Monday, May 27, 2013

Warming Up

Pianists often ask if they should warm up their muscles before playing or practicing. Traditional teaching often has students playing scales or other "finger exercises" before starting to play their pieces. I disagree with that approach. Read my posts on exercises and you'll see why. To summarize here: we need to be using our whole physical mechanism -- hands, arms, torso -- not just fingers. We do many activities during the day that use our hands and arms and we do not generally warm up before them. If you are using your body properly, rather than putting all the strain on the the smallest muscles (the fingers), you do not need to do warm-up exercises.

If the weather is cold or you are in a cold room and your hands are physically cold, then yes, you should actually warm them up (run under warm water, hold over a heat source, or put on gloves for a short while). But doing scales or exercises when the hands are literally cold would be the worst thing for them.

I have what I believe is a far better method of "warming up" or getting ready for playing. I call it "energizing." I'll describe it here and you can try it for yourself, but I feel it's most effective if you have a teacher actually leading you through it, because it involves a fair amount of imagery work.

Here it is:

Sit at the piano and close your eyes (keep eyes closed during the entire process that follows). Become aware of your torso, especially the shoulders, and let them drop and relax completely. Become aware of your buttocks and legs and let everything relax. Let your face and jaw relax. (If you've every done yoga or other such disciplines, this will all be familiar to you.)

Now let your arms just float up to a comfortable place, somewhere around mid-chest level. Let them just feel suspended in the air. Move the arms around slightly to make sure you aren't holding them tighter than necessary.

Put your attention on the space between your pointer and index fingers (2nd and 3rd). Put the attention on this space in both hands simultaneously. See if you can "feel" the air space between them. Or you can imagine a wedge of some very light foam between them. Or you imagine tiny electrical currents passing between them. Whatever imagery works for you. If it is working, you will start to feel a tingling sensation in the fingers. You are becoming aware of the energy coursing through them.

Now do the same thing, again in both hands at once, with the index and ring fingers (3rd and 4th). Take your time, see if you feel the energy before moving on to the next fingers. Use the same imagery for the ring finger and pinky (4th and 5th), and then the thumb and pointer (1st and 2nd). Your hands will feel electric with sensation.

Lastly, imagine a current of air under the palms, like a current of air a bird might soar on. Let your arms move gently around in space as if floating on this current of air.

Open your eyes but try to keep the sensation going. You can immediately go to playing any piece of your choice, or you can just improvise a simple melody and/or chords. Something lighter is preferable at first versus something that starts immediately with loud or demanding passages. If the imagery has worked for you, you will feel a heightened sense of touch. Your hands and arms will seem to know exactly how much pressure to apply to get the exact sound you want. After this energizing process, try playing as soft as you possibly can, and see if you don't get a very precise yet soft sound that may elude you at other times.

If this doesn't work for you the first time you try it, don't give up. It make take a few times to sensitize yourself. Try it again every time you sit down to play. I've never encountered anyone who doesn't get something from it. The more you do it, the less time it takes to start getting the "buzz" in your hands.

If you feel tense at any time during your practice session, or you feel you are not getting the sound you want, stop and repeat this energizing process.

In the age in which we live, when so much more is known about the body and the mind-body connection, and there are so many wonderful methods of achieving greater body awareness (yoga, tai chi, Qi gong, Feldenkreiss, Alexander Technique, to name a few), it seems such a waste to be using such old-school, brute force methods such as scales or Hanon or Czerny to warm up. The energizing process I've described here will help give you a physical and mental alertness, without tension, that is necessary for playing that is fluid and beautiful, and that will not cause any strain or injury.

Saturday, April 27, 2013

Coaching vs. Teaching

When I was a student at Manhattan School of Music, I had a teacher who had been a fairly famous pianist at one time. A student was considered, by most people I encountered, to be very lucky to have the chance to study with him. He was a kind and wonderful Austrian gentleman and certainly a very accomplished pianist, and for a time, at least, I adored him. But he didn't know how to teach (something I only realized towards the end of my four years with him, unfortunately). I'm not sure he really enjoyed teaching but he did it out of necessity as his own career in concertizing had waned. Possibly he enjoyed his few most talented and advanced students (I was not one of them!) who already played so well, that all he felt he had to do was help them with "finishing touches."  (The problem I noticed, however, with his students as well as students of other teachers, was that the students tended to start playing too similarly to their teachers, instead of finding their own styles or interpretations. We could often identify who the student studied with just from hearing his or her playing.)

