Dots and Ties

In this lesson we will explore two ways of lengthening a note's duration. The tie is probably the simpler concept, so let's start there. A tie is a curved line connecting two noteheads at the same pitch. Click the button below to add a tie to the example. When notes are tied together in this fashion, we simply add their durations together. In this case, the quarter note F (1 beat) is tied to another quarter note F (1 beat), which results in a single note F that lasts for 2 beats.

Let's compare what the music above sounds like with and without the tie:

Play without a tie

Play with the tie

Notice how the F on the fourth beat lasts for two full beats with the tie? This is useful in a number of situations, one of the most common is when a note needs to last longer than the given meter allows. This is the case with the example above: the F note beginning on the fourth beat has been made to last for two beats (which would be too many beats for its measure), so the use of the tie allows it to sound past the barline into the next measure.

The augmentation dot is a small black circle placed just after a note or rest and increases that note's duration by 1/2, in other words, it multiplies the note value by 1.5. Let's begin with a half note. Click to see that a half note is worth 2 quarter notes. If we add a dot to the half note, we add half its value. As we can see above, half its value is a quarter note, therefore the dot adds one quarter note to its duration. We now have a half note that lasts for three quarters instead of two.

Let's see this in action again with a quarter note. As we learned previously, a quarter note is worth 2 eighth notes. If we add a dot to the quarter note, we need to add half its value. In this case, half its value is an eighth note, so we need to add an eighth note. You might begin to notice a pattern here. Symbols that normally divide into two always become worth three when the dot is applied. In this case, a quarter that is normally worth 2 eighths is now worth 3 eighths.

We know that a dot adds half the note's value (or multiplies it by 1.5). But there is another way to think about it that might seem a bit more intuitive. We have seen so far that each dotted note presented has become 3 of the next shorter duration. Or we might say that dotted notes are always worth 3 of the next faster type of note. For example, the next faster duration of a whole note is a half note, the next faster duration of a half note is a quarter note, the next faster duration of an eighth note is a sixteenth, and so on.

To take advantage of this pattern, try employing this simple process: when you encounter a dotted note, try just saying this phrase to yourself, "this dotted note is worth 3..." and then filling in the rest of the phrase with the next faster note type, i.e. whole to half, half to quarter, quarter to eighth, eighth to sixteenth, etc.

Try employing this concept here, once you have an answer, click a button to see the answer:

Hopefully that went well! Just one more concept before you tackle your next exercise.

In the coming exercise, you will need to compare notes sometimes with dots and sometimes without. There are a few strategies you can employ to help speed up the process. One is, if the notes on both sides of the equal sign have dots, you can ignore the dots (you can cancel them out), as the relationship between the two notes hasn't changed. For example, there are two eighths in a quarter. There are also 2 dotted eighths (3 sixteenths each) in a dotted quarter (3 + 3 = 6). This will always be true. For example, there are four sixteenths in a quarter, there are also four dotted sixteenths in a dotted quarter. As long as you are comparing notes that both have dots, you can ignore the the dots.

The other type of question may involve comparing a dotted note to a duration that is smaller than the 3 to 1 ratio we have seen thus far. Up to this point we have seen that a dotted quarter is equal to three eighths. But what if you are asked how many sixteenths are equal to a dotted quarter? You just need to add a single step to your thought process: begin as before with your phrase, 'in a dotted quarter there are 3 eighths.' Then it's just a question of adding up how many sixteenths are in those 3 eighths. As you know, there are 2 sixteenths in each eighth. So the answer is that there are a total of 6 sixteenths in a dotted quarter.

Feeling like you need to go over that just one more time, but in a slightly different way? Check out these great explanations of the same concept: