Why subs aren't room dependent

Ғылым және технология

How is it possible a subwoofer can make bass in the same room where the main speakers cannot?

Пікірлер: 113

  • @bf0189
    @bf0189 Жыл бұрын

    Music is meant to be felt not just be listened to. A good sub is essential.

  • @googoo-gjoob

    @googoo-gjoob

    Жыл бұрын

    absotively

  • @edmaster3147

    @edmaster3147

    Жыл бұрын

    just go for a system with 18 inch woofers in the speakers, and if the situation makes subs a solution, it might be nice having two big ones :)

  • @Oystein87

    @Oystein87

    Жыл бұрын

    ​@@edmaster3147 No... Too big

  • @edmaster3147

    @edmaster3147

    Жыл бұрын

    @@Oystein87 It's just a matter of getting used to that two elephans are hiding in the living lol...But really, if it's all about the sound bigger is better. cheers

  • @Oystein87

    @Oystein87

    Жыл бұрын

    @@edmaster3147 Haha😅👍 Well.. Not always bigger is better.. Never that easy😉 Sound is never easy😝

  • @glenncurry3041
    @glenncurry3041 Жыл бұрын

    Yes thank you for helping us get through COVID with your videos, humor, knowledge and concern.

  • @richh650
    @richh650 Жыл бұрын

    Excellent explanation Paul on home sub placement!

  • @DaveC1983.
    @DaveC1983. Жыл бұрын

    Thanks Paul another great video, I love how you simpler audio advice for us newbies

  • @pablolubbert9739
    @pablolubbert9739 Жыл бұрын

    Hello Paul, I am a fan of yours, it is not only for your ample knowledge and how easily you pass it on to us, but also your great personality. You've said many times that to reach the best sound we need subwoofers and I agree, also that placement of speakers and subs will never be the same. So, please show us a room with FR30s and subs so that we can do an audition. Looking forward to that!

  • @grumpy9478
    @grumpy9478 Жыл бұрын

    when Paul sez not wanting to "hear" subs, I think he means "localize".

  • @alex_stanley

    @alex_stanley

    Жыл бұрын

    Agreed. And, the delocalization is best with two subs.

  • @ThinkingBetter
    @ThinkingBetter Жыл бұрын

    This is why a great system with lots of bass doesn't need large stereo speakers. Rather, a pair of smaller bookshelf speakers and one or two subwoofers can easily beat much bigger (and more expensive) stereo speakers without subwoofer.

  • @Oystein87

    @Oystein87

    Жыл бұрын

    Or just have both.. Bigger speakers AND a sub or subs.

  • @ThinkingBetter

    @ThinkingBetter

    Жыл бұрын

    @@Oystein87 Not really. When you have both you run into more cancelation control issues and having two totally different speakers outputting the same frequencies is never a good thing for the purest audio fidelity. Better is to cross-over the sub bass from your stereo speakers so the sub bass gets its full and cleanest potential. For example, if you have a high quality subwoofer that can play loud down to 20Hz, you can easily find your stereo speakers becoming distorted in the sub bass when you play loud, if they are allowed to try to play loud at sub bass frequencies.

  • @Oystein87

    @Oystein87

    Жыл бұрын

    @@ThinkingBetter Yes really. Adjust the sub properly and it plays like a dream❤️ And they are not really outputting the same freq when they roll off... That is exactly where the sub comes in. Done this for many years now and it works perfect every time

  • @ThinkingBetter

    @ThinkingBetter

    Жыл бұрын

    @@Oystein87 Done it for many years, and the best sub bass is done by speakers not struggling with sub bass. Lots of stereo speakers create insane amounts of distortion in the sub bass as the side speaker driver excursion becomes un-linear, bass ports create air noise, woofer cone motion creates phase distortion etc. The perfect sub bass is one that is well balanced (frequency response), low distortion and short decay.

