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I understand the meaning of music notations such as 3/4, 4/4 and so on. The first number is the number of beats per measure, while the second number is the note-duration (quarter, half, one-eighth) for each beat in the measure.

Does this mean that, a (hypothetical) music piece written as 3/4 with 4 measures in length can be expressed as 4/4 with 3 measures in length? Note that in both cases, there are 12 beats. It seems to me that by just changing the position of bars a 3/4 music can be expressed as 4/4 music, as long the original 3/4 music had 4 measures or any multiple of 4 measures (such as 8, 12, 16 and so on).

Is my understanding correct?

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There is usually a big difference in rythm. For example, normally the first beat of each measure is stressed. Even if that's not the case, if the piece was originally in 3/4 there should be some pattern (rythm, especially, but perhaps also melody and harmony) that fits in there. – leonbloy Aug 21 '14 at 4:37
up vote 25 down vote accepted

Time signatures and bars are not there arbitrarily, nor just to help count your way through a piece. They are there to provide guidance on the rhythm of the piece. Where it is accented, where it breathes.

Some composers do write pieces with no time signature or bars, as an indication that there should be no consistent rhythm. Eric Satie did this for several pieces.

Let's try doing what you've suggested with a well known nursery rhyme, first in 4/4:

| 1      2        3        4    | 1      2        3     4    |
| Half a pound of tupenny rice. | Half a pound of trea- cle. | 

| 1          2       3     4     | 1   2        3    4   |
| That's the way the money goes. | Pop goes the wea- sel |

You can see, this puts one line of verse in each bar.

Half a pound of tupenny rice.
Half a pound of treacle.
That's the way the money goes.
Pop goes the weasel.

If you perform it with a strong accent on the first beat, and weak accent on the third beat of each bar, the accents fall where you'd expect them, if you were speaking the line normally: "Half a pound of tup-enny rice."

Now what if we divide it into 3 beat bars instead:

| 1      2        3       | 1     2      3        | 1     2    3          |
| Half a pound of tupenny | rice. Half a pound of | trea- cle. That's the | 

| 1       2     3     | 1   2        3    | 1
| way the money goes. | Pop goes the wea- | sel 
Half a pound of tupenny
rice. Half a pound of
treacle. That's the
way the money goes.
Pop goes the wea-

As you can see, it makes a nonsense of the verse. Try clapping a 3/4 oom-pah-pah rhythm and chanting the verse along to it.

Or, going in the opposite direction, something that should be in 3/4:

| 1    2     3 | 1   2   3  | 1     2   3  | 1    2   3  |
| Here comes a | can-dle to | light you to | bed         |

| 1    2     3 | 1    2   3  | 1    2   3    | 1   2   3  |
| Here comes a | chop-per to | chop off your | head       |

... into 4/4

| 1    2     3 4    | 1   2  3     4   | 1  2   3 4 |
| Here comes a can- | dle to light you | to bed     |

| 1    2     3 4     | 1   2  3    4   | 1    2     3 4 |
| Here comes a chop- | per to chop off | your head      |

So, "Here comes a can-dle to light you to bed" becomes "Here comes a can-dle to light you to bed."

Of course, not all music has lyrics that you can "break" in this way. But even instrumental music has rhythm, accents, breathing space and flow, which change if you put the bar lines in different places.

It is possible to adapt a tune from one time signature to another while keeping the accented notes at the start of the bars - but this necessarily involves modifying the rhythm of the notes, for example, changing two half-notes into a single note. For example, listen to Bob Dylan's Highway 61 Revisited, which is in 4/4, then PJ Harvey's adaptation in 3/4 (or 12/8, depending on how you choose to count it).

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Thanks for detailed explanation. Makes it clear that bars/measures not only represent organization of notes but also accents -- something that I did not understand earlier. – a c Aug 21 '14 at 15:48

Your understanding of the math, as it were, is correct. And I would say yes, a multiple of 4 bars of music in 3/4 can be expressed as music in 4/4 (in a multiple of 3 bars), but I would dispute that the same can necessarily be represented as such.

