This page will cover D4 up to F4 and why it is called "LRLR". At the bottom of the is a link to a beginning exercises you can download.
Here is a quick lesson/reminder of what parts of each hand
is used for each section of the fingering chart.
is used for each section of the fingering chart.
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D4-F4
D4-F4 are pitches that are, at times, written in tenor clef. These pitches are also ones that do not follow a sequential pattern like the pitches in "The Spiral". The best way I know of remembering these fingerings is by the "LRLR" method.
The "LRLR" Method
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The name of this method comes from the order your hands move as you progress through D4-F4 chromatically: Left, Right, Left, Right.
1. Left D: To begin, we start with a fingering we already know from "The Spiral", D4. This is the 1st left hand move.
2. Right D#/Eb: Keep the fingering from D down and use your right hand to close the tone holes of your 1st, 2nd, and 3rd finger. 3. Left E: Keep the fingering from D#/Eb and move your left hand 2nd finger off the tone hole and then close your 3rd and 4th fingers. 4. Right F: Keep the Fingering from E and and move your 3rd finger in your right hand off the tone hole. 
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Exercise
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