  • @Oystein87

    @Oystein87

    Жыл бұрын

    @@ThinkingBetter Haha. The best is to have floorstanding speakers AND sub. MUCH more room filling sound and sounds more natural. Dude... Adjust the sub and actually get a good sub and all of those issues you mention are gone.. My 12" floorstanding and 12" sub plays in perfect harmony and balance each other perfect. They sound like one big speaker driver both in sweet spot and placing my head right next to them. So yeah.. Proves ypu wrong since MANY people have done this for years now with brilliant results.

  • @mariocassar6087
    @mariocassar6087 Жыл бұрын

    I beg to differ. The low bass extension depends mostly on the room dimensions.

  • @nomorokay

    @nomorokay

    Жыл бұрын

    You'd think so, but then how can headphones reproduce deep bass notes? And yet, the good ones do.

  • @stimpy1226
    @stimpy1226 Жыл бұрын

    Great question!

  • @bikdav
    @bikdav Жыл бұрын

    That's a great explanation. I wondered about that also.

  • @kevinfreestone9822
    @kevinfreestone9822 Жыл бұрын

    Very interesting. I must say that I love your posts. One point please, I was watching a KZread post the other day and the presenter spoke about taking two subs and pointing them towards a corner of a room. Granted, he was talking about a PA setup, but has anyone tried this approach?

  • @catdeddy8427
    @catdeddy8427 Жыл бұрын

    One other thing to consider is that we do not hear those extra low frequencies from a particular direction as we perceive directionality from the higher frequencies. The lows can emanate from almost anywhere in the room and we still hear them well.

  • @edmaster3147

    @edmaster3147

    Жыл бұрын

    Have you ever considered that the experience of sound is not only of the ear, but also of the other senses. Like feeling the sound waves, the speakers delivering heavy bass notes or perhaps a brass bass. Or an organ. It is known that bass in digital reproduction is quite difficult, losing the extra senses of the experience.

  • @electroimpyo
    @electroimpyo Жыл бұрын

    I love your channel and I am about to build a tube amplifier using pcl 82 and pcl 81

  • @daleboylen6427
    @daleboylen642710 ай бұрын

    I personally think there is a LOT more to this than speaker placement in a room. I think it has FAR more to do with low frequency phase shifts than room nodes. And, any driver has mass, suspension, and damping (by the suspension's resistive losses and the amplifier). Thus, it is a "damped harmonic oscillator"- in a Physics 101 book. A damped, harmonic oscillator also has a high-frequency limit, imposed by its moving mass- which equals phase shift in the highs, or time delay. It has phase shift in the low frequencies, because it has mass bouncing on a suspension (it's a mass/spring system), as described above. And since it cannot be an infinitely-rigid cone, it has cone breakup too, which imposes a ragged phase error across the roll-off region, a raggedness that changes with loudness too. The often variable pass filters on subs adds phase shifts as well. I'm not a fan of subwoofers. YMMV

  • @jtmcfarland3512
    @jtmcfarland3512 Жыл бұрын

    I think to clarify, we need to say subwoofers ARE effected by room design. It’s just a different effect and for different reasons.

  • @cravenmoore7778
    @cravenmoore7778 Жыл бұрын

    And a nice flower garden also

  • @stephenstevens6573
    @stephenstevens6573 Жыл бұрын

    If this is indeed the case(which I believe it is) then why do speaker designers concentrate so much, and brag upon how low their main speakers go?? Why deal with it at all, if the intent is to use a sub with them in the first place? I would think it would make more sense to just concentrate on the mids and highs and simply relegate the bass to a quality sub?😊

  • @PetraKann

    @PetraKann

    Жыл бұрын

    Sound wavelength is the key here. A 26Hz frequency coming out of a subwoofer or any speaker has a wavelength of over 13 metres. Even at 52Hz the wavelength is still 6 metres. We Cant physically or acoustically image a stereo soundscape at these wavelengths in a room that is smaller than these wavelengths. Psychoacoustics is another topic altogether

  • @slode1693

    @slode1693

    Жыл бұрын

    For one it's not necessarily the "intention" of the speaker designers to use a sub with them. And two from my albeit limited experience I've found the lower the mains go the lower you can cross over the sub and the better you can integrate a sub and make it sound like ALL of the sound is coming from the mains. Bass is less directional the lower the frequency, and if you can get the sub/s only putting out 40Hz at a flat response. Most of those rated down to 30Hz have a pretty good dip below 40. And I've helped setup 5.1 systems with decent satellite speakers and a sub crossed over at 100 Hz and the source of the mid bass is very apparent.

