Monday, January 28, 2019

Musical Numerology

I'm always fascinated by the connection between music and math. Music is full of mathematical relationships. And it seems to be the case that many people who have an affinity for music also have an affinity for math, and vice versa.

There is also a connection between music and numbers themselves. I'm calling this "Musical Numerology."

Many spiritual and philosophical teachings have discussed the importance of certain numbers in our cosmos and in creation. For example, the philosopher/teacher G.I Gurdjieff talked about the "rule of three" and the "rule of seven" as playing a large part in our solar system and in the organization of many aspects of life on earth.

There are three numbers which play an important role in music: three, five, and seven.

Three:
There are many instances of three in our culture, such as the Trinity in Christianity. In Western music, three can be seen in the construction of the most basic chord, a triad, consisting of three notes. In triads and in "expanded" chords, such as seventh and ninth chords, each tone is always separated by the interval of a third.
Many of our forms that larger pieces use are three-part forms. The most common of these is known as an A-B-A form, which consists of a first section (A) followed by a contrasting section (B), followed by another A section, which can be an exact repeat, or somewhat altered. One of the most enduring forms in our music is Sonata Form, which uses this ABA form on both a macro and micro level. Most symphonies, sonatas, concertos, and many of the large-scale pieces from the last three centuries or so have three movements (although many composers deviated from this and had anywhere from two to four movements); the first, in the original key, was often fast; the second movement often slower, and in a contrasting key, and the third movement again in the original key. The first movement itself is in "Sonata Form" which consists of three parts, an Exposition, a Development, and a Recapitulation.
This three-part form has proven to be so satisfying to both the composer and the listener that we just don't seem to be able to abandon it.

Seven:
There are many instances of the importance of 7 in religion and philosophy, probably starting with the Creation Story of 7 days. This of course is why we have seven days in our week.  In Western music we have a basic building block, the scale, consisting of seven tones. Composers have experimented with other options, but none of these have taken hold. There is something about the 7-tone scale that seems cosmically right. It is believed that the Greeks took the "distance" between a given tone and the tone that vibrates at exactly twice the frequency of  the first tone, and the division of that distance into 7 tones ensued from that. (They are not equal divisions of the octave, however.)That distance is referred to as the "octave." (There is quite a bit more complexity to this which goes beyond the scope of this post.)

Five:
The importance of five in music is one of my favorite things to talk about. Many cultures (not ours, however, as explained above) have based their music on a 5-tone, or pentatonic, scale. As an example, just about every Spiritual you can find has a melody based on 5 tones.
In Western music the importance of five can be seen in the Circle of Fifths. On the most surface level, this is a picture of the relationship of the tonalities to each other. The key of C Major has no sharps or flats; go up 5 tones (in that scale) and you get G Major with one sharp. The significance of this is that the most closely-related key or tonality is five tones away. On a deeper level, music tends to want to move by the interval of a fifth. This is seen in the roots of chords as they progress from one to another. The most common cadence (or ending) is V to I. (We use Roman Numerals when we refer to the degree of the scale.) The next most common is IV to I (which can be heard in the "Amen" of almost all religious music). It should be noted, however, that IV to I is also the relationship of a fifth, but going the opposite direction around the Circle of Fifths.  This is not just true of Classical music; in jazz, the most common progression is II-V-I; the II is five away from V, so II-V-I is a "chain" of fifths.

This post just scratches the surface of understanding Musical Numerology. There are hundreds of books and articles written on this subject. I always have felt that music is somehow an auditory representation of our cosmos, closely related to physics, math and astronomy. Hopefully this piques your interest to find out more about this amazing connection.

Sunday, January 27, 2019

Can you teach yourself the piano?

Over the years, many people have come to study with me having previously tried to teach themselves to play the piano. At some point, they get frustrated that they seem to be making little progress, and that it takes them forever to learn something new. In addition, once they learn it, they find they quickly forget how to play it.

