With an eighth note rhythm pattern you are strumming two times to every beat, down on the beat and up on the half beat.
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The simple explanation for a sixteenth note rhythm is "you strum twice as fast as an eight note rhythm". So in 1 beat you will strum down, up, down, up.
When counting out an eight note rhythm you say an "&" in the middle of each number (beat). Say this out loud and say it slow with about a second gap between each number "1 2 3 4 ", by doing this you are counting in quarter notes. Now don't change the speed of it and say an "&" in between each number, like this "1 & 2 & 3 & 4 & ". You should be saying something every half second or so (the speed it irrelevant it is the evenness in the counting we are focusing on). By doing this you are now counting eighth notes. Now place an "a" in the middle of each 1 & 2 & 3 & 4 &, make sure you keep the 1234 at 1 second intervals, it will sound like this "1 a & a 2 a & a 3 a & a 4 a & a ". Now you should be saying something roughly every 1/4 of a second, this is a sixteenth note count.
The tables below shows the three different counts, all you're doing is doubling the speed each time.
| 1 2 3 4 |Quarter Note Count
| 1 & 2 & 3 & 4 & |Eighth Note Count
| 1 a & a 2 a & a 3 a & a 4 a & a |Sixteenth Note Count
16th Note Rhythm - Pattern 1
This is the most basic sixteenth note rhythm, see if you can keep up with the animation or audio. Try to strum harder on the 1 2 3 4 counts, this will give a better feel when you're strumming.
It is very important you get the feel for this so listen to the example.