Also see: "Handshapes"
I recommend keeping a flexible stance on the right or wrongness of the various
handshapes for the letter "E."
The fact is the (amusingly labeled) "bear-claw" version of "E" (or "screaming
E") is rather common.
Some of my friends sign their "E" with a gap and you can see that version on the
hands of some Deaf vloggers -- especially when signing at high speed.
So while it is common for "ASL 1" teachers to emphasize the so-called "right
way" to do an "E" -- the reality is that there are many right ways to do an E.
"Co-articulation" effects are "real." This isn't the place to get into
co-articulation but, in brief, the letter before or after an "E" can influence
and radically mutate the articulation of (or way we sign) an "E." This mutation
is not wrong but rather is representative of "native-like" signing.
Which means that if you are "not" mutating the "E" when signed before or after
certain other letters -- your spelling is actually "less-native-like" and
probably slower or more time consuming to produce and to observe.
Ultra-clear signing is not the same as "native-like" signing (which is more
toward the ultra efficient end of the spectrum).
Regarding the many ways to do an "E" -- we could state that the number is
functionally "near infinite" when you consider smaller and smaller variances. So
if "one" researcher (or group of researchers) counts 57 different ways to sign
an "E" -- the next researcher might count 100 -- based on a more refined
definition of "what counts as a difference."
E:

You might see an "e" that rests only three fingers on top of the thumb
when someone is spelling a name or a word that places the letter "m"
before the "e." For example: "James."

Or suppose you spell the name "J-A-N-E?" The "E" might end up
looking like this:
Trick question: What letter is being shown here?
(The trickiness is due to not providing any context.)

Note: This letter is being articulated (spelled / signed) as part of a very
carefully expressed fingerspelled word. The non-dominant hand is actually
slightly off camera pointing to the fingerspelled word for additional emphasis.
It is being presented in a formally recorded session by a professional
newscaster who is striving to be clear. It would be inappropriate to label it as
sloppy spelling.
Instead what you should do is let the truth blow your mind and accept the
reality that what your ASL 1 teacher told you about [this letter and most of the
others] was actually only the tip of an iceberg and that the reality is [this
letter] has five very (*very*) common forms in real life along with a whole
spectrum of variations and that the fingerspelling charts need to be be changed
if the chart designers want them to be anywhere near accurate.
The word being spelled is "letter." The context is: "The couples have a
missing DNA letter in the 35th position..."
Source / credit: Abenchuchan, Alex (07/09/2019) Five deaf Russian
couples may undergo gene editing to prevent deaf children, The Daily Moth
7-9-19, retrieved from: https://youtu.be/VT7VhEkV9oY?t=382 (Time code: 6 :23)
Notes:
See: "Coarticulation"
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