What kind of speakers would suit my room? (newbie's questions)

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I recently moved into a new apartment. It's not the largest, nor has the best isolation from the neighboring flats (it's sufficient, though), but I won't let that spoil my joy and keep me from getting the best sound system I can afford.

First I was almost ready to go and buy a pair of speakers on impulse. Then I thought I want to make them myself instead, something simple in construction, but from good components. But the more I keep thinking the more I realize I'm a noob in audio and should ask for some advice. So I'm thankful to everyone who keeps reading, and I hope my questions make enough sense to facilitate some answers.
I have a long history of being fond of music and of hardware that really makes music enjoyable. I've built a couple DIY components, even a pair of speakers; I've listened to and compared more than a few over the years. So I have some experience, but totally not enough to know right from wrong or what works from what doesn't.

So here's the living room in its current state: Imgur: The magic of the Internet
Can I squeeze a 5.1 system in here? On the top photograph of the room, I intend to put a TV and the front speakers along the wall on the right and a sofa on the left, with some small gap between sofa's back and the wall. I imagine it's not perfect, but could be enough for the rear speakers?

If a surround system won't work in this room, do I want bookshelf or floor-standing speakers? I would still want to use a dedicated subwoofer, not for loudness, but for the deep bass extension. And from my experience with tuning the sound system in my car, I learned that the direction to the source of a bass sound can be determined to as low as about 45 Hz. Certainly 50 Hz. So the main speakers need to be able to comfortably play down to 50 Hz. I should add that I never liked the sound of a bass reflex vent, maybe it's just me but it seems to blur the bass a tiny bit. Would rather live with a bigger enclosure and go for sealed box.

I have an eye on a full 5 speaker Dali Ikon 6 surround setup (only lacks the sub) on a local classifieds board.
And I also learned about these Chinese ribbon speakers: Fountek NeoX 2.0, and now I want to buy 5 of them for the 5 surround speakers, but I have no idea what to pair them with in terms of mid- and low range.

Again, any advice is highly welcome, and thanks for reading!
As shown in the photos, the room looks quite bright, and without a fair amount of at least minimal acoustic treatment with floor coverings, and wall hangings to cut down/diffract first reflections, and soft upholstered furniture as opposed to leather/vinyl, I think almost any speaker system will sound a bit chaotic. Until that is tamed, this could be a case where less is more.

Provided you have wherewithal to built the enclosures, there’s no reason why you couldn’t get decent results with DIY speakers at a fraction of the cost of higher priced boutique/ famous maker types. While I’ve owned and built both types over the past 50yrs, I’ve come to generally prefer floorstanders for a variety of reasons. Even with main speakers with well extended bass response, using one or more subwoofer(s) in even a 2 channel video system makes a ton of sense - most notably in terms of evening out response throughout the room.
Indeed, the room was very echo-y when it was empty, now it's a bit better already and I'll keep adding soft stuff (although I'd like to avoid a carpet).
The idea of using a sub as a remedy to spatial unevenness of the bass sound field across the room did cross my mind, but using two subs is ingenious, I've never heard of a setup like that. I've always struggled with some kind of standing waves in the bass region in all of my rooms, in some spots bass was rich and in others it was absent entirely.
And I would prefer floor-standing speakers even if for no other reason than to avoid buying speaker stands - would rather add their cost to the speakers themselves. But wanted to run this choice by someone knowledgeable.
Stereo bass is the thing to do.
Do you have any box dimensions in mind?
Yep, as I mentioned, I did notice while tuning the subwoofer in my car that I was able to locate the direction sound was coming from even at rather low frequencies down to 45 Hz at least, even if not as clearly as in the midrange.

Currently contemplating a pair of full-range floorstanding front speakers, meaning built-in subwoofer drivers rather than a single separate box.

I'm not too constrained in space, especially vertically and along the wall. I would prefer the depth of the box to be reasonable so that it doesn't stick into the room too much, but even that is not a requirement. Let's say up to 50 cm width, 70 tops (outer box dimensions), up to 35 cm depth (less if reasonably possible, but also could be more), and up to the ceiling in height :)

Budget is a fuzzy thing, it tends to grow as you encounter compromises. Let's say 1000 USD for the speakers themselves, with a possibility of expanding it to 1500 (not that I would love it, but if it's the price of the great sound versus good sound, I've been waiting for it too long already).
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Spoiler alert: more observations / disjointed ramblings to follow.