What I needed, however, was a real teacher, someone who could help me with technical challenges. When I played I had fatigue and pain, and I did not believe that was just something to get used to or "muscle through." If I stopped practicing a piece for a week I could no longer play it. These and many other issues continued to plague me after years of lessons.
Many pianists who are quite accomplished do not necessarily know exactly how they do what they do, especially in the realm of technique, and therefore cannot help others. (Like athletes, they may have an innate physical talent that enable them to accomplish certain feats somewhat effortlessly.) In fact, much of the instruction I was given on technique I now know to be quite wrong, or at least wrong for me. There is not just one way of doing things; a lot may depend on the size of your hands, your particular body type and musculature, and other factors. (Even things like fast-twitch and slow-twitch muscles, a factor in many sports, may play a role.)
During the lessons he sat several feet behind me so he could not even see what my hands and arms were doing. How could he possibly help me with technique if he didn't even see what I was doing? He had a one-size-fits-all answer to technique: hours and hours of particular technical exercises. Those exercises caused me pain and fatigue and did not increase my technique in the long run. Yet he had no other solutions for me.
If I had been at the point where my technique was more advanced, perhaps I could have benefited from his vast knowledge of the piano literature. He could have possibly helped me with "interpretation" of my pieces. This is what I would call "coaching," essentially fine-tuning an otherwise high level of playing.

Thankfully, after I graduated from the conservatory, I found what I had been seeking: a real teacher. His name was Joseph Prostakoff. He didn't concertize (he said he couldn't deal with the nerves) but his first love was teaching. He had mostly advanced students and mostly students like me -- pianists who knew that what they had learned was not necessarily right for them and who were seeking something completely different. (Several well-known pianists who had significant physical problems and even injuries had gone to Prostakoff to learn new ways of playing.) It's not an exaggeration to say that I learned how to play the piano all over again, from the very basics of how to use my body, arms, hands, and fingers, right down to the physics of how the sounds are produced. He sat next to his students at the piano and his eyes and ears were on "high alert" to pick up the slightest unnecessary tension or strain in our bodies, the rhythm off by a fraction of a second (due to improper technique), the minutest variation in dynamics which was not intentional (again due to improper technique). And most important, he had a vast array of ways to deal with all of these problems. He always said he did not teach interpretation; instead, he wanted to give the me the tools to say what I had to say through the piano. I remember after we had worked on a particular passage, and I had played it with a freedom of technique and phrasing and a beauty and power I had not had previously, he winked and said: "You see, it's not because you understand Beethoven any better, but because you changed what you did physically." He was not against thinking about or exploring different interpretations, but what he made me realize is that you can't just slap "interpretation" (especially if it is not authentically your own) onto a faulty basic structure, like a coat of paint to hide the flaws underneath.

This is what I would consider to be real teaching. It would be finding the way to play which physically enables you to achieve the sounds you want. (If you've read my posts on technique, exercises, and so on, you'll see this is why I advocate never playing mechanically; it trains you to use technique and movements that don't produce the sounds you ultimately want.) It does not matter how brilliant your "concept" of a piece is, if you don't have the tools to physically produce those sounds.

I often see "Master Classes" offered with some pianist/teacher, and students flock to them (often at very high prices!). Most of these would be what I would call coaching. You could go to one and the teacher might tell you to play a passage louder, while another might tell you to play it softer. One might say you need more rubato and another may say need less. You are receiving their interpretation, which may not sound or feel at all authentic for you. Interpretation is just that: highly individual. There are certainly some pianists and teachers who are so brilliant and so perceptive it would be worth hearing their insights. But don't confuse coaching with teaching. If you are studying with a teacher who tells you to "learn the notes at home" so that the lesson time can be used for "polishing" or "interpretation," you have someone who wants to coach, not teach. If you are studying piano with someone but you feel your playing is not really growing, that you have problems which are not really being solved or even addressed, or you don't quite feel that you are 100% yourself at the piano, you may have a coach when what you need is a teacher.

Sunday, March 31, 2013

The Power of Music

In this post, rather than discuss specifics of learning and playing the piano, I want to share two inspirational stories with you. Both illustrate the extraordinary power music plays in our lives.

