You've read in my previous posts that I encourage students to play music other than classical music, at least a little, even if they are mostly interested in classical. It has a lot of skills to teach you.
When beginners start with me (and even not-so-beginners), I always start with playing by ear. They pick out the melodies for familiar songs such as Happy Birthday, Silent Night, Amazing Grace, and so on. I teach them about chords, starting with major triads, but they need to learn all twelve, not just the ones which fall all on white keys (which I've seen many students do). They harmonize the songs with the chords (just three chords for those songs), by ear, but with my guidance as necessary. We continue on to more songs, finding ones that require more chords.
Not only do you need to use your ear to determine which chords to select, you need to use your ear to tell you where they come. This will build your sense of rhythm and your understanding of musical architecture. Many people think the chord is one that has the melody note in it, but this is not necessarily the case. The musical architecture is more important here. You may not quite understand what I mean by architecture, but just for starters, read my post "Going Away and Coming Home."
Soon after, they learn all twelve minor chords, then augmented and diminished traids, then 7th chords, eventually learning all five kinds of 7th chords. At this point they know 108 chords. It is important to stress here that you must learn the chords by learning how they are built, not reading them from a book or chord chart. If you learn them by reading them or other methods which just show you which keys to play, you will never really know them well. It's the difference between giving you a fish and teaching you how to fish. If you currently have a teacher who cannot teach you this, or thinks it is not important, I strongly suggest you find a new teacher. (One of my current students had a previous teacher who told him that "the learning curve was too steep" to learn all about chords! Isn't that what a teacher is supposed to be helping you with?)
You originally learn all the chords in root position, but later your must also learn to play the inversions with ease. This means the notes of the chord are re-arranged. It is the equivalent of a whole egg vs. a scrambled egg. You must know the "egg" first, then you can scramble it.
In addition to being able to play dozens, if not hundreds of songs, you will be getting a lot of ear training and a lot of experience with chords. Not to mention that most people find this fun and satisfying. They can sit down at the piano and play for friends and family at a social gathering, playing music which many people may recognize and really enjoy.
The next step would be to play from "fake books" (also called "real books") where the melody is written in standard musical notation but the chords are written with symbols, which of course I taught them when the learned the chords. With this approach, you can learn and play many songs you might not have been able to figure out by ear. (Which doesn't mean you shouldn't still try.) You would continue playing the chords blocked (meaning all the notes at once) in root position in the left hand. This arrangement sounds perfectly fine, although it lacks something that a more complex and elaborate arrangement would have.
The next step, therefore, is moving the chords to the right hand, which frees up the left hand to play in the lower registers of the piano, which gives more richness to the arrangement, as well as being able to add some rhythmic interest. To put the chords in the right hand means that the melody note must always be at the top (the highest note). If it were not, we wouldn't identify it as the melody. (You don't want to "bury" the melody note inside the chord.) That means the chord tones will fall underneath the melody note. Therefore, many, if not most, of the chords will end up being an inversion (as opposed to root position). It takes a while (for many students) for the hand to just find those chords quickly, but eventually it will.
The left hand arrangement will differ if it is a slow, lyrical song, vs. an upbeat faster song. It is beyond the scope of this post to describe the myriad things the left hand can do. But even if it is simple, having chords in the right hand and even just one note (probably the root of the chord) in the left, will give you a very pleasing result. And remember, if you can do this, without having read the chords in notation, from a book, it means you really know your chords.
Even if you think you want to play 100% classical music, I believe it's wise to devote some time to doing this as well. I've had many people come to me for lessons, and they may play a Chopin Nocturne, but when I ask them to play a simple rendition of Happy Birthday they can't do it. They ask to see the sheet music! Or I will point to a place in their classical piece and ask what chord it is, and they don't have a clue. Even though I've seen it dozens of times, I'm still shocked when this happens. Chords are one of the building blocks of our music. If you play clarinet or any single-line instrument, you don't have many opportunities to learn about harmony (chords), unless you go to a good music school or conservatory, in which case you absolutely are required to learn them. But as pianists, we are virtually never NOT playing chords. So it behooves you to at least understand what you are playing, but even better, to achieve mastery of it.
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