Thank you every one. I've stared this thread in order to discuss why E difficult chord is. But the thread has gone to alternatives instead of E chord itself. Actually I have no problem and I can play E in low position. The reason why I wanted to discuss the reason of difficulty of E Chord is if we saw the reason, we may solve the problem. And I thought I had some clue of it. The difficulty of E is shown in the first post in this thread. It has a barre like form on 4th fret and the first finger on the 2nd fret of 1st string as shown below.
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When I practice new songs on piano, I practice right hand first. Right hand is melody line. Then I practice left hand which works for bass and chord. Finally I try to practice both hand together.
When I practice Travis picking (alternating bass) on guitar, I practice bass line with my thumb of right hand first. Then I practice melody line with my index finger. Finally I try to play both. I used this method to E chord. There are two parts which do not work together easily. I've practiced 4th fret first. Then I added 2nd fret. There is one curious thing happens in this thread. Rlink (#3 in this thread) who has big hands can play E, and Tootler (#18, just above this post) who has small hands can not. Why American vaudevillian can play it and English gentleman can not? The figure below may show you the reason.
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There are two ways for 4th fret on E as shown above. Big hand selected short barre of middle finger (2) on 3rd and 4th strings, because he can not play it with three fingers. On the other hand, small hand selected three finger style which is anatomically almost impossible to play E chord.
Actually I practiced Rlink's way. I practiced short barre first, but short barre was not easy. This short barre has a good analogue with mahjong. Mahjong tile is engraved and experienced mahjong players can read tiles by their thumb. It is called blind tile and often used for cheating.
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I can play blind tile and I think short barre is very similar to it. We need to feel the strings instead of push them and then hear the sound. Use baroreceptor and ear. We need to read the 3rd and 4th strings by middle finger instead of push them and then check the sound. It is like Feeley Meeley.
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Feel it blindly. Feel and push are different. Once I felt the strings, I've got a short barre. Adding index finger on 2nd fret was not difficult. I could play E finally.