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I'm in the very early stages of reading music. There are great resources on the internet but I'm struggling to find a suitable explanation for a 'Time Signature' that I completely understand. I think it's the bottom number I'm having trouble with. The tutorial I'm doing shows 4 quarter notes per bar, 4/4 time.

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As above, it then goes on to say that the beats are at 60bpm (the clicks it refers to is a metronome mp3 with the tutorial) - that's fine but what is it that dictates how many beats per minute each bar should be played at? Why 60bpm and not 120bpm or even 93bpm?? Basically, what is it that tells me that this 'piece' (however simple), should be played at 60bpm?

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On the face of it - nothing! The notes (or any notes on any music) are relative to each other, not to a particular speed of playing. Unless you are given the b.p.m. there is NO indication of exact speed. On a lot of serious (classical, et at) music, there will be a vague indication in a word at the head, like 'presto', or 'adagio'. Look on a good metronome, and there will be an idea of the band of b.p.m. for each tempo.

The above example says (you say) 60 b.p.m. So each beat - here as a crotchet, a.k.a. quarter note, lasts one second. I have met beginners who have seen this sort of thing, and have the belief that every crotchet in every piece of music has to last 1 second. UNTRUE !! With no tempo mark, it could be played at any speed, and for learning purposes, slow is usually good. For a pukka performance, the tempo needs to be available, and adhered to - within maybe + - 5%.

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Time signature and tempo are not related. E.g., if a piece is written in 4/4 (as in your case) you have no way of knowing how fast you're supposed to play it. In classical music it is common to give tempo indications by Italian words, like Andante, Presto, etc. (see this list). In popular music you would often encounter tempo indications like ♩=120, which means that a quarter note gets one beat and there are 120 beats per minute. If there is no tempo indication it is completely up to you how fast you want to play the piece. Of course, if you're practicing just play everything as slowly as necessary to keep it clean and accurate.

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The only thing that defines 60bpm for the example is the tutorial's statement that this is the speed. (Does it refer to an audio example?)

It COULD be indicated in the music. Maybe by a word - 'Allegro', 'Andante' etc. They are ballpark terms - 'Allegro', meaning 'Fast' might be 120-160bpm. 'Andante - literally 'at a walking pace' might be 76-112bpm. All open to discussion and interpretation.

You can be more precise with a Metronome Mark. Maybe "(quarter-note symbol)=120". And we don't always count quarter-notes. A 6/8 march might be marked "(dotted-quarter symbol)=116".

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