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Musical Mathematics

Dotted & Tied Notes

In music, there are many different lengths/durations of notes. The basics types are: whole notes, half notes, quarter notes, eighth notes, and sixteenth notes. In 4/4 timing, a whole note is worth 4 beats, a half note is worth 2 beats, a quarter note is worth one beat, an eighth note is worth 1/2 beat, and a sixteenth note is worth 1/4 beat. The reason why a half note is called a half note is because it is half of a bar long in 4/4 timing. Everything in terms of lengths of note is referenced as if it were in 4/4 timing.

However, what do you do when you come across a dotted note, or two tied notes? Understanding music has mathematics in it is the key to unlocking this mystery. A musical tie means musical addition. A musical dot means musical multiplication. So what’s the scoop?

In the first example in the picture is listed a dotted half note. The first dot attached to any note adds half the value to it (like multiplying by 1.5). So 2 x 1.5 = 3. Therefore a dotted half note is 3 beats long. The second dot adds 1/2 + 1/2 of the half. In other words, it is multiplying the original note by 1.75. In the second example is a double dotted half note. So 2 x 1.75 = 3.5. Therefore a double dotted half note is worth 3.5 beats. Every dot after that proceeds to add 1/2 of the previous dot’s note value onto it.

Now let’s get to tied notes. They are a bit easier than dots. Two (or more) tied notes mean you simply add the value of two notes together. In this example, you have a whole note tied to another whole note, then tied to a quarter note. Musical addition would say that the amount of beats you would hold this note for would be 9 beats, because a whole note is worth 4 beats, and a quarter note is worth 1 beat. Therefore, 4 + 4 + 1 = 9.

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