the content, but any other metadata attached to it. There are many other markup languages, like XML, EPUB, and RSS.

Music notation is a markup language. It contains not only the raw content (which we can call the notes), but also metadata, including time signatures, tempo markings, key signatures, ossia, etc. In fact, this is why there is a portable music notation format, MusicXML. Most importantly, without scripts, HTML is static, unchanging. Scores, without performance indications, remain static as well.

Just like you can define things like a <table>, <div>, or <script> in HTML, you can create <measure>, <clef>, and <pitch> in MusicXML. In most markup languages, you need to close your tags with a corresponding one: <table>content</table> or

<pitch>
    <step>C</step>
    <octave>4</octave>
</pitch>

CSS <-> Dynamics, articulations, etc.

CSS stands for Cascading Style Sheets, which contain the styles necessary for rendering the page. Styles can also be defined in the HTML, but for reasons such as the one in the scenario above, you might need different style sheets depending on the window size, or even the font size. It’s called cascading, because styles defined later override previous ones, just like corrections in scores. The difference in this comparison would be that we usually don’t put dynamics and articulations in a separate file, again, unless they’re corrections.

JavaScript <-> Performance directions

JavaScript is a programming language. Browsers can read these scripts and perform the work that is asked of them. For example, a browser could be asked to fetch a video, or calculate some numbers, or render 3D graphics, just like how performers can be asked to sing, hit the inside of the piano, or sit there in silence. These are not standard things in music, and equivalently, the things that JavaScript asks the browser to do are not able to be represented in HTML, because they often encode dynamic behavior.

In modern websites, most of the power and heavy-lifting is in the JavaScript. When you see a website (like mine) that is a SPA (single-page application, which means that clicking on different links within the site causes the content to be changed dynamically, and not through an entire page load) you can be sure that most of the work is being done by JavaScript. In fact, my HTML file is probably 30 lines long, whereas there are tens of thousands of lines of JavaScript. By using JavaScript, you can generate HTML on the fly, and so the user experience is more interactive and dynamic.

Programmer <-> Composer

In this case, we are talking about a front-end programmer. They program the HTML (in a very generic sense, keeping this high-level), just like composers write down the score.

If we are to make it more modern, programmers usually work indirectly with HTML, usually writing code that generates HTML (either on the server or client side). The equivalent would be a composer jotting down sketches, and then having an arranger flush out the orchestration, or a publisher cleaning everything up and typesetting it so that it is readable.

Client (Browser) <-> Musician

Musicians are trained and have musical knowledge within them to read the score, and parse the performance indications. Browsers each have a rendering engine – Chrome and Safari use versions of WebKit, Firefox currently uses Gecko, and Edge uses EdgeHTML. These all read HTML and can translate that into a web page, just like how musicians can read a score and turn it into music. Furthermore, all of the browsers have a JavaScript engine – Chrome uses V8, Firefox uses SpiderMonkey, and Edge uses ChakraCore. (The one clear takeaway is that programmers need to come up with better names.)

Server <-> Library/Music Store

To get the score we have to either get it from the library or a music store, if we don’t already have it. Similarly, the browser needs to get the HTML page from a server, if they don’t already have it in the cache. The server does a lot of things behind the scenes, just like a music store or library would have a lot of internal workings that you don’t see, such as how different pages are stored, how databases are accessed, etc.

 

I hope this gives you a bit of an understanding into what goes into rendering a page. I didn’t define every term in the scenarios, but I think given the parallel, they should be self-explanatory. And, if not, there is always Wikipedia. Let me know in the comments if there’s anything specific you’d like to hear about!

Things I Learned Making a Website from Scratch

I think I’ve reached a point with this new website where I feel comfortable saying it is pretty much done. I just wanted to do a quick post about the process, and what I learned. First off, all of the code is open source on GitHub: https://github.com/kamiyo/sycpiano. Thanks also to my brothers Jason and Andrew for getting me started and helping me with things, especially in the earlier stages. It took around 2 years! Don’t worry if the acronyms mean nothing to you – I’m going to do a simple musicians guide to web programming later!

Feel free to skip to the last section (Main Takeaways) if you want to read the main takeaways. The following sections are just me bragging a little bit about the web programming technical things I learned, so I can feel a bit better about myself and not like I’ve wasted two years in working on this website…

Going In

I had programmed my previous two sites myself as well, but I didn’t have the guidance of two programmers at those times. To go back further, I was messing around with HTML and CSS back in the blogger and Geocities days.

So I came into this process knowing a bit:

  • HTML
  • CSS
  • JavaScript (vanilla)
  • PHP (sorta)
  • MySQL (very basic)
  • Messing around with .htaccess

I was fortunate to have taken some comp sci courses when I was in school, so I had a solid foundation of any ALGOL-like languages (C, C++, Java).

What I Learned

The early stages of the website was all about learning the framework and modern JS. In my old site I just gzipped up the JavaScript file, and served it along with some libraries like jQuery through their CDNs.

My brothers suggested I use React as my framework, whereas for my previous site I used AngularJS (v1). They also setup a toolchain using Webpack and Gulp, running on NodeJS. Later on we dragged Typescript in.

So, things I learned:

  • Almost everything runs on JS now.
  • You basically never touch .html files anymore.
  • React
  • NodeJS
  • Reducers and state management
  • Typescript and Modern JavaScript (es6+)
  • Promises!
  • Using and creating a restful API
  • Using a build tool like Webpack
  • Postgres, using an ORM like Sequelize, and Full-Text Search
  • A bit about Nginx and some server stuff like using pm2 to keep the Node server running.
  • More familiarity with version control (git)
  • CSS-in-JS solutions
  • Canvas and WebGL animations
  • Using Chrome devtools

And not web-related, I learned a bit on using OpenCV and doing some facial recognition (trying to automate thumbnail creation of my own photos) and about constant-Q transforms when turning audio time data to frequency data (as seen in the music visualization). I’ll also do a post about that.

Main Takeaways

Mostly, I learned I have no design chops. I have the hardest time choosing colors and layout, and making user interaction decisions. So much of the design is literally hours of trial and error. The coding part is fine. It’s the design part that is hard.

It takes time. All the code planning, debugging, refactoring, especially when you don’t have experience working with a large codebase. But you learn alot. And you save money.

Everything is on the internet. Stackoverflow, GitHub issues and gists – if you have a problem, chances are someone else has had it before you.

Cross-platform is a b*tch. Just because it works on one browser on one device, doesn’t mean it will work on another one. I’m also starting to think mobile-first would be the best way to go (which is not what I did). It’s harder to do good mobile UI/UX compared to desktop. You can tell on my site mobile was (not-quite, but almost) an afterthought… or like a halfway-through-thought.

