Places this theme is heard in FOTR:

• During Bilbo's quiet words with Frodo at the Long Expected Party. The Hymn Chords precede and continue under A Hobbit's Understanding. (EE scene)

• In Moria, when Frodo says, “I wish the Ring had never come to me.” Gandalf encourages Frodo that he is meant to carry this burden, attempt this quest.  HS COMMENT

• At Parth Galen after Frodo wishes the Ring had never come to him. The Hymn chords (only) begin as we hear Gandalf's voice, "All you have to do is decide what to do with the time that is given to you." The chords continue under A Hobbit's Understanding which begins as we see the resolution on Frodo's face and he pushes the boat into the water.

• When Frodo hauls Sam out of the water and into the boat and Sam chastises him for trying to leave him behind. Sam has promised to stay with Frodo and he means to keep his promise.

• Just as the Three Hunters run off to follow Merry & Pippin and the camera cuts to Frodo & Sam climbing Amon Lhaw on the opposite bank.  On the rise, the two Hobbits contemplate Mordor and their separation from their friends.

One place this theme is heard in TTT:

• During Sam's speech in Osgiliath that begins with, "But in the end, it's only a passing thing." and ends with, "I think, Mr. Frodo... I do understand."

Michael McLennan's thoughts about this music:

written before any of the CR information

(From a SMME forum discussion)

If you think about where this theme pops up in the trilogy, so often it is for a scene that established the emotional link between Gandalf and Frodo. The wonderful scene where Gandalf says those memorable words 'All you have to decide...' features a lovely soft rendition of the theme, so that when Frodo remembers those words later on, the musical parallel is beautifully realised. Think then of the scene where the Fellowship laments Gandalf's passing in the Dimrill Dale - underneath that searing vocal is a string variation of this theme for Frodo. (Clearly the music that appears during the Dimrill Dale Lament and the Grey Havens is not the same as the Shire B theme, but it is musically related to that version of the Shire B theme I call Frodo's theme.) Though all the Fellowship grieves, the dramatic climax of that lament is Frodo's look at Aragorn. He feels the passing of Gandalf so dearly, as it is Gandalf who has guided his moves hitherto. The Frodo theme returns in The Return of the King as Gandalf farewells the four hobbits, and this variation is included on the album track 'The Grey Havens'. We then hear an even more plaintive version, not included on the album, as Frodo hands the book to Sam, and farewells Merry and Pippin. The Shire B theme then underscores Frodo's parting with Sam. Again here, Frodo's theme is underscoring a difficult decision - the decision to leave friends behind for good. (One of the beautiful things about ROTK is that it ends with another journey beginning.)

It is then, a theme for Frodo, and very often also for Frodo's relationship with Gandalf. What about its appearance at the end of The Two Towers, where Sam gives his great speech about the stories that really mattered? It's tempting to say this music is representing Sam, because he is the one speaking. I still think here, though, that the decision made here is Frodo's: having nearly given the Ring to a Nazgûl and come close to killing his friend, he makes a decision that the quest is possible - because of Sam's words. And Sam's word here, though less concisely eloquent than Gandalf's own bidding to Frodo - 'All you have to do...', is the impetus for Frodo's decision to push on.  We hear it also in FOTR when Aragorn sees Frodo and Sam climbing up the eastern shore of Rauros and says - 'Frodo's fate is no longer in our hands' - again it underscores Frodo's decision to continue to quest despite the breaking of the fellowship.

The theme in itself communicates something very different to me about Frodo as opposed to other hobbits, which is appropriate since he is a rare individual indeed. (Sidetrack: So often I hear of the heroism of Sam and feel that Frodo is unjustly subordinated to the position of - 'the one who Sam helped get there'. And this is wrong - Sam is important, but I doubt that had he carried the Ring to Mount Doom that even he could have thrown it in.) With Frodo's theme we hear something of that uniqueness and also loneliness in the character - he feels how alone he is in his quest whenever it plays. He is alone among hobbits in his inquisitiveness about the world and his perception of the weight of affairs that few other hobbits detect. Something about the melody of Frodo's theme captures that for me.

Though the connection is probably musically more tenuous, I feel that Frodo's theme is also suggested when the Fellowship laments Gandalf in the Dimrill Dale in FOTR, and at the Grey Havens, firstly when Gandalf farewells the Hobbits, and then (in an unreleased section) when Frodo farewells the other hobbits. Clearly there is strong similarity between the pathos-filled music in both of these sequences (which in turn are very similar to the string build-up to the statement of Frodo's theme at the end of TTT in the album track 'Samwise the Brave'). Whether this is an independent theme or is related, as I think, to what I call Frodo's theme, will doubtless be a matter for debate...

