First Time Using Lasso Tool, I Had A Lot Of Fun With This

Les Mis Shipping Showdown: Round of 32

turnchetta art by felicitymildradeworthington (deactivated)

I'm not beating myself up for no reason, I have to acausally incentivize my past self not to have fucked up

Triangle Tuesday 3: The orthocenter, the Euler line, and orthocentric systems

Previously, we have looked at two different ways to mark a point in a triangle. First, we drew cevians (lines from the vertices) to the midpoints of the sides and found that they all cross at a point, which is the centroid. Then we tried drawing perpendiculars to the sides from the midpoints, and those all met at the circumcenter. And you could do this with any point on the side of a triangle -- draw a cevian to it, or a perpendicular from it, and see what happens.

This time, though, we're going to do both. That is, we're going to work with the cevians that also form perpendiculars to the sides. These are the altitudes, which run from a vertex to the nearest point on the opposite side, called the foot of the altitude. The three altitudes all meet at a point H, and that's the orthocenter. (The letter H has been used to mark the orthocenter since at least the late 19th century. I believe it's from the German Höhenschnittpunkt, "altitude intersection point.") Anyway, let's prove that the orthocenter exists.

Theorem: the three altitudes of a triangle coincide.

Here's a very simple proof that the three altitudes coincide. It relies on the existence of the circumcenter, which we already proved before. Given a triangle ABC, draw a line through A parallel to the opposite side BC. Do the same at B and C. These lines cross at D, E, and F and form the antimedial triangle (in blue).

Then the altitudes of ABC are also the perpendicular bisectors of DEF. We proved before that perpendicular bisectors all meet at a point, therefore altitudes do as well.

That was easy. Let's do it again, but in a different way. It's not quite as simple, but it includes a large bonus.

Theorem: the three altitudes of a triangle coincide at a point colinear with the circumcenter and centroid, and GH = 2 GO.

Let's take triangle ABC, and let F be the midpoint of side AB. Then mark two points that we already know, the circumcenter O and the centroid G. We'll also draw the median (green) and the perpendicular bisector (blue) that run through F, leaving the other ones out to avoid cluttering the picture.

We already know from our look at the centroid that G cuts segment FC at a third of its length, so GC = 2GF. Let's extend segment OG in the direction of G by twice its length out to a point we'll label H, so that GH = 2GO.

Now consider the two triangles GOF and GHC. By construction, their two blue sides are in the ratio 1:2, and the same for their two black sides. They also meet in vertical angles at their common vertex G. So by side-angle-side, the triangles are similar, and it follows that HC is parallel to OF, and therefore perpendicular to AB. So H lies on the altitude from H to side AB.

By analogous construction, we can show that H also lies on the other two altitudes. So not only have we proved that the altitudes coincide, but also that O, G, and H all lie on a line, and furthermore that G is located one third of the way from O to H, in any triangle.

This proof is due to Leonard Euler, and the line OGH is called the Euler line. Not only these three points but many others as well fall on this line, which we will get to later on.

Let's look at some more properties of the orthocenter and the feet of the altitudes. I'm just going to look at the case of an acute triangle for now, and show how this extends to the obtuse case later.

Theorem: two vertices of a triangle and the feet of the altitudes from those vertices are concyclic.

Proof is easy: the two right triangles AHcC and AHaC share segment AC as a hypotenuse. Therefore AC is a diameter of the common circumcircle of AHcC and AHaC (following from Thales's theorem).

(Incidentally, look at the angle formed by the blue segment and the altitude CHc. It subtends the same arc as angle CAHa, so (by the inscribed angle theorem again) they must be equal. That's not a part of this theorem, so just tuck that fact away for a moment.)

Theorem: a vertex, the two adjacent feet of the altitudes, and the orthocenter are concyclic.

Same idea, but now the right triangles are AHcH and AHbH, and AH is the diameter of the common circumcircle.

(And incidentally, look at the angle formed by the new blue line and the altitude CHc. It subtends the same arc as HbAH, which is same angle as CAHa. So those angles must be equal too. Since both angles between a blue line and the altitude CHc are equal to the same thing, they are equal to each other. Again, not a part of this theorem, just something I wanted to note.)

So those are some interesting concyclicities, but now let's look at the pedal triangle of the orthocenter, which is called the orthic triangle.