Designing your own website means you can have it exactly the way you want. If you want a feature, you implement it. If you can’t, it’s because you’re not good enough, not because it’s not possible.

Modern web development seems to be “libraries, libraries, libraries” but it really does make it easier. Because of that, a lot of development time is spent also on building and making sure the shipped code is compact and performant.

Finally, just like how artists learn by tracing, composers learn by transcribing, and musicians learn by listening, it’s helpful to start coding from examples. I was sort of reluctant to learn React, and all this new stuff, but since my brothers helped get things started, I could study what they had written and learn from there.

And just like music, do it only if you enjoy it.

A look at transcriptions: Liszt’s Concert Paraphrase of Wagner’s Overture zu Tannhäuser

This article is cross-posted with American Pianists Association’s Beauty of Music, a regular feature on the American Pianists Association blog that covers variety of topics to help readers better understand and appreciate the music they love. Sign up for 88 Keys, the monthly newsletter of the American Pianists Association, to automatically receive each issue.

I was fortunate four years ago to be selected as the winner of the American Pianists Awards, becoming a Christel DeHaan Classical Fellow for the following four years. The competition was a year-long process, which included performances with the Indianapolis Symphony Orchestra, Indianapolis Chamber Orchestra, the Linden Quartet, and soprano Jessica Rivera. It was one of the most amazing musical experiences of my life! I also got to hang out with my fellow finalists, most of whom I was already friends with, and get to know the amazing arts community of Indianapolis.

Apropos to the concert Nikita Mndoyants will be giving for APA’s Grand Encounters, we will be talking about Liszt’s paraphrase of the overture to Wagner’s Tannhäuser. It is a piece that I have worked on as well, both in Liszt’s form, as well as in the original form when I was a violinist in the Conejo Valley Youth Orchestra. I am so grateful that we tackled this piece in youth orchestra, because I got to know this piece intellectually and emotionally before I ever set out to learn the transcription. The scrubbing and woodshedding I had to do, both on the violin and on the piano, for this piece will never be forgotten.

For your enjoyment while reading, here’s a recording from when I played this overture in a recital for the 2015 Cleveland Young Artist Competition as a guest artist.

Transcription, Arrangement, Paraphrase – what’s the difference?

Liszt used many words: phantasie, paraphrase, transcription, reminiscence, …sur de[s] [themes/motifs de] … , d’après, illustrations, etc. to describe his arrangements. I think you can tell to what degree of freedom Liszt is going to take his arrangements by the words he uses. It seems that transcriptions and paraphrases (and any which just bear the title of the original work) are his most true-to-the-source works.

Transcriptions exist not only in music, but in literature and spoken word as well. If you break down the word transcribe, it is literally “across-write” in Latin, and it implies writing or copying across different forms of media. In language, transcription is more akin to recording – you often get transcripts of speeches printed in papers or news sites. Transcription is also used in biochemistry, describing the creation of RNA from DNA. The “language” of DNA and RNA are very similar, but not quite, and so transcription seems to be a fitting word.

Picture showing DNA to mRNA transcription, which results in protein synthesis. From https://en.wikipedia.org/wiki/Messenger_RNA, uploaded by user Sverdrup

Arrangement is very similar to transcription – it usually means taking a piece and rewriting it for a different instrumentation. My inclination is to consider transcriptions to be more faithful and also more technically demanding than arrangements, which often tend toward simplification or for mass consumption.

Then what about paraphrases? In language, paraphrases are a rewording or approximate copy of something previously written or said. In music, paraphrases might be more flexible with material added in or taken out. Or they may have figurations that are completely changed, or in the case of the Tannhäuser Overture, meters altered. I don’t think Liszt would have really dared to do too much of that with the Beethoven Symphonies, for example.

Transcription as Translation

Another trans- word we should mention is translation. Transcription in musical terms is rather like translation, but instead of moving between languages, it is moving between instrumentation. This seems like a pretty obvious connection, but it becomes even more robust once we get beneath the surface. In any translation of text, there is always the consideration of how literal should the text be. If the translation is too literal, the translator runs the risk of losing high level meanings, such as idioms or figures of speech. On the other hand, if the translation is too free or stylized, the original meaning could be lost, as could cultural-specific ideas.

In transcription of music, these considerations are also important – there are certain passages or chords that can be played in one instrumentation that are impossible on another. The trouble is finding how to make it work on the new instrumentation in a way that is idiomatic, but at the same time retains the essence of the original (whatever the transcriber decides that may be). Furthermore, even the structure of phrases or large chunks of material may be altered to make the music more effective on the destination instrumentation.

The signature of a transcriber lies in how they deal with these challenges. Pianists and music lovers will be familiar with the different ways the details of transcription occur between arrangements by Liszt, Busoni, Godowsky, or Rachmaninoff, etc. It’s the fingerprint not only of their pen and hands, but also of their ears.

Konzertparaphrase

Either Liszt or his publisher titled this piece as a “concert paraphrase” and so we have to consider a bit what this means. Surely, compared to his “Réminscences” this piece is very faithful. However, compared to works like his arrangement of the Beethoven Symphonies, this piece might be considered ever so slightly less strict in its transcription.

I would say the baseline for this piece is a very straight-forward transcription of the orchestral version. For example, the opening wind chorale works very well as is on the piano. Even a lot of the string figurations are pretty much unaltered. But with that out of the way, we can start to see both the subtle and not-so-subtle changes that Liszt makes, and try to see why he made them.

Voice Leading on the Piano

I mentioned previously that the wind chorale in the beginning is mostly the same. The changes are minute, but interesting. Liszt adds some extra notes to make the voice leading work a bit better on the piano – the doublings in the orchestral version would cause some texture inconsistencies if transcribed exactly:

Notice in measure 5 and on, a literal transcription would result in the voice counts decreasing. Liszt was forced to add another voice in the bass.

When played by multiple instruments, doubled notes sound doubled. But on the piano, when two voices collapse to a unison, the audience rarely hears it as such, and it sounds more like a voice has dropped out. I would argue this is the reason why Liszt has made the changes above.

The opposite can also be true – sometimes Liszt will leave voices out, because in the piano transcription it will sound like there is an extra note if unison voices split up:

Here, a literal transcription would result both in an abrupt change in voice count and also an awkward chord to play, given that Liszt wants a left-hand only passage.

Another instance of changes occurring because of voice leading is during the second theme. He actually leaves out a dominant 7th chord (opting for a straight up major chord) – he probably thought it sounded better without the 7th, but it could also have been a voice leading consideration. In the orchestral version, there two contrapuntal lines that are of interest are E – E# – F# and F# – E# – E. The crossing is interesting, but in a piano transcription with limited voice independence, it seems more appropriate to focus on the one that is more interesting. Furthermore, the bass line is moving upwards F# – G# – A#, so Liszt seemed to want to focus on the contrary motion created with F# – E# – E. Again, he might have just left out the dominant chord because it wouldn’t sound good, but I think the underlying reason is the voice leading.