  • @stephenstevens6573

    @stephenstevens6573

    Жыл бұрын

    @@slode1693 all I am saying gentlemen, is that in my experience, you can get superior sound out of stand mounted bookshelf style speakers with a good set of subs as you can out of floor standers. I don't have a dog in this fight as after years of experimentation, I have returned to Magnapans and subs. That's where my sweet spot is. I am also interested in the new Magnapan subs. They sound very promising

  • @lexicon612

    @lexicon612

    Жыл бұрын

    OK Paul...I need clarification here. Not everyone's main speakers go down to 30Hz. I would venture a guess that most audiophile systems (main's) do not. You preach (as I do) the necessity of stereo sub's in any system (that does not go down to 30Hz) You walk the tightrope and call the imaging sub's do as "Musical Cues" . I call it what it is, Imaging. Are you now telling me that I need a 3rd sub somewhere in the rear of the room to "fill in the gaps" or just play 30Hz and below, only...Or does this advise only apply to people that have full range main speakers. Also how are you wiring that rear of the room sub. High level speaker wire or because it's only 30Hz and below, RCA or balanced summed (mono) is fine? Can I assume that proximity to each of the main speakers for stereo sub's is important, for proper "musical cues" imaging?

  • @slode1693

    @slode1693

    Жыл бұрын

    @@lexicon612 I've never heard Paul preach of "stereo" subs. Sub location is independent of the mains, rarely symmetrical, and has no (or should not have) effect on imaging. Thier only job is to improve bass at the listening position/s. Positioning of the sub/s is soley dependent on their impact at the listening position.

  • @genkifd
    @genkifd Жыл бұрын

    ok totally understand and also this explains why my floorstands i get cancellation around the 35hz region due to my small dedicated listening room. my dilemma how to get deeper bass without a sub (no space).

  • @alejandrobusquets6214

    @alejandrobusquets6214

    Жыл бұрын

    In principle, there is no way... Place the main speakers in the best possible position, specifically for the 120 Hz to 20 KHz range, obviously from the perspective of your chair. Now, look for a space: under a table, under an armchair, between walls (table rock); once you have the dimensions of that or those possible cavities, search the market among the subwoofers that can be placed under a coffee table, or an armchair, or on the wall. Sometimes a well-designed subwoofer, even as small as 8", can generate great sound from 22-24 Hz.

  • @genkifd

    @genkifd

    Жыл бұрын

    @@alejandrobusquets6214 only way for me is to use the sub as near field (as a coffee table). then the flexibility of a second seat is lost.

  • @richardsmith2721
    @richardsmith2721 Жыл бұрын

    I have a REL Strata for my ProAcs.

  • @bronymusiclover8891

    @bronymusiclover8891

    Жыл бұрын

    Ok

  • @MrPeeBeeDeeBee
    @MrPeeBeeDeeBee Жыл бұрын

    And some subs have a 0 to 180 degree phase adjustment. Does this mean that eg when set half way that my sub can half in phase and half out of phase? I always thought that speaker phase was either positive or negative but not a combination of both. So what is going on here?

  • @Rene_Christensen

    @Rene_Christensen

    Жыл бұрын

    0 vs 180 is a polarity flip. In the 180 setting all frequencies have their phase shifted 180 degrees. But phase can also be shifted on a continuous scale. I have a long video on yt on the topic. Just search Acculution.