Oh, hey, it's made up blue lines, just like the ones we were talking about. And we proved that the two longest blue lines make equal angles with the altitude between them. By symmetry, we can prove the same thing about all the angles made by the blue lines. So that means

Theorem: two sides of the orthic triangle make equal angles with the altitude between them.

Another way to say this is that the altitudes are the angle bisectors of the orthic triangle. And I admit that was kind of a roundabout way to introduce the orthic triangle, but I think it makes the proof of this property easier to follow.

Two other properties of the orthic triangle immediately follow from this:

In an acute triangle, the inscribed triangle with the shortest perimeter is the orthic triangle

and

In an acute triangle, the orthic triangle forms a triangular closed path for a beam of light reflected around a triangle

which are two ways of saying the same thing.

But those two properties only hold for acute triangles. What happens to the orthic triangle in an obtuse triangle? Let's push point C downward to make triangle ABC obtuse and see what happens. To make things clear, I'm going to extend the sides of ABC and the altitudes from line segments into lines. Here's the before:

And here's the after:

The orthocenter has moved outside of triangle ABC, and two of the altitudes have their feet on extensions of the sides of ABC rather than on the segments AC and BC. The orthic triangle now extends outside ABC, and certainly isn't the inscribed triangle with the shortest perimeter any more.

But look at it another way. We now have an acute triangle ABH, and the line HHc is an altitude of both the obtuse triangle ABC and the acute triangle ABH. Meanwhile, lines AC and BC have become altitudes of ABH.

So what we have is essentially the same acute triangle with two swaps: point C trades places with H, and Ha trades places with Hb. That means that our two theorems about concyclic points morph into each other as triangle ABC switches between acute and obtuse. Here's an animation to show the process:

And this is why I didn't bother with the obtuse case above -- each theorem of concyclicity is the obtuse case of the other.

So if we can just exchange the orthocenter with one of the vertices, what does this mean for their relationship? If you are given a group of vertices and lines, how can you tell which one is the orthocenter and which one are the vertices? Well, you can't.

Theorem: Given an acute or obtuse triangle ABC and its orthocenter H, A is the orthocenter of triangle BCH, B is the orthocenter of ACH, and C is the orthocenter of ABH.

The proof comes from consulting either of the "before" and "after" figures above. Take any three lines that form a triangle, red or black. The other three lines are then the altitudes of that triangle. The three feet are where a red and black line meet perpendicularly, so they are the same for all four possible triangles, which means all four share the same orthic triangle.

(Of course, if ABC is a right triangle, then we get a degenerate case, as you can see from the gif at the moment when C and H meet.)

Such an arrangement of four points is called an orthocentric system. Of the four points, one is always located inside an acute triangle formed by the other three, and it's conventional to label the interior one H and the others ABC.

Orthocentric systems pop up all over the place in triangles, so expect to see more of them as we go along. Now, let me do one little lemma about altitudes, and then I'll show something cool about orthocentric systems.

Lemma: the segment of an altitude from the orthocenter to a side of the triangle is equal to the extension of the altitude from the side to the circumcircle.

We can show this with just a little shuffling of angle identities. Extend altitude CHc to meet the circumcircle at C'. The angles CAB and CC'B, labeled in red, subtend the same arcs, so they are equal. Triangle ABHb is a right triangle, so angle HbBA, in blue, is complementary to it. The same is true for the right triangle C'BHc, so the two angles labeled in blue are equal. Then by angle-side-angle, triangles BHcH and HHcC' are congruent, and segment HHc = HcC'.

By the same argument, we can show that triangle AHHc is congruent to AC'Hc, which leads us into the next bit.

Theorem: all the circumcircles of the triangles of an orthocentric system are the same size.

The blue triangle has the same circumcircle as triangle ABC. From the foregoing, the blue and green triangles are congruent. Therefore their circumcircles are the same size as well. The same argument works for ACH and BCH.

So here is an orthocentric system with its four circumcircles.

The four circumcenters O, Oa, Ob, and Oc form another orthocentric system, congruent to the first one.

If you found this interesting, please try drawing some of this stuff for yourself! You can use a compass and straightedge, or software such as Geogebra, which I used to make all my drawings. You can try it on the web here or download apps to run on your own computer here.

I love Golurk's looming, awkward appearance, and how it seems like it's held up by ancient magitek. All of its details contribute to an aesthetic of ruin and age. It seems like such a mournful, protective force. I particularly like the jagged crack in its chest that has been repaired with the same substance as its wristbands. Sometimes I wonder whether it repaired itself, or if another entity did -- and who created it in the first place?

