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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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Numerically speaking, the way you explain it, that is true.

But that does not take into account the rhythmical meaning of the global tempo signature.

Rhythmic accents will manifest in different places in 3/4 vs 4/4. The tempo signature reason being to highlight/determine same.

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  • 3 weeks later...

If you were to be presented with "a stream of musical 'beats,' 120 'beats' per minute," then you would be entirely correct (maybe) to conclude that each 'beat' is 'a quarter note.' Hence, you would know that the bottom-half of the time signature is ... "X / 4".

 

But, very soon thereafter, you will also notice that this "stream of 'beats'" seems to be naturally divided into measures, and that, within each measure, some of the "off" beats seem to be emphasized:

  • "One two three ... One two three ..." (3 / 4)
  • "One two (three) four." (4 / 4)
  • "One two three (four) five six." (6 / 4)

 

Each pulse "is a quarter-note," in all cases, but "the beat" varies.

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