Some changes are more about voicing of chords, where because of the overtones of the piano, it sounds better to have a more open spacing of chords rather than closed. Take for example the left hand here compared to the original cello arpeggios. The difference is small, but the wide spacing sounds better than the closed one on the piano – the broken third in the bass can end up being very muddy.

The timbre of the hands

There is a part of every pianist that wishes their left hand were just as good as their right hand, whether that be control of sound, speed, voicing, or any technical matter. However, I think it is just as well that the hands have their separate character. Liszt thought so, too, because he uses both the visual and aural effect of putting melodies in the left hand. Take for example this second phrase of the opening:

Liszt goes through the trouble of crossing the hands so that the left hand can play the cello melody. Notice later he reverts back, but just the effect of having the melody suddenly be taken up by the left hand is a striking gesture. Not only is it visually interesting, but using the left hand ensures that the melody lies mostly between the thumb, index, and third fingers, which are the easiest fingers to use in terms of weight distribution. This allows for a warmer sound, emulating what the cellos would make.

Return of the theme after the first big tutti. When I perform it I cheat and use the right hand to help, but actually for the bass notes, so that I do not have to roll, but can also keep the left-hand character in the melody. I like the imitation between the right hand in the pickup to the 5th measure here and the left hand in the pickup to the 5th measure – both have a C# – F# leap.

After the fireworks of the first section, the chorale comes back, and Liszt again uses the left hand, this time completely solo, for the first sub-phrase of the main theme. The same effects as the above apply. This also allows the following più p to be even more special, with the addition of the right hand (and thus better control).

Aural Illusion

This isn’t going to be something about Shepard Tones, or weird tritone upwards-downwards ambiguities (which I spent too much time researching than I care to admit), but more about how our brains fill in notes that are omitted, or in different octaves. The closest visual analogy I could find is something like the Kanizsa Triangle, where our brains make a shape out of the negative space. Our brains ability to interpolate is a blessing to transcribers, because often times you just have to leave certain things out.

Kanizsa Triangle uploaded to wikimedia commons by user Fibonacci. We don’t see this as their disparate shapes, but rather as a complete composition.
Notice that the melody jumps between octaves. Left hand accompaniment has rests, but because they are filled in by the melody, the illusion is not broken.

One example is in the very first tutti section, where the right hand has to negotiate the broken descending scales. Here the melody alternates between being in both the right hand and left hand, and just in the left hand; thus, sometimes the melody fills up from the bass to the treble, and other times it only goes up to the tenor. No matter, our brains hear the melody as one line (especially if the pianist voices adequately).

Furthermore, the bass is always omitted when the melody is played, but because we still get an articulated attack, we don’t really miss the bass. As long as it is regularly occurring, our brains assume that the pattern continues.

A further striking example is in the main theme of the Allegro – Liszt doesn’t bother to put the melodic high note on the beat. He puts it on the second sixteenth note to make the tremolo pattern easier to play. You can try to come up with alternatives, but none will be as elegant as what Liszt came up with. I think this figuration works because our ears group the first two notes together, so it sounds like a broken downbeat. In fact, we roll and break chords so often in piano music that our ears probably have adjusted to that. It’s really amazing that it sounds better than trying to copy the original rhythm exactly.

Registration

One of the challenges for transcribers is what octave to put notes on the piano. Often we can just put it in the octave that the source is in, but some times that just does not sound quite right. Rather, we must put the notes in the same octave relative to the “normal” range of the instrument. Let’s say there’s a violin passage that’s quite high, like this:

Sorry the instrumentation is cut off. From top to bottom: clarinets, bassoons, first violins div. 4, second violins div. 4

If we put it directly onto the piano, it’s not going to sound as high or stratospheric as the original. In fact, we’re going to have to move it up to another octave so that it has the right sound.

Same ledger lines as the orchestral version, but there’s an 8va here!

Conversely, this passage in the violins is all the way at the bottom of the G string. Liszt opts to go all the way into the bass clef to convey the timbre of the low violin.

Octave considerations can also apply to whether to put a melody in octaves or unison. Even though two instruments (such as viola and violin) could be playing the same melody in the same octave, the effect is one of rich overtones. Liszt appropriately goes for octaves on this melody.

Making Some Noise

Liszt often gets a lot of flak for putting in runs and chromatic passages as fillers. This piece is no exception, but I do think many of them serve more of a purpose in this piece than others. The orchestral version is loud and full of energy and texture. With only two hands, ten fingers, and two feet, Liszt had to find a way to create the same kind of excitement.

In the transition between the first and second themes, Liszt changes the accompaniment figure from a sextuplet chromatic scale, to sixteenth-note chromatically ascending alternating sixths (whew). This change accomplishes a few things. First, it spans a bit more of the range; Liszt gets to cover a bit more harmonic ground and not have a huge whole between the melody and the bass. Second, it’s a bit easier to play metrically than the polyrhythm – it’s not a hard one, but it can affect stamina and pacing. Third, the rotation of the hand in the oscillating sixths allows for a bigger crescendo.

The beautiful soaring melodies after the second themes are accompanied by brilliant arpeggios. These arpeggios are not in the orchestral score, but they help to get across the effect of this nice legato melody after all of the octave chords previously. It also allows Liszt to showcase the ingenious dividing of the theme between the hands as the right hand climbs up the keyboard over and over again. In addition, the runs make it easier to fill out the harmonic content, since a pianist can’t even begin the span the actual voicing in the original.

Negotiating the melody is a challenge, both in voicing and timing.

“If it ain’t Broke…”

There’s two parts to this topic I want to cover. The first is regarding the relationship between exposition and recapitulation. In the second theme, Wagner changes the orchestration of the accompaniment quite drastically. There’s a bit more scrubbing the second time around, as well as rhythmic diversity (with triplets in the bass). Liszt saw this, thought “well it sounded so good on the piano in the exposition,” and just kept the figurations the same for the recapitulation. I won’t accuse Liszt of being lazy, because let’s face it, the pianist learning the piece is also glad that he or she doesn’t have to learn even more patterns and figurations. However, it’s interesting to think about how it could sound if some of the changes were incorporated into the transcription.

Second is the fact that there is plenty of the piece we didn’t talk about, and that’s because he really didn’t change much from the original source in those parts. The notes are good, and the phrases are good, so Liszt just has to make them fit comfortably in the hands, and he’s good to go. This even applies to that beast of an ending with the flourishing of octaves. There really is no other way that should be transcribed.

