A tieis a curved line that connects two adjacent notes of the same sound. This turns the two notes into one single sound and the duration of the tone is the sum of both note values.
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A dotcan be placed to the right if the note head, which lengthens the value of the note by half of the notes value. So if you have a half note, the dot adds on a quarter. A second dot can be added. The second dot is related to the first dot by lengthening the dotted note value by half of the length of the first dot. If you have a half note and add two dots, the first dot adds a quarter and the second dot adds an eighth note. This works the same for rests.
A note value can bedivided and subdividedin equal parts. Take for example the quarter note in the chart below. It is worth one beat, therefore it can be divided into two equal beats. One eighth note is worth half a beat, so two eighth notes equals one beat and make up one quarter note. For a quarter note to be subdivided, we divide it twice, or by four. We already know that by dividing a quarter note by two, it equals two eighth notes. Two sixteenth notes equals one eighth note which means it equals 1/4 of a quarter note. From this we can figure out that four sixteenth notes equals two eighth notes which equals one quarter note. These examples are calledregular divisions and subdivisions. If a division or subdivision has to have added number , it is called an irregular division or subdivision. Let"s use the quarter note as an example again. To divide a quarter note into three parts, it requires smaller divisions of three "eighth" notes. In the chart below, it looks as if the division is into eighth notes but since it is into smaller parts it doesn"t actually equal the true value of an eighth note. In this case, the division of a quarter into three parts is a triplet. An irregular division into fives is called a quintuplets, six is sextuplets, and seven is septuplets.Now actually determining whether the division is regular or irregular might seem a bit tricky, but let"s take a look at the chart and clear it up.
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First we have the quarter note which is one beat. Next, we have a regular division of two eighth notes.The triplet looks like three eighthns , but they aren"t equal to an eighth so it is irregular.The next division is the regular subdivision of four sixteenths into a quarter note.Here is a quintuplet. It is an irregular subdivision of a quarter because it is made up of 5 sixteenths that aren"t equal to an actual sixteenth.This is a sextuplet.This is a septupletIf the quarter were to be subdivided into a regular subdivision again, it would be divided into eight 32nd notes. It is regular because the 32nd notes in this grouping are actually worth a 32nd note. To make it an irregular subdivision, you would have to add another 32nd note, but then the 32nds wouldn"t be worth their original value. This would make it a ninth.