I recently read the book entitled The Secret Piano, by Zhu Xiao-Mei. It is the true story of a young woman's life in China during the 1970s and 1980s. Zhu Xiao-Mei touched her first piano at the age of three. Her mother played and they had a piano in their tiny apartment in Beijing. The family was already experiencing adversity due to the regime of Mao. It was thought to be bourgeois to own a piano and the family kept the piano a secret. Nevertheless, Western music was still allowed, and Zhu attended the Beijing Conservatory. But soon after, the Cultural Revolution swung into full force. Gradually they were no longer permitted to play Western music. Musical scores were burned. Professors were humiliated, beaten, forced to clean toilets. Some committed suicide. The students, including Zhu, were sent to labor camps far away from their families. At these camps they endured brutal conditions, deprivation, disease, and brainwashing. They were forced to spy and inform on fellow students who did not conform to the Communist ideas. Zhu describes how the lack of any music in their lives was one of the worst forms of deprivation. She and other students tried to find ways to secretly bring music back into their lives. At one point, amazingly, she was able to smuggle her piano, sent from Beijing, into the camp, and hid it in a freezing room, where she would go to play whenever she could. They risked punishment and death, but the need for music to fill the soul-crushing routine of the camps was stronger than their fear. Zhu was in the camps for over five years. Although she survived, her youth had been stolen from her.
As the Cultural Revolution thawed, she was able to return home to her family and found her way back to playing the piano. Eventually she was able to emigrate to the U.S., where she had to clean houses and babysit to make her way. She did whatever she needed, including a marriage of convenience, to allow her to stay in the U.S. and study piano. She longed to see Paris, and decided to move there. Eventually she found friends and influential musicians there who believed in her. She was able to make her first recording, of Bach's Goldberg Variations, to concertize, and to buy her own piano. She still resides in Paris.
The book is a moving account of how her deep love of music and her desire to play, against all odds, kept her alive and sane.

The second story is from a film, for which I have only seen the trailer, entitled Landfill Harmonic.

Cateura, Paraguay, is essentially a city built on top of a landfill. Many residents work as recyclers and scavenge through the landfill in search of sellable goods. In an area where musical instruments would cost more than a house and would be out of reach for all who live there, one man uses his carpentry skills to make full-size cellos and violins from scrap metal and wood. Orchestra director, Luis Szaran, and music teacher, Favio Chavez, have taken these recycled instruments and created The Recycled Orchestra, an entire orchestra made from trash. The film shows how trash can be transformed into beautiful-sounding instruments, but more importantly, it shows how music has transformed the lives of human beings. Music brings hope to the lives of children whose future might otherwise be spiritless. Landfill Harmonic is subtitled "The World Sends Us Garbage. We Send Back Music." It releases in 2014.

Please watch the trailer here:

http://www.landfillharmonicmovie.com/

Both these stories make me reflect on the times when I don't feel like practicing, or I choose to watch TV instead. Or the times when I grumble that I don't play as well as I would like to, or that the pieces are so difficult! I hope I never take for granted the presence of music in my life and the freedom to pursue my life as a musician.



Tuesday, February 26, 2013

Playing from Fake Books

Among my many students (most of whom are adults), some play exclusively classical music, some play exclusively pop and/or jazz, and many play both. In my previous post (Feb. 2011) entitled "Bridging the Great Divide," I discuss the benefits of playing multiple styles. I encourage that philosophy among my students and I practice it myself.

Here I'd like to elaborate on the benefits of learning to play from Fake Books (also sometimes called charts or lead sheets). For those of you unfamiliar with this: there is nothing fake about Fake Books. They are simply a method of writing out a piece of music (usually a song, but not always) where the melody is written in standard notation, and the harmony, or chords, are written in symbols. The player learns what these symbols mean and puts the two elements, melody and harmony, together. The chord symbols seen in the fake book give the basic information, the idea being that the player puts his or her own interpretation into the song by the arrangement made of those chords.

There are several benefits of incorporating this method of playing/learning into your skill set.

1. It is a great way to learn harmony and theory. Why learn about harmony from a dry book on the subject when you can learn it by playing music that is fun and beautiful? When you learn to read from chord symbols, you must learn how every type of chord is constructed. This means basic triads, 7th chords, 9th chords, even 11th and 13th chords (when you get more advanced). More importantly, you learn them not just mentally, but your hands learn to find them, fast, and to move smoothly from one to another. You learn first to play them in root position, and later in all possible inversions, and later in different types of arrangements, such as broken chords, and different "voicings" (how the chord tones are split between the hands). When you start to see and hear how chords progress, that is, move from one to another, you learn a great deal about musical structure. While this is not the entire body of what is called musical theory, it is, nevertheless, a huge component of it.

2. You can apply your understanding of chords to classical pieces. I find this skill so valuable, in learning pieces quickly, in memorizing, in accompanying (when you may have to sight-read a new piece and play the essential elements but not necessarily all the details). Virtually every piece of music in the classical world is based on chords (yes, even polyphonic music, which appears to be individual melody lines woven together, makes chords as the result of their melodies). For people who don't understand chords, any piece of music must just seem like a lot of random notes. When I play classical music I always know what chord I am on -- it has just become second nature and I barely have to think about it. When it is very complex, I take the time to analyze the chords and often write the symbol into the music. I can't stress enough how much easier it makes it to learn, and especially to memorize, a piece.

3. You are freed from the tyranny of the written note. I find it so surprising, and a bit sad, that so many pianists can only play something if they learned it from the written page where every single note was given to them. So many people who "play the piano" can't get through a simple song such as Happy Birthday if they didn't have written music to learn it. As you know from previous posts, I stress the importance of playing by ear, and that also means learning to harmonize songs. When you play from a fake book, it's true that it is still a written form, but the idea is that you learn to make your own arrangements, put your personal stamp on the song. This means a bit of improvising, playing that comes directly from your heart, mind and body. As we know from history, the great composers were all great improvisers. The improvisations of Beethoven, Chopin, Liszt and many others, are legendary. We need to incorporate some of that spontaneous outpouring in our playing. Fake books can help us do that.

4. It is fun, and perhaps that's the best reason of all! I recently gave a Valentine's Day concert where I played 28 wonderful songs about love, from such great composers/songwriters as George Gershwin, Cole Porter, Rogers & Hammerstein, Irving Berlin, Lerner & Loewe, Randy Newman, and Joni Mitchell. Some I learned from written-out arrangements, some from Fake Books (so the arrangement was my own), and some were completely by ear. I had fun doing it and the audience loved hearing these familiar songs, even without their lyrics.

If the idea of playing from Fake Books is new to you, I urge you to give it a try. While it is possible to learn a great deal by reading about chords, it is best if you can find a teacher to help you through the process.

Wednesday, January 30, 2013

Get Physical!

People who don't play an instrument perhaps don't realize how physical, how athletic, it is. Great musicians may make it look easy, but anyone who plays, especially at a high level, knows that there is intense physical activity going on. Pianists spend thousands, if not hundreds of thousands of hours, working on technique, to develop the speed, power, and coordination necessary for much of the piano literature.

However, there is a tendency to draw a distinction between technique -- the physical side of playing -- and "expression" -- the artistic side.  Some people believe you can practice technique without expression and it will still be of benefit. That is why most teachers will give you technical exercises which are not meant to be beautiful pieces of music. I don't do this, and I believe practicing in this way does more harm than it does good.

The reason for this is simple: when someone plays beautifully and expressively, there is something physical they are doing which makes it sound that way. While you must start with the intention to play beautifully, that intention has to translate into something you do physically to achieve the sound you desire. Therefore, if you practice a piece of music purely to master the technical aspects, and do not infuse it with your full emotional involvement, you are doing something physically that you do not intend to use later when you play "expressively." What could possibly be the point of practicing in a manner in which you don't intend to ultimately play?

Another problem is trying to approach the music too intellectually, separating the mental from the physical.  Some musicians spend a lot of time trying to decide on, or develop, their "concept" of the piece. There is no doubt that a Beethoven Sonata, for example, has great depth and requires a fair amount of understanding of music to truly grasp what is going on. However, just because you decide on your concept of the piece does not necessarily mean you can translate that into physical movements which will create the sound you want. You may wish to phrase it in a certain way, but if your movements are jerky, or you play with too much emphasis on the small movements of the fingers (as opposed to large movements of the arm which blend the smaller movements into a long phrase), you won't get the phrasing you want, regardless of your "concept."

I am not advocating being a dummy and not thinking about the music. However, in a contest between the mind and body, the body will always win! (It's a survival mechanism). I have been reading a great deal lately about our "animal brain" and how it rules a lot more of our actions than we care to admit. I believe that how we move, our day-to-day ordinary walking and so on, is governed by that animal brain, and our movements when we play the piano are no exception. However, we can communicate with the animal brain and change how we move, but it has to be done with very subtle methods. Most people just practice and play the same way, over and over, and don't fundamentally change anything. With my own playing, and with my students, I try to do things which give the body the experience of doing something differently, and the body will often be able to pick it up, sometimes rather quickly. For example: do you want to play an ascending scale or arpeggio very rapidly and smoothly? Try playing a glissando and then immediately play the scale or arpeggio, to give the body the experience of a long fluid movement. This is called "transferring." (See my previous post on Creative Practicing for more on this subject.) The reason why this works, I believe, is that you have communicated with some very deep part of the brain that controls movement. You've given it a taste of a new way to play, and the body, as I often say, "wants to do what it just did," so it essentially copies the coordination from the "easy" part to the "harder" part. I want to underline, however, that it still must be with emotional involvement, meaning that you still feel emotionally connected to what you are doing. Otherwise, as mentioned, the physical movements will be different than what you will need when you want to play expressively.