However, this is exactly why this piece is so difficult to play. The fact that it is so close to the original version, and that Liszt made very little compromises, especially in the little figurations, means that the pianist really has to be an orchestra. That means singing individual voices, having different colors, filling out the entire dynamic range, and building up the stamina to perform such a work.

Addendum

This article wouldn’t be a Sean Chen pianonotes without some re-transcription. As a reward for getting through the entire article, I’ve engraved some of the additions I made to the piece when I performed it. The best part about transcriptions is that you get to hear the piece as the transcriber heard it the original source. Here, we get a glimpse into what Liszt heard when he heard the piece performed live (I assume he did hear it). But, I’m fully of the opinion that if you hear different things, it is okay to add them or change some things in a transcription. You can probably find where these changes should go easily. Without further ado:

Right before the first tutti section.
Those tremolos in the violins are exciting. This is a simple change, but I think makes it sound better than straight eighth notes.
I added some counterpoint back in from the orchestral version. My favorite is the little turn flourish near the end.

Date with an Orchestra

Today, we’re going to be going through a few tips that I have picked up and figured out throughout my time playing in front of an orchestra. It also helps that I have been with someone for a long time who plays in an orchestra. As with performing recitals and auditions, the best and most effective way to learn how to be the best soloist you can be in front of an orchestra is by doing it over and over again. There simply is no better way. However, I hope some of these suggestions can help accelerate that process. If you have any other tips, please leave them in the comments!

Preparation

Get the Full Score

As you might gather from a previous post, I’m a big fan of having different sources for my information. Having the full score helps you be informed of what’s going on in the orchestra part, more so than having a piano reduction, though the latter might be easier to read. Not only does the full score allow you to see what instruments are playing what, it also allows you to double check the notes and dynamics in your reduced score. You can also work on your score reading!

Listen

This sounds simple and obvious, but listening to recordings helps! That way you know your entrances, and you know what the orchestral part sounds like, as opposed to only hearing a second piano reduction. This offers yet another way to check your notes. If you hear something funny or fishy, check your score – maybe the recording has a mistake, but more often than not, you might discover that you’ve misread some notes or rhythms.

Play Along

I like to play along with a recording of the concerto, preferably with headphones. Knowing not only how the orchestra part sounds, but also how it sounds like while you are playing your part is very helpful, since the difference in timbre between instruments can throw you off. For example, a certain melody might sound clear in the piano reduction, but when you listen to the recording (or show up to rehearsal) you realize that it’s actually not as easy to discern within the context of the rest of the orchestra. Or, some rhythms might be very disorienting (see the 5th page of reduction for Rachmaninoff’s Third concerto – the offbeats in the winds are really confusing).

Conduct

Sometimes, it’s very useful to conduct yourself, away from the piano, or even with a recording. It gives you a good sense of timing, and you get to familiarize yourself and internalize any interesting meter changes. You don’t want leave any of your counting and synchronization solely to “I just feel it,” or “I just go by how it sounds.” Yes you should feel it, and know how it sounds, but we want no excuses!

Sing Along

I find it very, very helpful to sing certain important parts while playing through the concerto. For example, in the second iteration of the first theme of Rachmaninoff’s 3rd (the third and fourth pages, if anyone is looking), the piano has accompanying figures, and I like to sing the main melody while playing through it. It allows you to get the entire picture in your ear, keeps yourself from rushing or slowing down, and makes sure you don’t get confused in phrases where the piano begins with a sixteenth-note rest. You can also figure out what sort of timing you might have to take when you are accompanying a solo wind melody or something similar.

I sang along a lot while learning Bartok’s second concerto – I needed to make sure I knew what to listen for, and not have anything catch me off-guard in terms of rhythm or number of repetitions of certain accompaniment figures.

Learn the patterns

This seems elementary, but all musicians should learn the different conducting patterns. You don’t want to look up from the piano, and not know what beat the conductor is on because you’re not familiar with the patterns.

Knowledge

There are certain infamous parts of pieces, where you must utilize all of the above techniques to make sure you have that section down pat. One of these is in the twenty-second variation of Rachmaninoff’s Paganini Rhapsody, 7 before rehearsal marking 65 – this section has piano runs accompanying a melody in the strings. Jerry Lowenthal told me I had to learn the orchestra tune by heart here and how the piano part fits in, because just relying on feeling can be iffy and scary, especially on stage. I would also advocate conducting this passage to know which beats the phrases begin and end on, because they shift around each successive phrase. So, an example of the “facts” I would tell myself are:

1st Phrase – starts after second beat, peaks on the downbeat of the next measure

2nd Phrase – starts on the second beat, again peaks on the downbeat of the next measure, just like the first phrase, but the run goes on for a beat longer up to the second beat.

3rd Phrase – starts right before the third beat, and peaks on the third beat of the following measure, and the run goes on for even longer, going up to the third beat

4th Phrase – starts only one triplet-eighth after the previous phrase, peaks again on the 3rd beat.

5th Phrase – I would say this one is a “normal phrase” since it starts after the downbeat, and the phrase lasts exactly two bars.

*N.B. when I say “beat” here, I mean in terms of quarter notes. This variation is actually in alla breve.

This enumeration makes the passage even more solid in your head. Knowing these things can help you when you’re not quite clear, and especially when on stage things become a bit unclear and uncertain, either because of how it sounds on stage or because of your nerves.

Tips for the First Date

Wait a bit…

The first thing one learns about playing in front of the orchestra is that they are almost always behind the conductor. No, it’s not that they or the conductor are incorrect, it’s just how orchestras function. First, the plane of the beats is not at the bottom of the conducting motion, but somewhere in the middle after the rebound. Second, there is always a delay in reaction, and so most orchestras naturally have that built in so that people know where their colleagues are going to play.

So, as soloists, we have to account for that, very notably in something like the opening of the Grieg Concerto, or in any final chord of a piece. Furthermore, if we want to land on a chord together at a certain time, we sometimes compensate for that by possibly giving an earlier cue (sometimes that’s not possible), or just waiting a hair before getting to the arrival point.

…but don’t wait too much

At the same time, you have to trust the conductor to follow you, and just do your thing. It’s actually very easy to be too adjustable, and you end up getting slower and slower because you’re trying to accommodate being with the orchestra. (I find this is something that I need to tell myself quite frequently).

The Concertmaster is your best friend

No, not literally, unless of course he or she in fact is. What I mean is that the concertmaster is your window into the orchestra. Sure, you can watch the conductor, and you should. But oftentimes it can be a lot easier to line up with the group if you watch the concertmaster instead. This can include playing with pizzicati (seriously, try this next time) – if the conductor just conducts the group without worrying about you, and you just watch the concertmaster, I guarantee it will be more together than if the conductor tries to follow the soloist; or with any big chords.

