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Does the time signature dictate what chord pattern you use on the left hand?

For example, in "row your boat" a 6/8 time, I'll repeat the chord twice. So if I'm playing the 3 notes of the chord and play it twice I'll get to 6 notes which matches the time signature.

And in "london bridge" which is a 4/4 time I play the chord using two notes (say the 1 and the 5), and I'll play these twice 1 5 1 5 so they match each beat.

So the chords tones in the left hand essentially match the beat (or go between) the beat. Therefore the time signatures have a direct influence on the chord patterns you play on your left hand. Does this sound right?

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That doesn't sound right. The left hand pattern may be influenced by the time signature however it is completely up to the composer/performer what chords are written/played.

For example. There is nothing stopping the chord tones from being played/notated as triplets in 4/4. In fact that might make more sense to a reader rather than changing the melody line to dotted crotchets.

Time signature is simply notation, or a method or writing something down. It does not really have any effect on the 'music' or the way the 'music is'. As long as the writer understands how to write what he intends or is imagining and the reader understands what he is reading, time signature doesn't restrict chord patterns in any way.

different rhythms same key signature

Same key signature but different rhythm, threes, vs twos. It would be possible to write exactly the same rhythms in 6/8 or any other key signature really. 6/8 or compound time might be more effort than it is worth. Anything else might be a little unclear. (Imagine writing that in 5/4 or some silliness)

As a player who is improvising or comping it might be easier to do what you're describing but there is no reason why it has to be like that at all. As you improve you might choose to employ polyrhythms, or any number of more 'interesting' comping patterns.

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Time signature does three things in western classical music: it tells how many beats are in each measure, it tells which beats are strong, and it tells whether the beats are divided into two or three parts.

In chord-structured harmony the bass lines often follow the structure provided by the time signature. Generally, lower notes provide more grounding and heaviness to the line, so they are placed on the strong beats.

Thus, in a 3/4 time there will usually be a low note on beat one and higher notes on beats 2 and 3. In the example axerotolerant gave above, even in the triplets, the low note is on the beat and the higher notes are on the weak parts of the beat. In 4/4 time, the strong beats are 1 and 3, so lower notes will be on those beats and higher notes on beats 2 and 4. In 6/8 time, the strong pulses are on the 1st and 4th eighth notes.

To go against this pattern creates syncopation because the heaviness of the low note will bring attention, and thus an accent of sorts, to a normally weak beat or part of a beat.

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