Best Underdog Whose Name Starts With "G" 📂🇬🖋️

Round 2 - Match 4

Our Contestants:

This poll is part of an event that allows the early eliminees from the main tournament have more time in the spotlight!

That's Danish; IKEA is Swedish.

the bluetooth chip in my beloved ikea eneby speaker (with the gay pride front cover) decided abruptly to stop connecting to devices today TT__TT i cracked the thing open of course and had a look but unplugging and replugging various cables had no effect; next course of action is probably to try to resolder the bluetooth daughter board (which i HAVE identified, thank you ifixit) except i still haven't unpacked my soldering iron post move and now it's buried in the shed in one of several boxes all of which are behind the woodworking bench and like three bikes. fortunately the 3.5mm jack still works so i THINK my strat is going to be to just fucking plug in one of those bluetooth 3.5mm adapters until i can get my tools unfucked enough to hopefully fix it properly. and of course i can't just get a replacement because ikea has discontinued the eneby because fuck you that's why

anti AI guys keep making AI sound so fucking cool

Turnchetta playlist for @lesmisshippingshowdown

This is for @lesmisshippingshowdown which allows fanworks to give extra points in the polls. We are trying to get the very canonical and important pairing of Turning Woman #3 (a chorus member from the 2012 movie) and Musichetta (Joly's never-onscreen girlfriend from the book) onto the next round.

Even if you don't have a clue what Les Miserables is, can you vote Turnchetta here? As a favor? And if you're not sure, maybe this playlist will convince you of their deep canonicity and long-term importance to the fandom. Or just do it for chaos. Either one as long as you do it.

Spotify playlist:

Tracklist

Three Coins in the Fountain - Connie Francis

Musichetta stupidotta, scanzonata, innocente - Commenti Sonori

My Baby Loves A Bunch of Authors - Moxy Fruvous

What's Love Got To Do With It - Tina Turner

You Turn The Screws - Cake

Turn, Turn, Turn - Dolly Parton

Who Will Shoe Your Pretty Little Feet - Tennesse Ernie Ford

The World Spins Madly On - The Weepies

Sunday Bloody Sunday - U2

飛哥跌落坑渠 (Teddy Boy in the Gutter) - 李寶瑩, 鄧寄塵, 鄭君綿 歡場三怪

Turn Around - They Might Be Giants

Tangled Up In Blue

Heartaches by the Number - Cyndi Lauper

Three Times a Lady - Sissel

Let's Face The Music And Dance - Diana Krall

Turn The World Around - Womansong

Liner notes and Youtube links under the cut. (Fanmix liner notes means "write a synopsis of an entire hypothetical musical" right? That's how I've always done it.)

These are largely old standards, which meant I had a range of cover options, and I went with women's covers most of the time. However some of them I couldn't find an exact match on Youtube and Spotify so a few tracks will be different between the two.

Three Coins in the Fountain - Connie Francis

This was the first song I thought of for a Musichetta and Three mix! You can read this either as the three being Musichetta, Joly and Bossuet, and only one of them gets a happy ever after - or you can read it as Musichetta, Three, and one of their other working woman friends, and only one of them ends up marrying rich.

2. Musichetta stupidotta, scanzonata, innocente - Commenti Sonori

We needed an actual musichetta on this mix. The title translates as "Muschetta stupid, carefree, and innocent" - this is her in her early days, working, spending time with the girlfriends of her youth like Three, dreaming of a superb future.

3. My Baby Loves A Bunch of Authors - Moxy Fruvous

Here she is getting as she gets more involved with the students, gets drawn into the artistic world, goes to fancy parties, becomes someone's mistress.

4. What's Love Got To Do With It - Tina Turner

That world of surface romance and semi-transactional sex starts to harden her, even as she has one (two?) boys who delight in her and she in them.

5. You Turn The Screws - Cake

In the full musical version this would be a duet between Three and Musichetta where they are growing apart as she draws further into the political, literary, and bourgeois world of her students and Three commits to staying as she is and they both become scornful of each other's priorities. They see each other in passing around the Corinthe and don't speak. (This is probably happening around the time of the July revolution.)

6. Turn, Turn, Turn - Dolly Parton

And time passes and everyone gets older, and maybe it can go on like this forever but time passes and it won't, but it's always been that way. (This song is a quote from the book of Ecclesiastes which is very good poetry to read when you're disillusioned with the world and not sure what the point of keeping going is when it's just more of the same.)

7. Who Will Shoe Your Pretty Little Feet - Tennessee Ernie Ford

There start to be ominous undertones in Musichetta's world. It feels like July 1830 only somehow not the same. Her sweet boys fuss over her but at the same time start making noises about what she'll do when they're gone (but with very little understanding of what she *will* do if they're gone. She doesn't disillusion them of course.

8. The World Spins Madly On - The Weepies

This song plays while both Musichetta and Three are hold up in their separate apartments across town from each other, hearing the gunshots go off and staying in bed, Musichetta thinking about how she's abandoned her boys to fight without her and Three thinking about how she's let Musichetta get involved in all that without her

9. Sunday Bloody Sunday - U2

They wake up and go down to the Rue Chanvrerie and get blood all over their pretty little feet and their eyes meet while they sing.

10. 飛哥跌落坑渠 (Teddy Boy in the Gutter) - 李寶瑩, 鄧寄塵, 鄭君綿 歡場三怪

This is a reprise of the first song, courtesy of 1960s Catonese cinema which rewrote the lyrics as being about a girl of the town finding her boy stinking and disgusting in the gutter. I think it's supposed to be a scathing parody and he's just drunk and wearing too much perfume, but to the extent of my ability to translate the Cantonese, I think it also works here, as Three and Musichetta find the remains of her boys and Three is scornful of her squeamishness while hiding her compassion for her grief

11. Turn Around - They Might Be Giants

Trauma. They don't deal well with the survivor's guilt.

12. Tangled Up In Blue - Indigo Girls

This is the key to the whole love story, I knew this song in the Indigo Girls cover first, so it's always been a song about start-cross lesbians; they knew each other once, and they weren't even that different in class, but one of them ended up drifting and taking whatever manual work she could to get by, and one committed to spending time with college boys and reading medieval Italian poetry, and they keep coming together and separating again because they can't stay apart but they can't compromise with each other either. This is Three's song for Musichetta (how the specific incidents in the song line up with the plot is up to the person who ends up writing the book.)

13. Heartaches by the Number - Cyndi Lauper

This is Musichetta's song for Three - from her POV Three keeps leaving and breaking her heart while stays still, even though at the time Three left she thought it didn't matter and she didn't care, looking back from this end she can't stand it, and she's determined the next time she sees Three she makes it clear how much it hurt her.

14. Three Times a Lady - Sissel

And here she finally meets up with Three again but instead of pouring out her hurt she ends up pouring out her love instead!

15. Let's Face The Music And Dance - Diana Krall

Well, says Three, the world is awful and nothing we do matters, so we might as well keep trying to make it better (this is Three admitting that she loves Musichetta too, and her boys and their lost causes weren't all wrong.)

16. Turn The World Around

(Couldn't find the version on spotify on Youtube, so this is a random women's community chorus.)

With Musichetta's and Three's views reconciled, they realize that the key is to forget everyone's old grievances and come together in solidarity to make the world better for everyone with everyone's skills and resources together, and it does matter, and they lead the Turning women (who have also all paired off now) in this song instead.

Curtain call!

Bad analogy : Like playing badminton with a tennis racquet on a squash court :: Worse analogy : Like playing worseminton with a tennis racquet on a squash court

This is the Eposette Sonatina (as opposed to a Sonata, because I think I played a bit too fast and loose with the form to call it that) I've been working on as a steal for @lesmisshippingshowdown ! It was a bit of a rush job since I only started it last week, but if you listen I hope you enjoy! I like to give a narrative to the music I write, so I've posted an 'analysis' explaining the narrative of this Sonatina under the read more of each movement - warning: it gets long! Bear in mind, it's going to be a very vague plot since it's just the idea of what's going on in the music, not a fully developed story

Before I start with an analysis of the movements, I want to break down the instrumentation. The brass and woodwind instruments are each meant to be the "voice" of a specific character, while the string and percussion are the accompaniment generally either representing the physical or emotional atmosphere. The instruments used are

Piccolo - This is Cosette's instrument. I chose it because of it's clear, cheerful, and bird-like tone that I thought suited her.

Oboe - This is Eponine's instrument. I wanted an instrument with a lower range and more "scratchy" sound than the Piccolo, both because of how Eponine's voice is described, and because I think it suits her personality.

Bassoon - This is Valjean's instrument. I want it to be a low-pitched instrument, with a warm sound. Originally I considered the Double Bass but I decided I wanted him to be a woodwind like Cosette.

Trumpet - Gavroche! Trumpets can sound both playful and heroic, which I thought was perfect for him. Also, his first appearance in the Sonatina is to annoy Eponine, which I feel suits a Trumpet pretty well.

Saxophone - Thenardier. So fun fact, to write this song I used MuseScore, which anyone who uses it will tell you... the soundfonts for the instruments are not the best, so I used the free BBC Sounds Orchestra plugin to make the instruments sound 1. more like the actual instruments and 2. prettier. Guess what instrument the plugin doesn't have. The Saxophone. I think it works though, the other instruments have a much smoother sound while the Saxophone comes in sounding abrasive, which was my intention anyways for choosing this instrument. I debated using a different instrument because technically the Saxophone wasn't invented until after Eponine died in canon, but I just feel like it's sound is so good for Thenardier.

French Horn - Javert. Brass instruments have a bit of an association with authority in Europe, so I knew I wanted him to be brass. I already gave the Trumpet to Gavroche (for completely different reasons), and I thought the Tuba was too low and the Trombone was too welcoming for Javert so... French Horn!

Harp - The Harp is the only constant in the entire Sonatina. It's there more for atmosphere, but to me it alternates between being Paris, water, and the sky.

Viola, Cello - Originally added to the score by mistake, but I decided to keep them!

Violin, Double Bass - I won't lie to you, I added these because the final movement felt too hollow without them. They can represent whatever you want, their real purpose is just to make the song sound more whole and warm.

Celesta - Generally, the night sky.

Glockenspiel - Generally, stars (in their multitudes).

None of the movements have all of these instruments at once, The first two movements have three instruments each, the third movement has everything but the Violin, Double Bass, Celesta, and Glockenspiel, and the final movement has everything but the French Horn and Saxophone.

Movement I: Retrouvailles

Instruments: Piccolo, Oboe, Harp

0:00 - 0:05 : This first bit of melody here is inspired by the sound of lark song, I though it would be a nice idea for her melody.

0:00 - 0:22 : This is the introduction to Cosette, the melody is largely quick in rhythm to try and convey her personality as being cheerful a full of love of life.

0:22 - 0:47 : This is the transition to the B section, I imagine this as being a transition along the streets of Paris from where Cosette is to where Eponine is.

0:47 - 0:54 : This is Eponine's theme. It's slower in rhythm and largely descending to try and portray the underlying sadness in her life.

1:00 - 1:24 : Here Eponine pulls herself into a cheerful mood and bumps into Cosette.

1:24 - 1:51 : Eponine and Cosette, not recognizing each other, have a brief pleasant conversation.

1:52 - 2:01 : They introduce each other, Eponine gives Cosette one of the letters from her father asking for money.

2:01 - 2:12 : Both girls begin to find each other familiar.

2:12 - 2:17 : Eponine realizes who Cosette is. The Oboe plays a dissonant note as Eponine's kneejerk response is a mix of jealousy and resentment.

2:17 - 2:25 : Eponine tries to shut down her initial reaction, realizing that in their switched positions Cosette is much kinder than Eponine was.

2:25 - 2:30 : Eponine half admits who she is.

2:38 - 2:51 : Cosette realizes who Eponine is, and in doing so remembers her childhood and panics.

2:52 - 3:15 : Cosette's theme has returned, but now in a minor key. What she has remembered has thrown her off, and made her feel off center.

3:15 - 3:34 : Transition to the Thenardiers residence.

3:34 - 3:51 : Eponine reflects on the encounter with Cosette, feeling like shit about it.

3:51 - 3:55 : Cosette's little motif plays at the end to show that both of them are on each other's minds.

Movement II: Regrets en variation

Instruments: Oboe, Harp, Trumpet

00:00 - 00:14 : Eponine is reflecting on her childhood with Cosette, feeling uneasy, the melody ends with a reference to Cosette's two note motif.

00:14 - 00:31 : Eponine realizes the unease is guilt, and that she doesn't know how to excuse it.

00:31 - 00:36 : Just as Eponine starts to really work herself up, Gavroche appears.

00:36 - 00:44 : Not knowing what's bothering her, Gavroche mimics Eponine's moping.

00:45 - 00:46 : She snaps at him.