You would think in these days of having YouTube and all kinds of people giving tutorials online that one could just learn that way. How tempting, to save the many thousands of dollars one would spend on years of lessons and just use the internet instead. Unfortunately, it is almost never successful.

Another method people often try is just to teach themselves the names of the notes on the staff, and then try to pluck their way through a piece, slowly, note by note, one hand at a time, and often trying to memorize a measure or two as they go. (When reading is difficult, people try to memorize right away; but this is like cramming for a test -- the memory doesn't stick long term.) With this method, they usually don't learn to read rhythm correctly and have to supplement their learning by listening to the piece on the internet to get the rhythm right. This method is excruciatingly slow. It often takes many months to "learn" one short piece. People taking this approach will be likely to choose pieces that are light years beyond their abilities. Even if they manage to play the piece, slowly and haltingly, they are not really learning any skills, and will have to repeat the process with the next piece. They know the piece doesn't sound beautiful when they play it, but they can't figure out what to do about it. Many people mistakenly believe that learning to play is simply a matter of hitting the right notes. If this were true, there would be many more great pianists than there are. Just like playing by copying someone on the internet, this method also never works.

Here are some of the reasons.

1.The physical aspect
Playing the piano (or any instrument) is highly physical, much more so than it may look to a non-educated observer. It is just as physical as any sport, and in fact, probably more so.
Without developing a good technique you will be limited as to what you can learn to play and master. And you run the risk of doing harm to your hands, fingers and arms by practicing with bad technique. Even something so basic as sitting at the wrong height can cause problems such as carpal tunnel syndrome.
For this reason you must have a teacher who is observing you as you play, and teaching you technique. Watching someone play on YouTube is not the same as having someone working with you one-on-one. And the person you are watching online may have bad technique as well, but you can't always tell by how it looks on camera. In fact, the camera is usually just showing their fingers. You can't see at all what is happening in their arms, which is equally, if not more, important. When most people watch a video of someone playing, they are just trying to copy "the notes" and are not focusing on technique. With this approach, you will have to start at square one learning each new piece of music, because you won't really have learned skills. I say to my students that I am teaching skills, not pieces.

2. Understanding
In most of the videos and tutorials I've seen, the person giving the tutorial just focuses on showing you the notes to play. If you spend a great deal of time watching it over and over, you can eventually copy what the person is doing. But you won't know why. Very few explain in any detail why you would play a certain jazz tune, for example, in this way. Or they explain it in terms which they understand, having played for years, but which you, as a beginner, will not understand. So again, you are stuck with just copying what you see. You won't have the understanding to apply it to another piece of music on your own. So you are locked into finding a video for everything you want to play.
This is so time-consuming you will probably eventually give up.

3. Expression
When you watch a video and copy the person, you are also copying their interpretation of the music. This is true regardless of the genre -- classical, jazz, etc. Consciously or unconsciously, you will tend to play the piece just like that person, with the same dynamics, nuances of timing and phrasing, and so on. Once you hear something a certain way, that may just be how you will continue to hear it, especially if you are a beginner. And why would you want to play like someone else? Hopefully, one of the reasons you want to play the piano is to express your self.

4. Ear training
Playing an instrument is an "auditory sport," I often say. As such, you need to be training your ear. This aspect of music education is often overlooked. If you are not working on your ear, you can't progress as fast or play very complex music. It is also the reason you may not be able to memorize, or, if you do memorize a piece, you quickly forget if you don't practice it constantly. Watching something online requires mostly using your eyes and is doing very little to develop your ear.

Learning to play the piano takes a lot of work and dedication, but of course can be hugely rewarding. If you are going to invest the time and energy into learning to play and adding the joy of playing to your life, it is essential to invest in good training. It is not easy to find a teacher who has the knowledge and experience to teach all the many aspects of playing the piano, but the posts in this blog may give you some insights into what to look for in a teacher.