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(from cue notes that pertain to Sam's speech in Osgiliath)

Frodo’s Decision / Variation of Shire B

This is a particular variation of the Shire B theme that appears in FOTR:EE more than once. The Shire B theme is the melody of the chorus of song Shore wrote for FOTR, ‘In Dreams’. If you can imagine the chorus of that song in your head – ‘but in dreams, I can heard your name, and in dreams, we will meet again’ – that’s the Shire B theme. This particular variation of the Shire B theme shares the first three notes in common with that theme, and has appeared in a couple of places in FOTR. Firstly, it can be heard as Gandalf says his famous line to Frodo in Moria about how 'all WE have to decide is…' etc. (That cue is unreleased.) Secondly, it is heard in the ‘Breaking of the Fellowship’ cue as Frodo runs to the shore and pushes his boat out into the lake (FOTR, 17, 0:21-0:51). Thirdly it is heard when Frodo’s hand pulls the drowning Sam out of the water (FOTR, 17, 1:58-2:15). Fourthly it is heard when Aragorn indicates to Legolas and Gimli that ‘Frodo’s fate is no longer in our hands’ (FOTR, 17, 3:05-3:24). Fifthly, it is referenced as the Three Hunters are seen running up Amon Hen and the film cuts to Frodo and Sam walking over Amon Lhaw (FOTR, 17, 4:19-4:38)Lastly, it is referenced here in TTT:EE as Sam describes to Frodo how he has always wondered how the great stories of old could have happy endings.

Note that I’m not saying this is an independent theme. I think of it as a derivate of the Shire B theme, but one that seems to be consistently used whenever Frodo makes an important decision that involves him learning something more about the greater moral universe in which he is a hero. For that reason I call it ‘Frodo’s decision’. Elsewhere (perhaps one of Doug Adam’s FSM articles?) I’ve seen the Shire B motif referred to as ‘A Hobbit’s Understanding’, and that also is an excellent and very appropriate name for this motif, which has much to do with a particular hobbit’s understanding of the part he must play in the battle against evil. Not because that’s the only occasion for its use – but because it’s shorter than always referring to it as ‘that variation on the Shire B theme that appeared etc…’ This marks the last use of the ‘Frodo’s decision’ theme in the trilogy. It’s a shame there wasn’t room found for it in ROTK, but in between the Shire A, Fragrance of Ithilien, Shire B, West, Secondary West and Wisdom of Gandalf themes, that film’s finale was thematically crowded enough as it was.

FarFromHome's thoughts about A Hobbit's Understanding and the Hymn Setting of the Shire A melody:

Magpie notes: FarFromHome is using some pre-CR terminology here. Gandalf's Wisdom was one fan name for the music we now know as A Hobbit's Understanding. And by Shire Theme, she means most often, the Hymn Setting of the Shire Theme. But what she's really considering is the melody and not setting. She's looking at how the Shire A melody (the verse portion of the Shire Theme) interacts with the melody of A Hobbit's Understanding which is an expansion of the Shire B melody. So anytime you see "Gandalf's Wisdom" or "the 'All you have to decide' theme... think A Hobbit's Understanding. Anytime you see 'the Shire Theme', think of the familiar Shire A melody, most often here (but not necessarily exclusively)  in the Hymn Setting.

One of my favourite uses of the Shire theme is when it's combined with the theme sometimes called "Gandalf's wisdom", which plays under Gandalf's words, "All you have to decide is what to do with the time that is given to you" in Moria. When Frodo recalls these words before crossing the River, this theme begins and it continues and develops as Sam arrives and almost drowns. Then it resolves into the very pure 'hymn' version of the Shire theme as Frodo reaches out to hug Sam.

The same combination of themes is repeated soon afterwards, as the two hobbits look out over the Emyn Muil - first the "All you have to decide" theme as Frodo speaks of never seeing the others again, resolving into the Shire theme after Frodo says "Sam, I'm glad you're with me" and Sam smiles in return.

TTT has the same sequence - the "All you have to decide" theme under Sam's speech, and the Shire theme (this time on a deeper woodwind instrument - clarinet or cor anglais maybe?) as we see Frodo with tears in his eyes, finally over his Ring-induced despair and connecting with Sam again.

In ROTK, the final appearance of the "All you have to decide" theme begins as Frodo turns to say goodbye to Sam at the Havens, but this time there is no resolution into the Shire theme. It ends on a note of finality as Frodo turns from Sam to board the ship. The absence of the comforting Shire theme here speaks volumes.

(By the way, you wondered about the Herbs and Stewed Rabbit scene as one where the Shire theme might be expected. I would say that the reason the Shire theme isn't used in the scene is because of Gollum - it's not a scene of comfort and closeness between the hobbits, it's mostly about Gollum and Sam's very uncomfortable relationship. If the scene had played out like the book scene, where Frodo and Sam share the stew while Gollum is off hunting, the Shire theme would surely have made an appearance. But in fact, in the movie, they don't even get to eat that delicious-looking stew. Always seems such a waste, especially as poor Aragorn has to eat that really awful stew made by a certain Shieldmaiden of Rohan!)

One little point on a comment of yours:

When Sam makes his speech at Osgiliath, there's a moment when the camera goes to Gollum and PJ asked HS not to use the Shire theme there. (From TTT appendices material)

I remembered this little moment from the extras too. In fact, PJ specifically asks Shore to hold off on the Shire theme until we see that Sam has connected with Frodo - the camera shifts to Frodo, who has tears in his eyes. This underlines, for me, that the Shire theme is being used here, in parallel to the boat scene at the end of FOTR, to show the emotional connection that lifts Frodo's spirits again. In the book, when Frodo realizes that he doesn't have to go alone to Mordor after all, and that Sam is determined to come along, there's a lovely sentence: "A sudden warmth and gladness touched his heart." The Shire theme at the end of these fraught, emotional moments is the perfect echo of these words of Tolkien's, for me.