The bar line placement of a piece of music has tremendous impact upon live musicians' interpretation of, not to mention ability to read, a piece of music. So while you might get the same output from a simple MIDI synthesizer, you won't get the same response from real musicians. (And depending on the circumstances, some of them might return your music with the comment that you should have metered it differently!)

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Thank you for answering. Can you please clarify what do you mean by representation as opposed to expression? – a c Aug 21 '14 at 2:37
"expressed" means "you can write it that way, and it's the same notes in the same order". "not represented" means "despite all that it's not the same piece of music, because the way the notes are played is different". The most obvious way to see this is to consider which notes in the bar are stressed. The MIDI synth maybe won't stress anything unless specifically told to, but the real musicians (including for that matter the conductor) will. – Steve Jessop Aug 21 '14 at 2:48
So, didn't you mean to say 'not represented' then? – Lee Kowalkowski Aug 21 '14 at 10:25
Sorry @LeeKowalkowski -- that was a kind of odd sentence construction. I'll change "argue" to "dispute" to make it clearer. – NReilingh Aug 21 '14 at 12:25
Makes sense. Thank you all. I agree "dispute" is the better word in this case. – a c Aug 21 '14 at 15:37

A nice example of a composer playing with the written vs sounding time signature is the second movement of Ravel's G Major Piano Concerto. It is written in 3/4 and sounds like it's a slow waltz in the left hand, but the left hand isn't playing a normal 3/4 waltz rhythm — it is playing eight-notes putting the pulse on beat 1 on the second eighth note of beat two. The right hand plays in a normal 3/4 giving the whole piece a really interesting unsteadiness. First few bars of Ravel Concerto in G 2nd movement

Here's a video:

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Simple test for you to try. Take 'Frere Jacques', a well known song. Re-write it in 3 time.Ask a player to play it. Chances are that it will sound very different. That's because the emphasis in a song comes on the first note of a bar.Particularly notable when words are involved ! In 4 this is every 4, in 3, every 3.It also puts the 'main' notes in different places in he bars, which will mess up the harmonies.

Tunes used specifically for dancing will be badly affected. They rely heavily on the dancers knowing or feeling where 'no. 1 beat' is. Yes, in theory it COULD work, but in practice, generally, it won't.

3-legged race, anyone ?

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I play fiddle for Morris Dancing. There is a tune from the village of Bampton called Old Woman Tossed Up (In a Blanket, presumably). It is written in 6/8, but it sounds like it was a 9/8 tune which was rebarred haphazardly. Many of the old Morris Dances have odd rhythms, as they were collected by and from people who were really drunk, so anything is possible. I've been playing that tune for between 10 and 20 years, and still can't get it right. Right now I would have to look it up in the book.

So, the tune has a rhythm, especially simple folk tunes, and the notation doesn't change it. Or, another way, the notation (3/4 X 4 bars vs. 4/4 X 2 bars, or 6/8 vs. 9/8) doesn't change the rhythm.

I hope this make sense.

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Back a few hundred years, it was common for music to insert a bar or two of 3/4 into a basically 4/4 piece (or vice versa). Often two parts would effectively be in different time signatures. The term for this is hemiola.

Wikipedia describes this far better than I can:

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While it is interesting, I fear that this is not really relevant to the question. – Lee White Aug 21 '14 at 8:30
Also, a hemiola switches between 6/8 and 3/4 (or two bars of 3/4 and 3/2, or possibly 10/8 and 5/4 etc.) but it doesn't make sense for power-of-two meters. – leftaroundabout Aug 21 '14 at 8:51
... and you don't need to go back a few hundred years. Lots of modern music (even rock/pop) sometimes slips a 3/4 bar into 4/4 songs. – slim Aug 21 '14 at 9:43
...and 5/4...and all sorts. Listen to Closest thing to Crazy. – Tim Aug 21 '14 at 9:44
It's not even really "switching" time signatures. It's just using accents and rests to give the meter a different feel. – Ely Beau Eastman Aug 21 '14 at 14:00

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