Furthermore, the concertmaster is probably the musician in the orchestra that hears the soloist the best, and can see you out of the corner of his or her eye. That means that they are able to pick up on any subtle (or not-so-subtle) rhythmic nodding or accents (for stability of course), or if you are wanting to change the tempo. And the soloist hears the concertmaster quite clearly as well, so that’s another reference for being together with the group (assuming the rest of the group is with the concertmaster).

Adjust your dynamics

The reality of playing with orchestras and in halls that are big enough for an orchestra is that we as soloists need to project more (play louder) than we are used to by ourselves in the practice room. This is especially true when the orchestration is thick or in a register that covers the piano. Conversely, in solo passages, then we can utilize the full dynamic range of the piano, especially the softer parts. Just be aware of chamber-like passages where you might be prone to covering up the solo instruments.

Eye contact

It’s nice to occasionally look up at the conductor; eye contact allows you to synchronize rhythmically and musically. Furthermore, if there is a duet between the soloist and a solo part in the orchestra, having that direct connection can help with the ensemble and the expression.

Before, I talked about following the concertmaster for pizzes, but another useful tip is to watch the cello and bass players (if they’re in your line of sight) especially to sync up the left hand with them – many times you don’t have the time or luxury to look over at the concertmaster.

Respect the Protocol

I’ve really never heard this brought up except by my teacher Edward Francis, but the etiquette for entering and exiting the stage is important. On entrance, first shake the concertmaster’s hand, then take the bow (no pun intended). After the concert, shake the conductor’s hand (they might even give you a hug), the concertmaster’s, then take your bow.

Check with the orchestra people whether an encore is okay. Depending on the length of the concert and/or encore, they might not want you to play – if the orchestra is unionized, they could go into overtime, and then have to deal with financial issues. This could be a problem especially for smaller orchestras, so just be aware of that.

 

Hopefully all of these things can help make playing in front of an orchestra less stressful. Once you know what to expect, it’s not bad. In fact, playing in front of an orchestra is one of the most thrilling experiences I know of. I think it really is a unique experience to solo musicians; in no other field do you get to take part in such a collaboration and dialog to bring amazing masterpieces to life.

Doing your Due Diligence

Hey all! I wanted to do a short post today on examples of why it is important for pianists to consult many sources when they’re learning and studying a new work. We are so fortunate in this day and age to have relatively easy access to so many forms of media, whether it be open-source first edition scores, recordings, secondary sources, or even manuscripts. All from the computer of our computer desk! Yes, sometimes even after all this studying you may still not have conclusive evidence about certain things, but at least you are more informed in the choices you make regarding interpreting the text.

Throughout the years studying and listening to different people play these following works, I’ve found some interesting misreadings. These are just a few that have been fueled by what I’ve heard most recently, but there are definitely more. Misprints in editions also often occur (the Bärenreiter Brahms Horn Trio and the Universal Edition Strauss Violin Sonata have been the most egregious recent ones) and we have to be very careful when we’re learning new repertoire.

Rachmaninoff Rhapsody on a Theme of Paganini Op. 43

We’ll start with a simple one. The edition I learned this piece from was the Kalmus, and I think it’s just a basic reprint of the first edition. The end of Variation 11 always confused me, because after a series of sixteenth rests, there was an eighth rest. However, if you take into account the notes that follow, the beats didn’t work out. It wasn’t until I looked at the full score where I found out that there was a missing triplet sign. Might not change much in the grand scheme of things, but it’s kind of nice knowing that the beats add up.

Prokofiev Piano Concerto No. 2, Op. 16

I haven’t gone through the whole piece in detail yet, but I noticed this interesting misreading in many people’s performances, both in recordings and live. This misreading depends on the edition you use.

This is in the 1st movement cadenza. Because some of the solo editions break the measure across the system break, the accidentals which should carry through aren’t given courtesy markings. The G’s should be sharped on the sf chord.

Rachmaninoff Concerto No. 3, Op. 30

This is in the cadenza section as well, and again it is because of a measure break. This time, rather, it is that the full score has a break in it, and so the accidentals should be assumed to reset; however, in the piano reduction score, the break is in a different location in the measure, and so it seems as if the accidentals carry through. This is one of those cases that I thought I was being very detailed by playing the A and the B naturalized, but it wasn’t until I looked at the full score did I realize that they were indeed flatted. You can also listen to Rachmaninoff play it himself, and he does the flats, and the subsequent high E is also flat (I didn’t highlight it, but it’s obvious).

Happy Pianoing!

Beethoven Sonata Op. 27 No. 1, Quasi una Fantasia, Quasi Quit Piano

This sonata is affectionately known as “the other one,” since Op. 27 No. 2 is the “Moonlight.” I really enjoy this piece and spent a lot of time working on it. Before I got very comfortable with it, however, I used it for my Juilliard Artist Diploma audition, and I think I played it pretty mediocrely, resulting in not getting accepted (I thought my other stuff went well, but who knows). I was going through a mini crisis at that point trying to decide if I should continue onward with my studies, but fortunately I persevered. I then went on to study with Hung-Kuan Chen at Yale, who really helped me out with getting this piece down and comfortable. Out of my audition repertoire, this was probably the “easiest” on the surface, but I think it’s a much harder piece to play well and convincingly than many other pieces (the other pieces on my list were Prokofiev 8, Schumann Kreisleriana, some etudes, and Bach Keyboard Sonata in A minor).

We’re going to just talk about the first movement of Op. 27 No. 1. I’m really using this piece as an excuse to talk about certain pianistic concepts in context, so many of the ideas will be applicable to many if not all other pieces. I’ll try to be as stylistically agnostic as possible and present the various considerations we have as pianists, though some interpretation is bound to creep in since I’ve spent a lot of time on this piece. And, this list is not exhaustive; other pianists might focus on different things and reach different conclusions. Enjoy!

Legato

We have to talk about legato. I often ask students in masterclasses, “How do you create legato?” Invariably, the answers are always vague, with words like smooth, connected, and lyrical thrown around. Now, if you were playing a stringed instrument, the answer might be easier: as long as there aren’t any string crossings, you keep the bow moving in the same speed, and play the next notes. We aren’t considering phrasing or anything else here, just pure legato. Now, if there is a string crossing, what string players might do is have a bit of overlap, so that at a small instant in time, both strings are being played.

On the piano, we can’t actually hold notes. The loudest part of our notes are the attacks; at any subsequent point in time, the volume will be less. We always have to deal with decay, and just playing the notes one after another doesn’t result in a very convincing legato.

So for piano, an important key to legato is overlap of notes. This is actually a trick used in MIDI (see Fig. 1 below) when you want to create a legato sound – you actually hold the previous note slightly into the next. This creates a blend of sound, sort of like a cross-fade in audio processing. Then, as a pianist, you can use the amount of overlap, from barely any to almost all of the next note, as a tool for color and expression. You can even go the other way, and not overlap at all, in which case you get non legato or staccato or any other gradation of it.