If you try to tackle technically challenging music head on, so to speak, by just playing it over and over, you may win the battle but lose the war. You may play the music with some degree of speed, power and accuracy, but it may not be beautiful. If you approach it as a "difficulty" to be overcome, the body responds with different movements than it does it you approach it as something easy and natural. That is why I say "don't practice the difficulty." Try to find ways to make the body experience it as something easy and fun. Another way to do this is to create a fun little improvisation similar to the phrase you are working on. Then immediately play that part of the piece and you will be amazed at the result. When my teacher, Joseph Prostakoff, first introduced me to this approach, and I expressed amazement at how well it worked, he would say, "You see, it's not because you understand Beethoven any better, but because you changed what you did physically!"

Try to approach playing your instrument as just that -- PLAY. No one ever gave a gorgeous performance that didn't feel physically fun and exhilarating to them while they were playing. While music certainly transcends the physical, the sensation of physical pleasure is a good place to start. Try not to over-think it. Always be emotionally invested in it. And do get physical!



Sunday, December 30, 2012

Pianist, or Musician?

You may wonder about my title. If one is a pianist, isn't one automatically a musician? Not necessarily.

I've encountered many people who are pianists, that is, they play the piano with some degree of proficiency. Some even play with emotional involvement and expressiveness. But to be a musician, I believe, requires something more.

To be a musician, to me, means a broad and deep understanding of music. For instance, many people coming to me for lessons who have played and/or had lessons previously do not know the basics of how our music (Western music) is constructed. If I ask them what key a particular piece they have played is in, they don't know. They may not even know what it means to be "in a key." They may have practiced scales as an "exercise" but don't know that scales are our basic tonal material, our "alphabet," if you will. Some have told me they never knew why, for example, a given piece had to be played with all F-sharps instead of Fs; they never knew that means it is in the key of G Major (or E minor). They may have read and learned to play "the notes" of the piece, but they don't understand what is behind the notes. If I ask them to identify the basic harmonies (chords) of a section of the piece, they can't; in fact, many do not even realize that chords are the basic building blocks of most of our music. To me it is just unfathomable how one could play a composition and somehow think it is just an assortment of notes, and not realize the underlying structures which make it a unified whole.

To be a musician also means a broad range of musical skills. Again, many people have learned to read music and can play the notes as represented on the page. But if I ask them to play Happy Birthday by ear and harmonize it with three simple chords, they can't do it. How can this be? The Chopin Nocturne they just played for me is much more complex than Happy Birthday, but they could play it because the page told them exactly which notes to hit, and when, and they simply "obeyed." But if they have to play music where the knowledge must come from within them, they are unable. I cannot call this person a musician yet. For this reason, I have all my students play simple music by ear, learn about chords (simple first, then more complex, such as 7th chords) and their relationships to each other, how they "progress" from one to another. A real musician can't be comfortable playing in just the key of C and maybe one or two others; a musician must play in all keys with ease. For this reason I have my students do a lot of transposing.

Not everyone wants to be a composer. And not everyone wants to improvise. But any musician should certainly be able to sit down at his instrument and play something without the need for written music. (There is a joke among jazz musicians that goes like this: How to do you get a musician to stop playing? Put sheet music in front of him.) I make sure all my students can improvise at least some simple melodies on a simple chord progression, and have it make sense. (I show them how to choose a short motif and build upon this, rather than just randomly search for notes.) If you can only read music and can't do this, it is like being able to quote from a book but not able to construct a sentence of your own.

I consider it my mission to help create musicians, not just people who can play the piano. Music itself is an incredible mystery: how it makes sense to us, why it moves us the way it does, why it has become such an important part of life in every culture on earth. Yet, a great many aspects of music can be understood and grasped by our minds, and this knowledge does not lessen the mystery; I believe it increases the sense of wonder we have for music. The more you know, the more marvelous it is. If you play an instrument, I encourage you to strive to be a musician.

