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I would like to ask what is the importance of tempo and time-signatures. By this I mean, aren't tempo and time-signatures all interchangeable. For example, a 4/8 60 BPM can be also described as 4/4 120 BPM (or at least something like that). Or a 60 BPM tempo can be transcribed to a 120 BPM tempo just by changing the note durations?

Apart from readability, what other importance is there that a specific tempo or time-signature should be used?

Thank you!

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This question is really great. It tackles some of the fundamental concepts in music. :) –  Saeed Neamati Jul 24 '11 at 9:31
    

3 Answers 3

For the most part, the time signature indicates what kind of feel the beat of the piece has. Consider waltzes, usually written in 3/4 – the beat goes ONE two three, ONE two three, ONE two three. Although you could write it as ONE two three, FOUR five six, ONE two three, FOUR five six with a time signature of 6/4, there's no point because the beat still naturally repeats every three beats. The time signature is also chosen by the composer as an aid to the musician to give a hint to which notes might be stressed when reading a piece for the first time.

In response to whether it's possible to rewrite a score with double or half the tempo marking with no change in the music: when a piece is written in cut time (2/2), different conductors will conduct it with either two beats per measure (as written) or four beats per measure (like 4/4 - one quarter note per beat). These two approaches give the music different sorts of feeling – from my experience, a piece conducted in 2/2 usually feels more smooth and connected with much less emphasis on the individual beats.

In short, there's no reason why you can't write a piece with a time signature and tempo different from what might feel natural, just as there's no reason that you can't write a novel without any paragraph breaks, but it makes more sense to do it in a conventional way and makes everyone's life easier.

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Nice and simple explanation! The comparison with books also seemed to strengthen the point. Thanks! –  user488792 Jul 24 '11 at 6:24
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Interesting thing about waltzes: sometimes they go ONE two three ONE two three ONE two THREE one TWO three. Waltzes play around with the beat more than most other dances do. Sometimes the time signature is just a scaffolding to hang the real rhythm on. Just as in poetry where the phrases don't match the actual line ends: "To die, to sleep, / No more, and by a sleep to say we end / The heart-ache, and the thousand natural shocks / That flesh is heir to; 'tis a consummation / Devoutly to be wished." –  Mark Lutton Jul 24 '11 at 22:27

Simple rule: Changing the bottom number of a time signature, and the tempo correspondingly, has no effect. As you say, 4/8 at 60 bpm is the same as 4/4 at 120 bpm. It's also the same as 4/2 at 240 bpm. Likewise 3/8 at 80 bpm is the same as 3/4 at 160 bpm, and so on.

Changing to top number is a different story, as the other answers allude to. That changes the number of beats in a measure, which can greatly alter the feel. ONE two THREE four is very different from ONE two THREE four or ONE TWO THREE FOUR.

One exception is when the top number is a 6. 6/8 is usually emphasized ONE two three FOUR five six whereas 6/4 is often ONE two THREE four FIVE six, so the bottom number changing results in the rhythm changing. This is probably the most common exception but not the only one — the time signature never determines the rhythm, they just have common rhythms associated with them.

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One of the greatest analyses I've ever seen @Matthew. +1 –  Saeed Neamati Jul 25 '11 at 14:47
    
So overall, it constitutes to the 'feel' of the music as well as readability and convenience? –  user488792 Jul 26 '11 at 4:16

Actually, 4/8 at 60bpm could be written as 4/4 ALSO at 60bpm.

Meters (what the time signature denotes) have two properties: whether they are simple or compound, and whether they are duple, triple, or quadruple (though some argue it is impossible to aurally tell the difference between duple and quadruple). The first property refers to how the beat is DIVIDED - simple beats are divided in 2, and compound beats are divided in 3. The second refers to how many beats are in a measure.

Marches are nearly always in simple duple (usually 120bpm), meaning they have two beats in a measure, and the beats are divided in two. They can be written in 2/4, 2/8, 2/2 (cut time) etc. Semper Fidelis is an example of a march in COMPOUND duple - 6/8. The dotted quarter note gets the beat, and there are two beats per measure, but the beats are divided into three.

In simple time, the possible top numbers of a time signature are 2 for duple, 3 for triple, and 4 for quadruple. The bottom number represents the beat note. In compound time, the possible top numbers are 6 for duple, 9 for triple, and 12 for quadruple. The bottom number represents the DIVISION of the beat (the beat of 6/8 is actually 3 eighth notes - a dotted quarter note).

Now, this explanation is based on the Common Practice Period (1600-1900) standards. Modern composers sometimes break these conventions and even use irregular time signatures. But this is still very useful knowledge.

As for tempo, it is simply how fast the composer wants the perceived beats to go by. As for whether he uses quarter notes, eighth notes, half notes, 128th notes or whatever for the beat or beat division, I think that is simply up to whatever he wants it to look like. :)

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Good use of terminology, "duple, triple, and quadruple". +1. However, the first property denotes how many beats there are in a measure and the second property denotes how long each beat is. –  Saeed Neamati Jul 25 '11 at 14:55
    
By first and second property, I meant simple or compound refers to how it's divided, and duple, triple, or quadruple refers to how many beats there are in a measure, not referring to top and bottom number of the time signature. I suppose I should say METERS have two properties, not time signatures. –  MarioAran Jul 25 '11 at 18:38
    
6/8 can be done either as ONE two three FOUR five six or ONE two THREE four FIVE six, depending how the composer chooses to use it. In some pieces, the two may both be used for the same measure in different parts to create a hemiola effect. (Paul Creston's setting of Psalm XXIII is a great example of this.) –  jwernerny Jul 26 '11 at 17:10
    
Technically, 6/8 SHOULD be ONE two three FOUR five six. ONE two THREE four FIVE six should be written as 3/4, or is heimiola. –  MarioAran Jul 26 '11 at 19:06

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