TL;DR: The phrase make moan was once quite common, so its repeated appearance in Keats' poetry isn't surprising. His exact meaning is open to interpretation, and probably isn't always the same.
The Oxford English Dictionary lists make (one's) moan as a previously common form, with two possible definitions.
moan, n.
1. a. Lamentation, complaint; an instance of this. Freq. in to make
(one's) moan: to lament, grieve, complain. Also in extended use.
Now chiefly Sc. In recent use coloured by association with sense
2.
[twenty-two attestations omitted, dating from ?c.1225 to 1992;
seventeen of these use some form of the verb "to make" with moan]
b. A request, prayer, or entreaty. Freq. in to make one's moan: to
entreat. Obs.
[nine attestations omitted, dating from a1325 to 1878; five use
"to make"]
[definition 1.c. omitted, as it does not take the form "make moan"]
("moan, n.". OED Online. September 2016. Oxford University Press.)
So I don't think it's particularly surprising that Keats, writing in the early nineteenth century, used the phrase "make moan" multiple times.
Keats' intended meaning for any particular instance probably varies and may be intentionally ambiguous, though it is probably closer to definition b. than definition a. in the lines you reference. Certainly the adjectives "sweet" and "delicious" suggest that the moans were pleasing to the hearer, which seems much more likely for requests, prayers, or entreaties than for lamentations or complaints.
This seems clearest in Ode to Psyche where both instances of "making moan" can easily be read as "saying prayers/entreating [the Goddess Psyche]". The deliciousness of the virgins' moans is fairly understandable in this context, as prayers are typically understood to be pleasing to their objects (even for gods who don't require literal sacrifice of delicious food, as in this blog post).
The line in La Belle Dame sans Merci is a little harder to parse. The phrase appears during what could be seen as a courtship, a seduction, or an abduction and rape; which way you see the overall situation will determine whether you think she is lamenting/complaining, entreating/requesting (begging?), or just making an inarticulate sound of some sort. Note that later in the poem "she wept and sighed full sore"—immediately after, we are told, she fed the protagonist sweet treats and "said—/‘I love thee true’."
It is also entirely consistent with the OED's definitions that some of these usages were "coloured by association with sense 2" (which is essentially the same as the one @HotLicks cited in the comments):
2. a. A long, low, inarticulate sound made by a person expressing mental or physical suffering or (in later use also) pleasure; a
similar sound produced by an animal. Generally suggestive of a sound less harsh and deep than a groan, with which it is often collocated in late Modern English use.
In which case I think it is reasonable to conclude that "sweet" and "delicious" moans are, indeed, intended to be ambiguous with regard to sexual connotations. This interpretation seems especially likely in the case of La Belle Dame sans Merci, which explicitly deals with love and kisses.
Here is the wording of the lyric that appears in Edmund Fellowes, English Madrigal Verse, 1588–1632 (1920):
Though Philomela lost her love,
Fresh notes she warbleth, yet again.
He is a fool that lovers prove,
And leaves to sing to live in pain.
The main differences between this version and the one that the poster cites are in line 2: "notes" for "note," and "yet" for "yes!" There are also some differences in punctuation—most notably the period at the end of line 2 in Fellowes's version as opposed to the semicolon in the poster's version.
The period ending line 2 is significant, I think, because it supports the suggestion that Spagirl makes (in a comment above) that there may be no connection between the "He" in line 2 and any character in the Philomela myth to whom lines 1 and 2 may allude.
On the face of it, the song first offers two lines about the behavior of the nightingale (imagined as a transformed girl), which sings though she is alone and lovelorn. Then it turns to consider a person (I nominate the songwriter) who has chosen (perhaps) to test the love of two lovers (I nominate himself and his beloved) in some unstated way; and finally it accompanies that person as he leaves the presence of the lover[s] to sing alone in pain—like the anthropomorphized nightingale.
The particular line of interest—"He is a fool that lovers prove"—may use the verb prove in the now semi-archaic sense of "test" that tchrist points out in a comment above (as my initial reading of it does). But another possibility involves an even more out-of-the-way meaning of prove, which Merriam-Webster's Eleventh Collegiate Dictionary (2003) gives as follows:
prove ... vt (13c) 1 archaic : to learn or find out by experience
This meaning of prove is the one that Marlowe has in mind in "The Passionate Shepherd to His Love" (written no later than 1593):
Come live with me and be my Love,
And we will all the pleasures prove
That hills and valleys, dales and fields,
Or woods or steepy mountain yields.
Marlowe isn't offering to establish by ratiocination that such pleasures exist; he is urging his love to experience them with him.
This sense of prove invites a different interpretation of line 3—something like
He is a fool who learns first-hand the ways of lovers
—namely that they will break your heart, and you will find yourself, like Philomela, flitting from tree to tree as the night deepens, singing your song of sorrow and hard-earned wisdom.
Either reading requires a little help from the listener/reader to make perfect syntactical sense. Specifically you have to supply a dropped auxiliary verb:
He is a fool that lovers [doth] prove,
Without the (arguably) missing doth, you have a statement that seems syntactically straightforward ("He is a fool whom lovers test [or learn by experience]") but doesn't stand up to logical scrutiny (why does a lover's decision to test you or experience you make you a fool?).
But once you interpolate the doth, the singer's complaint makes sense—and you get to choose between interpreting the lyric as a lament for having needlessly and foolishly put one or more lovers to the test, and interpreting it as a lament for having been victimized by foolishly learning through bitter experience about lovers and their deceits. On that front, my advice is "When you're dealing with a songwriter, never bet against the more self-pitying meaning."
Best Answer
This line refers to leaves that have been stepped on to the point where they are black instead of the color they were when they fell off the tree.
The word "tread" means (one of its meanings) "to step on." So you can tread on the leaves as you walk along. If you have stepped on the leaf, we can say you have trodden on it.
So the speaker is saying (at this point) that that road has not been walked on. The leaves have not been stepped on so they have not turned black from being crushed or ground into the dirt or anything.
In this case, the narrator, reflects that, of the two paths he could have taken in life, he chose to follow "the one less traveled by," and he believes "that has made all the difference." Basically, the narrator reached a point in his life when he was faced with decision to either conform to society and live a "normal" life, or to live his life in way that embraces individuality or an less conventional existence than the first path.
The road that fewer people had taken ("was more grassy and wanted wear") was more inviting to the narrator, so he made the choice to follow the path that fewer people had taken. The narrator believes that chosing to follow the norm would have been the wrong decision.
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