00:46 - 1:00 : Gavroche gets Eponine to admit what's bothering her

1:00 - 1:07 Gavroche essentially says "oh well", since there's nothing that she can do about it now, and tells her to not be a dick to Cosette if they run into each other.

1:07 - 1:23 : Eponine agrees with him, he brags about being wise which she thinks is funny, and they sit together.

Movement III: Réconciliation du trio

This movement is traditionally a Minuet & Trio in a Sonata. I've swapped the Minuet for a Bourree, and this is ironically the first movement in my sonatina to NOT be a trio.

Instruments: Piccolo, Harp, Bassoon, Viola, Violin, Oboe, Saxophone, Trumpet, French Horn

00:00 - 01:05 : Cosette reflects on her childhood and her current life The melody starts with a version of Eponine's motif, but with the notes played at half the rhythmic value, as Eponine is on her mind.

01:05 - 01:19 - Cosette calls for Valjean and asks him about her childhood. He is evasive, Here, the viola and cello pass a contrasting melody back and forth to show the clashing between what Cosette wants Valjean to tell her and what he wants to tell her.

01:19 - 01:39 : Cosette admits to Valjean that she remembers some things, and reassures him that she can handle whatever he isn't telling hre.

01:39 - 02:14 : In the repeat, Valjean tells her what he can without mentioning his own past. She realizes he is still hiding something, but he assures her that it has nothing to do with her and he will tell her eventually. Reassured, Cosette feels secure in her identity and makes peace with her memories.

02:14 - 02:28 : Cosette thinks on it and decides she is glad to have run into Eponine since it gave her the clarity of remembering how she came to live with Valjean.

2:28 - 2:37 : Upon remembering Eponine, Cosette feels sympathy for her situation.

2:38 - 2:47 : She remembers the letter Eponine gave her, adn decides to go with Valjean to offer them help.

2:48 - 2:54 : This new section is a waltz, since it features Thenardier I thought it would be fun to reference his songs in the musical. Cosette and Valjean arrive at the Thenardier's, where they exchange pleasantries with Thenardier and Eponine.

2:54 - 3:07 : Thenardier begins to recognize Valjean. Valjean, Eponine, and Cosette all try to evade this.

3:07 - 3:18 : While note convinced, Thenardier allows them to keep up the charade.

3:18 - 3:27 : Thenardier realizes who Cosette and Valjean are.

3:27 - 3:30 : Thenardier attempts to blackmail Valjean. Gavroche arrives on the scene.

3:30 - 3:34 : Valjean and Eponine try to bluff their way out of it. Gavroche realizes what's happening.

3:41 - 3:44 : Thenardier insists he knows them while Cosette and Valjean continue trying to deny it. Eponine threatens to scream for the cops if he doesn't leave them alone. He continues

3:44 - 3:48 : Eponine screams. Javert can be heard approaching. Thenardier panics.

3:48 - 3:50 : Just as Javert is about to arrive on the scene, Eponine, Gavroche, Cosette, and Valjean flee.

3:51 - 4:11 : Javert confronts Thenardier, who tries to talk his way out of the situation. Both instruments play some dissonant notes to portray how each of them is threatening in their own way.

4:15 - 4:44 : Cosette, Eponine, Valjean, and Gavroche have a conversation as they are secure that they were not followed.

4:44 - 5:20 : Cosette and Eponine discuss their shared past, making it clear to each other that there is no underlying resentment.

5:22 - 5:57 : Cosette reflects on the past few events, finding that even though it was scary she feels content knowing it's behind her. Valjean is just happy that she's happy.

Movement IV: Romance Finale

I've run out of time to post the analysis! Safe to say, it's mostly just Eponine and Cosette continuing to meet with each other and their relationship growing romantic. When you hear the Bassoon that means Valjean is interacting with them, when you hear the Trumpet then Gavroche is there. The first section takes place in Cosette's garden where her and Eponine have a pleasant conversation, during the first waltz it's meant to show that Eponine is on friendly terms with Valjean as well and is regularly around as Cosettes friend. The first time the trumpet plays it's Gavroche popping up to tease his sister, but he quickly gets distracted by talking a mile a minute to Valjean. After that each section is essentially just Eponine and Cosette growing closer and their relationship becoming romantic.

Instruments: Harp, Celesta, Glockenspiel, Oboe, Piccolo, Violas, Cellos, Violins, Double Basses, Bassoon, and Trumpet.

EDIT: I realized that the player might not showing how long the song is, so the final movement is 7:55 according to musescore