The other component then, is the hierarchy of volumes of the notes in a legato. When just thinking of the two-note slur, we know that the second note generally has to be softer, and by quite a bit; if you play it about the same velocity as the first note, it is liable to sound like an accent. Now, in a longer legato, you can’t keep playing the next note softer, because you’ll end up at pppp after a few notes. Here’s where shaping and phrasing come into play to make sure it notes aren’t sticking out. If you are getting slightly louder throughout the legato, make sure there aren’t any unplanned decreases in velocity. If it is a general tapering, you don’t want any notes that are louder than the previous.

Fig. 1. Demonstrating Legato with MIDI

A melody played without any dynamics or overlapping.
Melody played with overlap but no dynamic nuance. Already, there is more connection between the notes, even given the mediocre piano samples.
Ahh, overlapped and phrased. Though this was quick and rough, it already sounds much better. Notice that the overlaps are different amounts. The velocity of the notes are also smooth. Not bad for MIDI.

Finally, on non legato, we have to watch out that our notes are not too short. This is a judgment call, and requires adjustment in different venues and on different pianos. However, one must always be careful that the pitch is heard. I’m not a big fan of short notes where you can’t hear the pitch.

Color

We hear this term a lot, but rarely know what the person is saying when they want “more color.” In a way, it’s not a very helpful term, but we can talk about a few things that might help with “color.”

First is voicing. Simple voicing can be thought of as just bringing out the top, or the bass, or both the top and bottom voices. But, at its most complete, voicing is the relationship between all of the notes in a chord, so when we voice chords, we can’t just look at the top and the bottom. Every note in the chord needs to be balanced so that we can achieve the sound we want. Looking for a darker color? Try voicing with more bass and tenor. Looking for more body? The middle voices can help with that. Looking for more sparkle? Don’t just think about the top note, but also try to balance the second-highest note so you could some good overtones going on.

Then, you have the right pedal. Pianists tend to go on autopilot with their right foot, but I think the pedal can be one of the most expressive tools in our arsenal. My former teacher Edward Francis used to always ask, “What part of your body plays the pedal?” The answer is “Your ear!” This facetious response points to the fact that the pedal really can’t be dictated; its use must be adjusted to the piano and the hall. Every piano has a different “curve” to its pedal, if you think about a graph where the x-axis is distance depressed, and y-axis is the sustain. In fact, different sections or strings of the piano might behave differently, and we need to adjust relatively quickly to these differences.

So, color from the viewpoint of the pedal can be using less, using more, using none at the attack of the note but then adding some as the decay kicks in, or even putting the pedal down before you play a note. Then, you have full-pedal, half-pedal, a quarter, three-quarters, or any amount. We should use the full range of pedal that the piano has to offer, not just binarily.

Now on to the una-corda (or more like due-corde in modern pianos). Again, I would advocate for using the entire spectrum of the shift pedal. Depending on the piano and how old it is, the hammers might have developed hard spots where it has been hitting the string, and the parts in between will be softer. You can hear this as you gradually shift back and forth while repeating a note. Sometimes, when we want a color change, we have to find the perfect amount of shift, because oftentimes, doing a full shift results in a very unattractive sound because of the grooves on the hammer or other mechanical issues of the piano (like hammers hitting the next note).

Subito

The last technical thing is how to deal with the subito p and f. Really, a pianist just has to become comfortable with how much space is needed before or after, and adjust it to the hall and piano. It is our job to find a way, using both pedal and timing, so that the piano is effective and that it will actually be heard after the forte section.

 

Andante.

Oh boy, this movement… So simple, yet so difficult.

Structure

This sonata is interesting in its construction, because it is almost a reverse sonata: the first movement is a rondo, second movement scherzo-trio, third movement slow, and fourth movement sonata-allegro (Daniel Shapiro has pointed out that it is sonata-rondo.) (the order of the scherzo-trio slow movements is not set in stone as sometimes Beethoven has the slow movement come first, and other times not. The outer movements however are.)

So, we have a rondo, not even a sonata-rondo: A B A C A, and since each part is repeated (or written out with variations), it is more like AA BB AA CC AA. Easy enough.

Harmony and Counterpoint

Really, the simplicity is evident. Lots of tonic and dominant, with secondary keys on super-tonic, and then the parallel major of the relative minor (C Major in this Eb piece). Within each key center, there isn’t much craziness either.

I think the counterpoint makes this piece quite difficult, as the left hand is less accompaniment-y compared to other examples; it has its own character, and even gets the melody switched onto it in some of the variations. Furthermore, there is some four-voice action in many of the phrases. I can almost imagine this being played by a string quartet.

So what’s so hard?

First, tempo. We have Andante in cut-time, which means you should feel each measure in two. The difficulty then lies in finding a suitable tempo that is not too slow (since it’s not Adagio), but slow enough that it doesn’t sound hurried.

Second, phrasing. The right hand is two quarters and a half, with the quarters being portato (slurs with staccatos). Should we interpret this as down-down-up? Up-up-down? Then we have to fit it with the larger phrase. Do we emphasize the first and third or the second and fourth measures of the phrase more? How do we really do the portato on the notes? And, all of this in pianissimo!

We haven’t even talked about the left hand. That legato line is really hard to get smooth and even, especially with the crossover. Then we have a non-legato arpeggio going down at in the last measure of the phrase.

And… that’s just the first four measures.

Here are some ideas

Regarding tempo, I think the Andante can be really thought of in the quarter-note tempo, and I like around 80 bpm, a bit faster. That seems to be within the range of a typical Andante. However, one should feel the phrasing and beats in terms of the half-bar, as the time signature suggests. I think if you instead do Andante in terms of the half-note, it will be way too fast. Conversely, if you think quarter-notes as your unit of time, your playing will become too vertical.

Of course, there will be fluctuations depending on the music. For example, in the B section, there is a slight character change, and even a chance for some nice color changes. In sections with nice slurs, you can play a bit differently, maybe with more friction (or more flow!). But overall, I think the above suggestions hold well for the piece.

Fig. 2.

Demonstration of typical strong and weak beats in various meters.

After I studied with Matti Raekallio, I was convinced that oftentimes music phrased from the start of the phrase sounds more elegant and stylistically correct, especially for pre-romantic music. That’s not to say you must always do it that way, and in fact that would be awfully formulaic and mindless. However, it’s a good guideline, because the position of beats has always been held in an important hierarchy: there are strong beats and weak beats. In 2, the first beat is strong and the second weak; in 3, the first is strong and second and third are weak UNLESS it’s a dance where the emphases might be displaced; in 4, strong-weak-strong weak, with a larger grouping of strong-weak between the first and second halves of the measure; etc. Again, this is a general guideline that is oftentimes subverted. But, it’s important to know what’s normal so that you have something against which to juxtapose the strange and abnormal.

