Music is Math... 1-2 + 1-8 = ? ! Segment One

3-4 2-8 + ...AT 180 MILES AN HOUR!!!

Well....maybe not THAT fast but musicians do process a lot of math in their heads VERY quickly... and they don't even realize it because they are so busy having fun and making wonderful music! Every time they play their instrument

Let's explore what Music and Math have in common. Musicians use numbers to count beats. Mathematicians use numbers to count all kinds of things. Musicians divide notes into smaller notes. Mathematicians divide numbers into other numbers. Musicians add note values together. Mathematicians add numbers together. Musicians use note symbols to represent fractions. Mathematicians use fractions. Can you find a common word between each colored sentence? Math + Music Forever ! I bet you could think of more things if you had time.

Let's compare musical notes with math fractions. Chart 1 Let's compare musical notes with math fractions. Did you know that each note symbol actually represents a fraction? A whole note: is just our way of saying "one whole" or "1". A half note: is our way of saying "one half" or "1/2". A quarter note: stands for "one quarter" or "1/4". An eighth note: stands for "one eighth" or "1/8". A sixteenth note: stands for "one sixteenth" or "1/16". Yes, there are even smaller notes but we won't worry about those right now.

Music is Math... 1-2 + 1-8 = ? ! Segment Two

This is a chart of musical notes and how they break down into their smaller parts. Let's see if it can help us do some musical math. Chart 2 + = N Can you change the musical note symbols into math fractions? Check out the next slide for the answer.

N N N Did you figure it out? Good job! 1-2 1-4 Oops, mathematicians! + = Did you figure it out? Good job! 1-2 + 1-4 = N Oops, mathematicians! Now we have created a problem for ourselves. Can you tell what it is? Right! We can't add these unlike fractions together. We have to divide the by to figure out how many quarters it is. Then we can add them to get "N". 1-2 1-4 So let's do that. 1-2 .-. 1-4 N = Just invert the dividend, multiply, and 1-2 x 4-1 = OK! Then N = ... Of course musicians have been conditioned to know the answer, or they could just look at their chart if they were really stuck. Hey!

but in a different way...I get it now! But N= either way. 2 No peeking! Wait a minute! This chart shows the same thing as a Math visual but in a different way...I get it now! But N= either way. 2 So now we can add the like fractions + =N N= Final answer 2-4 i-4 3-4 Right! But musicians would just have been taught that there are two quarter notes in a half note so they could tap their foot to the right amount of beats. We don't always realize its Math, so its a good thing we go to Math class! By the way, the "tie", ,is our musical "plus" sign. Its how we add our note values together. Wow! A musical "+"! I am really getting to understand how Music and Math are partners that can help people understand both subjects.

We'll try a fraction division problem. Hey! Let's have a race! We'll try a fraction division problem. You solve it with Musical Math. I'll solve it with Mathematics. Let's see who gets the right answer first! OK, but we both need to show our work. Ready, set.......change the slide!

N N N N 1-2 .-. 1-8 .-. 1-2 .-. 1-8 1-2 8-1 x 8-2 .-. = = = = N = How many are in a ? 1-2 8-1 = N x N = 8-2 8 2 =N .-. Got it! the Final Answer is... Got it! the Final Answer is...

Who turned out the lights? Hey! Who turned out the lights? So, did you get the answer? Yeah, but I couldn’t see to write it down! Oh well...let's just say it together. N= 1,2,3...

"4"

? ! 1-8 + = 1-2 Music is Math... Segment Three

34 34 The Math Behind the Music N=3 N=3 N=3 The time signature or "meter" is located in the beginning of a piece of music. 34 34 N=3 N=3 N=3 The music is divided up into boxes called measures. Each measure MUST contain the SUM indicated by the TOP number of the time signature. The SUM must be reached by adding musical note values.

34 A note to Math teachers. Students should skip this slide. The BOTTOM number indicates which note symbol receives the value "1". In this example, the 4 stands for "quarter" as it does in Math. So, the quarter note is worth "1" beat. In this example each measure must add up to "3" quarter note beats. Yes, advanced Mathematicians, it could be called a "ratio". It is easier to just learn how note values group or divide up to make beats. Musicians must understand PARTS OF A WHOLE and ratios. That's what Musicians do, VERY QUICKLY and The next page contains Musical Math problems. We hope you will try a few with us. YOU CAN TOO!