Even a small throw rug on the floor and wall hanging such as tapestries at first reflection points between the speakers will help tame things quite a bit. There’s lots to be found on the subject - including tutorials on DIY solutions - but full on gonzo treatments can get costly and bulky, particularly when trying to deal with overwhelming bass problems. Which, as it turns out is exactly what the use of multiple - and often smaller - subs can mitigate. That is also a subject on which a wealth of advice and tutorials are to be found. Check out the numerous You Tube videos by Audioholics - while not without his own “agenda” Gene has been campaigning tirelessly against snake oil and voodoo for decades.

I couldn’t agree more on the subject of floorstanders, with a couple of caveats:
1) As not all rooms can accommodate full sized enclosures for upwards of 7 channels - and let’s not even talk about Atmos :eek:- small bookshelf sized boxes that can be wall mounted on brackets certainly have their place. I’m doing exactly that in my own system.
2) While there may not be consensus on the subject here, and I won’t go into all my reasons, but a favourite hobby horse of mine is discrete center channel. As that is an area often constrained as to physical size of enclosure, a smaller design may need to be tailored to fit available space. Fortunately there’s lots of talent resident here up to that task.
With the very flexible bass management available in the DSP of modern era surround receivers that would have been a pipe dream when some of us here started out in this hobby 40 or 50 years ago, many models allow for the HP filter turnover points can be separately adjust for each channel, which means the centre channel can be smaller than the main L&R without a huge loss of quality. Even so, I’d endeavour to use drivers with as close to the same sonic signature/voicing across the front row. I’ve found that the peripheral surround effects channels needn’t be of the same caliber, power handling or bandwidth.

I’ve been playing with a variety of configurations of layout and gear in the same room for my now 7.1 surround system for well over 30yrs, and have been happy with the current set up for at least 3 - close to a record for me. ;)

Edit - your reply above posted while composing this, so I’d like to add one more point for now regarding multiple subs in a surround system: something I think you’ll find in any deep dive in the subject is that the key to them working in terms of mitigating uneven distribution is that they are not necessarily co-located with the mains. Please research the work by Floyd Toole and Earl Geddes - some which can be found on this site, and spend some time watching the YouTubes by Audioholics. While some find Gene’s “it’s science, folks” approach a bit perfunctory or even arrogant, I think you’ll thank me for it.

And yes, the perfect is the enemy of the “good enough”
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Many thanks for sharing your experience and the great advice! Definitely going to watch those videos in large quantities.
So do you think a 5-channel system could work in my 20 square meters (215 sq. ft) room? The ceiling height is only 2 meters 60 cm, sadly. I imagine that's also not great.
Sorry for the delayed reply to your latest queries.

Yeah, it does sound like the room is a bit small for a “serious” multi-channel system, but having heard several sound-bar and wireless sub combinations, of which I can understand the life-style / convenience appeal, but the sonics I heard (Vizio/Samsung? - I’m not even sure) - were only a modest improvement over TV’s own speakers. If I was in your shoes, I’d probably start with 3.1 using a smallish trio across the front, and a pair of small subs woofers not co-located. And even if your situation doesn’t allow space to add more channel for fuller immersive sound, I’d still recommend a proper surround receiver for the wealth of functionality baked into their DSP.
I happen to be a big fan of single driver/full-range speakers, and have waxed rhapsodically countless times that applications such as yours are an area where they can shine. But even compact 2-way or coax projects/kits such as numerous described on Part Express would work just fine - just use the same across the front row, and something much smaller for the surrounds, should site conditions and budget allow.
Enough of my bloviations, time for some voices to join the choir.
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In deference to your neighbors and cognizant of the challenges you might experience in selecting and then building loudspeakers, would I be out of line in wondering whether you might be better off with high quality headphones? There are a number of excellent headphones amps available (including DIY options here at diyAudio).

Just a thought...

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