The relationship between music and math is inescapable. Think of any musical instrument as a big counting and calculating machine.
Bach, for example, used a system (see the drawing further below) called “figured bass,” in which numbers (figures) were used as a type of shorthand that showed which groups of keys (chords) to play with a minimum of confusing graphic notation.
These numerical relationships between members of the chord groups are identical with the numbers in Piano By Number.
Modern “guitar” chords such as you will find in all pop sheet music (Cm6, Dmaj7, etc.) use numbers in a similar but simplified way.
On the level of physics and acoustics, all musical sounds can be expressed as ratios of other sounds.
Rhythm in music is a simple mathematical device in which time is divided into units and then presented in a dizzying variety of combinations and patterns.
When introduced properly, playing the piano can be a very positive force in a young child’s life. If you can interest the child in the piano in a friendly way, the learning will start.
If you force it, you may as well be asking them if they want more homework or vegetables.
The piano has many attractions for a small child.
Unlike the violin or guitar, or almost any orchestral instrument, every note is laid out in a row in front of you. One finger, one note. Try that on a violin!
For children, this means that they may begin making music as soon as their index finger can remember a few patterns.
Thus the layout of the piano keyboard is inherently friendly to the child. And if one begins with only the white keys, it is easy to begin navigating and building habits.
Next to attract the child is the simple math involved.
For example, if the keys are numbered from 1–12 as in Piano by Number, the child immediately sees a graded, ascending relationship between the numbers and the keys.
And when fingering is introduced, this mathematical basis is reinforced, for now the keys are numbered, and the fingers are numbered as well. For beginning hand positions, C position for example, the finger numbers and the key numbers are identical.
Several abstract math skills are instantly explored at the piano. Simple counting, pattern recognition, left/right, up/down are all explored the instant a child touches a group of piano keys.
The relationship between math and the piano, and music theory in general, becomes even more elegant and complex the further one goes into music theory.
At simple levels that a child can reach, many of the concepts of beginning keyboard harmony prepare a child for the concepts of algebra.
For example, when a child sees the chord symbol: Dm (D Minor) they are required to decipher the first letter as a group of keys having a certain mathematical basis, placed at only one type of location of the keyboard.
But Dm, as above, requires in addition the deciphering of the second letter, the small m, which then requires the lowering of the middle key of the chord (can you find the middle key in all this calculation?)
You may have noticed the similarity, in concept, of Dm and, say, a mathematical equation such as A/B –2 = ? (my apologies to the math buffs.)
In other words, piano, like the higher levels of math, requires knowledge of basic procedures that are then modified in more and more complex ways.
The difference between math and music is, of course that a child can use math to play POP GOES THE WEASEL on the piano, and will only use math to someday balance their checkbook.
Kids resist vegetables in the same way they resist math.
Kids do not resist music and the piano if presented properly.
Kids love the bubbly stuff that is music, and the piano can be the vehicle that gets them directly involved with the math in music.
Ask a kid if they would rather do math or music, and they will say “music,” not realizing that on so many levels, they are one and the same.
Piano is thus “fun math.”
Copyright 2013 Walden Pond Press
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