Sunday, November 25, 2012

The Cosmic Mystery of the Musical Scale

You may wonder about my title: how could the musical scale have anything cosmic, or anything mysterious, about it? You've probably all the heard the familiar do-re-mi-fa-so-la-ti-do many times, and if you are a musician, you've played it hundreds or probably thousands of times. If anything, it may even seem quite mundane.

Quite to the contrary, I find the scale to be fascinating, and an endless source of wonder in respect to how it is the life force behind all our music. (I am speaking here of the Western scale and Western music, though the same concept can be applied to other music and their scales.) It is not only the tonal material which our music uses, it is also the organizing principal, that which gives the possibility of movement and architecture to our music.

Try the following experiment: play an ascending scale, for example the C major scale, on the piano or any other instrument. Do it in the following manner. Play C (do) and then D (re). Listen to what wants to happen. Does the re want to move forward or fall back to do? I think you will find it does not yet have enough momentum to move forward, but can easily fall back to (or resolve to) do. Now play C-D-E (do-re-mi). What does that want to do? It has more momentum than the previous step, but barely enough; it can also easily fall back to re and then do. Now play all the way up to F (fa). You will hear an unmistakable difference -- a feeling of starting to travel or make progress....yet.... it is still somewhat easy for it to fall back to re, at least, if not all the way back to do. Now play all the way up to G (so). If you are really listening you will hear that feeling like you have reached the crest of the hill; there is no going back, only forward. As you play the scale up through A (la) you will feel the momentum increase. When you get to B (ti) the urgency to get to the final C (do) is very strong; you simply cannot go anywhere else. The final tone, ti, is often called the "leading tone" for this reason. (I thank the great writer/musicologist Victor Zuckerkandl for introducing me to this fabulous experiment over 40 years ago in his book The Sense of Music.)

I suppose there are two camps on this matter: one that says we hear it this way because we are so used to it operating in this way in our music, and another camp which would say it is something inherent in the scale itself. I am in the latter camp. There is something about the dynamics of the scale which cause us to experience it in this way, which is why, I believe, this particular scale took hold and became the basis for our music for so many hundreds of years. It gives a dynamism, a richness to the music that you simply don't get in, for example, a pentatonic (5-tone) scale.

The example we've just used is the scale we know as the Major scale (the Greeks called it the Ionian scale). What about the others? The minor (Aeolian) scale has some of the same feeling, but lacks the drive at the end with the leading tone. For that reason, the minor scale has been altered since about the mid 1600s (the so-called "harmonic" minor) to have a ti, or leading tone, raised to be the same as the major scale. The other scales, Lydian, Phyrigian, Dorian, etc, have to a large extent fallen out of usage (some ethnic music still uses them, and pop and jazz musicians use them as a basis for improvisation but they are rarely the basis for an entire piece of music).

Coming back to the dynamics of the scale tones, you will see that the first tone of the scale (do) feels like the center, or home. The 5th tone (so) feels as far as you can get away from the center, or home, before you feel like you are returning to it. This sets up one of the most important aspects of the scale, the polar opposites of the one/do and the five/so. You will see the importance of five in our music everywhere (the Circle of Fifths). The Greeks called the one-five relationship in music the Golden Mean or the Golden Ratio and considered it to be the "perfect" relationship. (Mathematically it is the ratio of 3:2) It was used in painting and architecture as well.

It is difficult to say whether the dynamic qualities we experience in the scale are all the result of mathematics. Some have believed so, and some believe it even goes beyond mathematics to the nature or the structure of the universe. The mystic G.I Gurdjieff (1877-1949) and his student P.D. Ouspensky believed the scale had cosmic meaning. In his book In Search of the Miraculous, Ouspensky devotes pages and pages to Gurdjieff's concept of "octaves" - the musical scale taken as a sort of universal yardstick for determining the measurements and proportions of all of nature's parts. (See www.progressiveears.com/frippbook/ch07.htm).

With my beginning students, and even some more advanced students coming to me from other teachers, I always have them learn to play a scale (with simple fingering, 4 notes in the left hand and 4 notes in the right) at the very first lesson so they can begin to really hear the scale and understand how it is constructed. I make sure they understand I am not giving it as a "finger exercise" to be done over and over; it should just be done a few times, just to experience it. How sad it is that thousands upon thousands of musicians have done endless hours of scale practice, and yet perhaps never really heard or understood the magic and mystery that is our simple musical scale.