An agogic accent is an emphasis by virtue
of being longer in duration. – wikipedia

Now, even having decided that, the right-hand phrasing is still difficult, because the half note, which is on a weak beat, is accented agogically by its length. So we have to counteract that natural accent… or do we? Maybe we do want the second beat stronger, in which case it would sound up-up-down. But, we do have to consider that the start of the measure should be strong…

Personally, I think there is a balance, and each pianist has to find for themselves how they want to phrase these measures. Even after all that deliberating and phrasing, it must be done in a subtle way as to not disturb either the dynamic or the character.

Fig. 3.

Quick and dirty MIDI rendition of the left hand in the first two measures. Notice the overlaps, velocity differences, and directions of phrasing. And all on MIDI.

The left-hand presented a huge problem for me. After hours of practicing and working with Mr. Chen, I realized that not only was my cross-over from the thumb to the third finger bad and slow, but my thumb was prone to come in early, because of how I was playing my thumb. Basically it came down to the fact that I use more finger action and less rotation on my third and second finger, but more rotation on the thumb. The contour between the black and white keys can also prove a challenge to getting it completely even. Then, I had to make sure that the amount of overlap between the legato notes stayed the same whether there was a crossover or not.

That’s my experience, and you will most likely have different problems since our hands are so different. My suggestion is to sit down and diagnose why the legato is not even: see which fingers are coming in early or late, and see if you can spot a pattern in the unevenness. Then from there, you can try to find a physical reason for the inconsistent notes, and once you pinpoint these habits and tendencies in your technique, you can begin to address them. Don’t let yourself off easy!

The Feel

Finally, for this first movement, a big challenge is what to do in the large scale. Many of us, especially if we’ve been taught a certain way, feel that music should always be going somewhere, that there should be a starting point, a direction, and an arrival. This is certainly true of a lot of music and of many phrases. But, I think this movement as a whole defies that notion. Sure there is “movement” within each section and within phrases, but there is something very static about the larger picture. Each section is self-contained, and the character within each section is mostly unchanging. Maybe we are too obsessed with always going somewhere, especially being young and impatient and uncomfortable with being still. Perhaps this music should just be, and we should just let it exist and be content with it.

I had the hardest time with this concept. I tried to show too much and do too many big-picture ideas when what I needed to do was to focus on and internalize every detail of the music. All of the musical decisions have to happen within the character and “space” of the piece, and I had to learn to feel comfortable staying in that “space.”

Learning How to Learn

I was originally going to dedicate an article on Hamelin’s Toccata, talking about the technical and musical challenges, and what is unusual or particular about the piece from a pianistic standpoint. After looking at the piece a bit, I’ve concluded that it is a fairly standard virtuosic work, relatively conservative in the context of Hamelin’s other pieces. To be fair, I have not practiced this piece, only read through it a couple of times and listened to some of the performers play it. But, there are no striking registrations, crazy fugues, strange figurations, or near-impossible runs. Just fast and exciting.

Furthermore, I don’t want these posts to really be music-theoretical, unless the topic is specifically about that. I think we would benefit more talking about stuff more piano-related, instead of things like how he uses polychords, hemiolas, augmentation, chromatic build-up over a pedal-tone – things that are very intuitive that I just end up having to make up terms for. We shall leave that for the theorists.

So, I am going to be talking about how to learn new repertoire, new in both the sense of it being something not of the common practice era, and also in the sense that it is a new piece that you may not have known previously. As always, this is from my point of view and my experiences. Other pianists might have developed other techniques or take things in a different order with different priorities. However, I hope that some of these ideas will inspire you to discover other ways to learn music efficiently and deeply. And, if you’re not a musician, I hope my suggestions can stimulate analogous ideas in other fields.

A borrowed title

No, I did not come up with the title of this article myself. In fact, there is a course on coursera.org called “Learning How to Learn” that I highly recommend (no I’m not being paid for this suggestion, I promise). All of the concepts they present on learning and test-taking are applicable to us as musicians and performers. Furthermore, all of the information is from research on how the mind works, and it is great for people of all ages. I highly recommend watching the videos, even if you think you are an efficient learner. It’s sometimes good to have those ideas told to you explicitly.

Getting it in the ear

I would argue that atonal or less-tonal modern music is harder to learn not because the non-tonality is factually harder to learn, but because it is not in our ear. The ear plays such an important role in sight-reading and learning music (at least for me). When I decide to start practicing a piece from the common-practice era, I’ve usually heard the piece at least once, if not dozens of times, and have probably read it a few times as well. Even in this Hamelin Toccata, when progressions and patterns are more similar to passages from some common-practice pieces, I find myself being able to read faster and assume more of the notes aurally.

Try reading a tonal piece that you have not heard before – like a Medtner sonata or the Scriabin 8th, or even something like the Mompou Variations on a theme by Chopin – you’ll find it surprisingly hard to sight-read because, though it is tonal, you don’t know how it goes and you need to actually read each note. Contrast that to reading a Beethoven sonata you’ve heard. You don’t actually need to read all of the notes because you can fill most of it in by assumption (and be correct when doing so).

Of course, this is assuming a general level of complexity in the piece – I’m sure you would be able to sight-read a Soler piece that you have not heard before relatively easily. If that’s not the case, get on it! You can get better only by doing it more.

So, one of the first things we as pianists have to do when learning a new piece is to get it in our ears. I would advocate for reading through the piece frequently when starting off. You may also speed up the process by listening to recordings, though then you run the risk of getting an interpretation stuck in your head if you only listen to one rendition over and over. Reading and listening not only puts the sound world into your head, but also gives you a good idea of the large-scale structure of the piece. It allows you to subconsciously prep your later practice plan: you begin to have an idea of what parts are more difficult than others, what parts fit your hand relatively well, and what parts are just plain confusing and will cause problems later when trying to memorize it.

Caveat: reading is not quite possible on the hardest of pieces, like a Ligeti etude or a Xenakis piece.

Let it grow on you

Many pianists have pieces they really don’t like. But I don’t think many of them have pieces that they know really well AND they don’t like. Personally, whenever I’ve started a piece that I disliked for whatever reason, I find myself saying, “This piece is actually not bad” after I get to know it and actually learn it. So, give it a chance. I’m not particularly fond of this Hamelin piece that has been commissioned, but I don’t know it well, and who knows? Ask me again in a few years and my opinions on it might very well have changed!

