Fascinating English -- the etymology of "hap", "haply" and its many derivatives

The English language is a wonderous treasure-trove ( "trove" from the French, "trouver", "to find", thus, "treasure-'find'" ) of history's twists and turns and how these have informed, and guided meanings. Immense consequences for people and society spring from this and have done so throughout history. It is no exaggeration to say that the history of English words--their etymology--is a window on the history of English society and its people--now, all English-speaking people wherever they live.

Take, for example, the now rather archaic word, "hap"--from which our terms "happen", "happenstance," "haphazard," and "hapless" sprang. "Hap", the word, its variants and history are a marvelous example of this theme's key points.

From The Oxford English Dictionary:

hap (hæp), sb.* arch. Also (3. heppe), 4-6 hape, happ. (Early ME. a. ON. happ neut., chance, hap, good luck. The same root is found in OE gehæp, adj. fit, hæplic equal)

(adj.
1) Chance or fortune (good or bad) that falls to any one; luck, lot.
2.) (with pl.) An event or occurrence which befalls one; a chance, accident, happening; often, an unfortunate event, mishap, mischance.
3.) To have the happ or fortune (to do something.
4a. ) To chance to be or to come or go casually; to make one's appearance; to 'turn up' occur.
4b.) with on, upon, (occas. of) ; 4c.) with into Obsolete, excep. U.S. ; 4d. happen in happen along, around, back, by, over, (U.S.) happen in with to fall in with, to meet casually;
5.) (transitive) To meet with casually, to incur.

(examples in writing date from the beginning of the 13th C. (1205)

and verb, (intransitive), To come about by 'hap', or chance. a. with the event expressed either by a substantive or pronoun preceding the verb as subject, or by a clause or infinitive following it, the verb being then generally preceded by it. Formerly with auxiliary be instead of have.

------------------------------

* sb. : substantive
arch. : archaic

ME : Middle English
ON : Old Norse
OE : Old English
(Letters of the Old English alphabet: https://www.old-engli.sh/dictionary.php )

But "hap" appears in other contemporary English terms and suggests surprising, or, if not surprising, then interesting avenues the origins on which to speculate:

"perhap", "perhaps", literally, "per" ("by") "hap" : "by chance"
"happily", "happed",
"mayhap": pehaps, maybe, perchance.
(archaic) "behap"
did a noun form "glist" once precede the use of "glisten"? Were "like", ("liken") and "list" ("listen") once etymologically related in meanings and usage?

(from "The Tempest" III, ii.

TRINCULO
"Your lieutenant, if you list; he's no standard."
...
STEPHANO

If thou beest a man, show thyself in thy likeness:
if thou beest a devil, take't as thou list.

And, with its still most-common "-en" ending, "happen", we have a form which has many examples in English and, "taking them 'apart' " is an interesting and suggestive exercise:

the term "fast" (adj.) was long used to mean "secure": "make fast", and as a verb form, it still takes an "-en" ending: "fasten" (See, at Wikipedia: "-en") :

... "From Middle English -(e)nen, -(e)nien, from Old English -nian, from Proto-Germanic *-inōną. Cognate with Danish -ne, Swedish -na, Icelandic -na. Suffix
-en

When attached to certain adjectives, it forms a transitive verb whose meaning is, to make (adjective). Usually, the verb is ergative, sometimes not. The same construction could also be done to certain (fewer) nouns, as, strengthen, in which case the verb means roughly, "to give (noun) to", or "to become like (noun)".

‎white (adjective) + ‎-en → ‎whiten
‎quick + ‎-en → ‎quicken
‎strength (noun) + ‎-en → ‎strengthen
‎haste + ‎-en → ‎hasten
‎night + ‎-en → ‎nighten

.

Likewise for these terms, now often rarely used or quite archaic:

"hard", "harden"
"haste", "hasten"
"oft", "often"
"soft", "soften"
"heart", "hearten"
"hold", "holden"
"gold", "golden"
"bare", (?) "barren"