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I am trying to study music theory which would help me learn various aspects of music, so I started with basics and then time signature. It states that for a music to be in compound time each beat is divided to three notes but the diagram(in the book that I'm following) shows: enter image description here

how are the notes first divided to three but in the second they're again divided in two. Is this some kind of an error?

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Let's forget about the graphic and just go over what the diffrences between simple and compound time signatures which lies in how the grouping of each is done.

In simple time, you just have one grouping of notes per measuer like in 2/4 you have a group of 2 quater notes per measuer, 3/8 you have a group of 3 eighth notes per measuer, 2/2 you have a group of 2 half notes per measuer, ect.

In compound time, you have two levels of grouping. One level of grouping is to add another beat grouping, typically grouping in 3, to give the time signature more of a simple feel like the ones above and the other is grouping the remaining groups.

For example in 12/8, we group the 12 eigth notes into groups of 3 which we have 4 of total. We then look at the group of 3 eigth notes as a dotted quarter note and now we can break the measure up into a quadruple meter feel, but there is still the underlying groping of the eigth notes which is why we call them compound time signatures which is because we are using multiple groupings.

The diagram you came across is very confusing in nature because it approaches it from an odd angle at just looking at subdivisions in isolation which isn't the clearest way to demonstrate that. Try looking at Music thoery.net's lesson and see if that clears it up for you.

  • I have rarely seen a more confused and unhelpful answer! I guess that deserves some sort of a prize? – Laurence Payne Mar 26 '16 at 16:49
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    @LaurencePayne what's confusing about it? That's exactly what is going on in compond time signatures and even the link provided explains it in almost the exact same way. There's a reason why the tempo marks in 6/8 are set a dotted quater note as that is where we break up the measure in that meter, but the subgroup of 3 eighth notes is still observed inside that grouping. – Dom Mar 26 '16 at 16:53
  • @Dorn, it was really helpful, but I'd like to confirm this: is one half note's value equal to three quarter note, one quarter is equal to three eight and so on? – lind Mar 27 '16 at 6:35
  • No, one half note is always equal to two quarter notes. In compound time, the "beats" are written as dotted notes. The dot increases the length of the note by half, so a dotted half note equals three quarter notes. In 6/8 time, the two beats in the bar are dotted quarter notes, each divided into three 8th notes. – user19146 Mar 28 '16 at 2:27
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The first level is "How many beats in a bar"

The second level is "Do they subdivide into twos or threes?" This is the simple/compound question.

There are further levels!

Your book is not being very helpful in writing every note as a crotchet (quarter note).

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