The Metronome is your friend

I’ve heard my teacher say it, you’ve heard your teacher say it, we all know we should use it, but, but, but…

Just use the metronome. I’ll talk about the metronome more thoroughly in the next article, but don’t just do slow practice, and definitely don’t just play fast. Mix it up a bit.

Survey the Land

I mentioned it briefly, but I want to cover more in-depth the concept of having a good idea of the general structure of the piece. Identifying different sections of the piece, whether that be a character change, a key change, a meter change, contour change, or just even a page-turn, can help you organize your practice. It can also help with memory. We will talk about memory more in-depth in a later article as well, but for now, know that having these goal-posts are a good technique for memorizing and dealing with memory-slips. (Hey, this sounds like building repertoire by moving outwards from the must-have pieces!)

You can even start seeing patterns in the structure – maybe there are two passages that are similar, or the same but transposed, or maybe there are passages that are easy and you don’t need to worry about them so much. An example:

Prokofiev 2nd Concerto, first movement. You know the cadenza is going to be the hardest and most problematic part. That means you would probably work on that first, so you can get a head-start on it. It doesn’t mean you won’t practice the other parts. You realize that the first section has two statements of the theme, and that the two statements share a chunk of the material. That means you don’t have to explicitly learn the two parts, but you have to make sure that you know the differences between the statements – that they end in different dynamics and go onto different versions of the “second theme,” etc.

The second section is sort of like variations (and modulations) on a new theme. You identify to yourself the characteristics of the variations: first is piano solo in A minor – nothing too bad besides maybe articulation considerations. Second variation is piano accompaniment in A minor. Those hand crossing and bass jumps seem kind of nasty; I would make a note to really know those notes and the changes in the harmony. Then there is a sort of bridge/development variations which leads to the next variation of piano solo in D minor – there are some unison runs, but all-in-all not bad. The runs continue into the last variation where the orchestra again has the theme. Those weird scales can be problematic, so I would sit down and really internalize those accidentals.

This is just an example of surveying the piece to really make practicing efficient – once it is clear in the mind, it will be clear for your body.

Back to the Basics

Sometimes, you there’s just no way around learning pieces like your teacher first taught you: hands separately, measure by measure, line by line, page by page. This method is great for thorny pieces like Carter’s Caténaires or any Ligeti etude because they’re basically impossible to read. I remember trying to read through these pieces, and even after a week, it still felt like I was reading them for the first time. Things would sound different every day – I would go, “wait was that accidental there yesterday? I also don’t remember that treble clef being there, and could have sworn that that was a fourth and not a fifth.”

This method shouldn’t be used blindly, either. Don’t just start from the beginning and do measure by measure by measure by measure. Group them. Do the first measure, then the next. Then maybe try putting the two measures together. Then do the next two measures, and then the four measures all together. Maybe try to build the whole line now. After you have two lines you can put them together, but you also need to spend some extra time on the measure before and after the line-break because you have yet to practice those measures together. Same thing with the lines before and after the page turns. Again, it is important to mix it up with large and small sections so you can both concentrate on details as well as get into the flow of it.

When I was learning Ligeti’s L’escalier du diable, I had to do this entire process twice: once to be able to play through with the score, and a second time for actually memorizing it.

Spaced Repetition

Don’t procrastinate. It is better that you start the piece earlier on (so you can get it in your ear), and read it once in a while before you really start diving into it, than it is to plunge straight into a week-long cram session. I believe this is why pieces that you learned when you were young stick better in your head than more recent pieces. Those old pieces you probably have brought back a dozen times throughout your educational and performing career, whereas those new pieces you probably played them 5 times in a span of two months, and haven’t touched since. The spaced repetition over years allows your brain to marinate the information, and every time you bring it back it is reinforced.

So, it is a good idea to read new pieces earlier on, even if you don’t have the time to dedicate to working on it in detail. Just let your ears soak it up slowly.

Convince Them

The hardest thing about new works isn’t their technical difficulty, it is how to perform them convincingly. Playing the notes well and accurately is relatively easy (most of the time), and with a lot of new music, that probably is enough to sell it to the audience. But, as musicians, we don’t let ourselves get away with the minimum – we always strive to find meaning, interesting things, expression, colors, or stories in the music we play.

Part of accomplishing this is to make sure you are practicing the musicality while you are doing your slow practice. You should never practice the notes devoid of expression, whether that expression is coming from articulation, dynamics, phrasing, or something else. If you practice robotically, you will play robotically, or end up spending a lot of time undoing that and adding musicality to it. And the worst thing you can do is play like a robot. (Well, you could play like a robot and miss all the notes. But we’re assuming a level of competence here.)

Many people have trouble with the atonality of pieces, and if you play it like it’s a dissonant piece, you’ll never get the audience on board. Rather, it is important to find musical interest in the piece – it can mean tracing how the dissonances “resolve” relative to one another. Or maybe the dissonance is a product of individual lines that can be brought out at different times to make more sense. Or perhaps the dissonance is secondary to the registration shifts. Sometimes, the rhythm is more important. I’m not saying that we must fit music into common-practice boxes that we feel familiar with, but it can provide a good basis for understanding newer music. You also have to remember that music does not exist in a vacuum; there is always something of the old in the new.

Play it Through

For your friends; for your girl/boy-friend(s); for your parents, your stuffed animals, your neighbors, your cat. The more experience you have going through the piece in an environment that is more stressful than your normal practice routine, the better. You find out how much stamina you need and where you are liable to lose focus. Sometimes memory issues or technical challenges don’t show themselves until a run-through.

I really love recording as a technique. I feel like my mental state changes the moment I press record. Not only does it force you to go through the whole piece without stopping, hopefully without making any huge mistakes, but it also results in a product that you can listen to afterwards. And there’s no better teacher than listening to yourself, realizing your habits and hearing how the piece comes across as a whole. Sometimes you’ll find yourself cringing at certain things, but then concluding that, “eh, it wasn’t as bad as I thought.” Other times you’ll say, “All the notes are there, but somehow the feeling wasn’t quite right.” It gives you direction for how to guide your future practice sessions, and informs of what you need to fix and where.

Sit down with a score and headphones and really be your own teacher. Mark it up, and you’ll even find yourself saying the exact same things your teachers say. “Why did you rush here? Don’t play these downbeats so vertically. Can you not throw away the last note of each group of sixteenths?” And, you can be as nasty or nice to yourself as you want!

No such thing

There are lots of sayings of “There’s no such thing as a bad ____, only a bad ____.” We can put “piece” and “performance” in there and get a sentiment that I mostly agree with. Though, I think it is more that we as performers can make a bad piece good by delivering it well – in the right context and with the right conviction. I think this “how do I make this work” attitude is applicable even to the most commonly played piece. After all, people are always asking musicians to perform with fresh ideas. Hey, maybe it isn’t a bad idea to treat old music like new music sometimes!