  • @MrPeeBeeDeeBee

    @MrPeeBeeDeeBee

    Жыл бұрын

    @@Rene_Christensen Thank you

  • @baronsamedivitus
    @baronsamedivitus Жыл бұрын

    Subwoofers are room dependent. The smaller the room, the bigger the room gain.

  • @lexicon612
    @lexicon612 Жыл бұрын

    OK Paul...I need clarification here. Not everyone's main speakers go down to 30Hz. I would venture a guess that most audiophile systems (main's) do not. You preach (as I do) the necessity of stereo sub's in any system (that does not go down to 30Hz) You walk the tightrope and call the imaging sub's do as "Musical Cues" . I call it what it is, Imaging. Are you now telling me that I need a 3rd sub somewhere in the rear of the room to "fill in the gaps" or just play 30Hz and below, only...Or does this advise only apply to people that have full range main speakers. Also how are you wiring that rear of the room sub. High level speaker wire or because it's only 30Hz and below, RCA or balanced summed (mono) is fine? Can I assume that proximity to each of the main speakers for stereo sub's is important, for proper "musical cues" imaging?

  • @JohnOBryan
    @JohnOBryan Жыл бұрын

    This topic as well as a number of other topics Paul talks about, it's hard to comprehend it unless you've experienced it.

  • @Oystein87
    @Oystein87 Жыл бұрын

    Well.. Yes, you DO want to hear the subs but just as adding the lowerst bass to the main speakers and not actually hear where the subs are placed.

  • @janinapalmer8368
    @janinapalmer8368 Жыл бұрын

    I've said it before ... and I'll keep on satin' it ..... if you have 3 speaker locations in a room ..all capable of going down to nearly 20Hz , then you are BOUND to get interaction between the sound waves .....

  • @Bassotronics
    @Bassotronics Жыл бұрын

    Luckily I’m able to hear down to 15Hz or so. Lower than the average human. And before someone says that I’m lying, mind you that I’m a producer for a record label that specializes in deep bass and infrasonics so there you go…

  • @MrPeeBeeDeeBee

    @MrPeeBeeDeeBee

    Жыл бұрын

    Yes you will hear 15hz...if it is loud enough

  • @edmaster3147
    @edmaster3147 Жыл бұрын

    I found that stereo bass is quite important, even in the low frequencies. And the lower they go, the better, there i agree with Paul. And I love big woofers, but most people won't get a nice set of 15'in or 18'inch in their living. A series of small drivers, like in the PS speakers, might be fast, but there is something about the sound of really good big woofers....

  • @lexicon612

    @lexicon612

    Жыл бұрын

    Most audiophile's use smaller sub's because the drivers recover faster and add definition & texture to each bass note reproduced. In my experience Larger sub's are for impact. Conversely I have heard that open baffle 12" sub's are remarkably fast and articulate in GR Research designed sub's. Have yet to experience them. Looking forward to it, though.

  • @edmaster3147

    @edmaster3147

    Жыл бұрын

    @@lexicon612 So often smaller cones are suspended much stiffer and wouldn't that make them less sensitive thus less responsive? And in need of more power, therefore prone to distort? My ears are in favour of large cones and I didn't hear small and arrays of small sounding more detailed.

  • @lexicon612

    @lexicon612

    Жыл бұрын

    @@edmaster3147 Expert speaker designer's like GR Research use 6.5 inch arrays in their flagship designs to cover the lions share of the audio spectrum, yet use 12 in servo sub's in their open baffle subwoofer designs. GR Research designs every aspect of their drivers including stiffness. Manufactured in China. That may be the difference. In general a larger cone mass will take longer to recover from any bass note produced than a smaller woofer...When the next note starts and the larger driver has not yet recovered from the previous note, that's when the smearing and boomy starts. In general smaller drivers recovery times are shorter than larger drivers. (less distance to travel & less cone mass and weight) Open baffle is a whole new world. My next audio adventure is going to be GR Research NX-Studio Kit (Pair) Someone else would be better suited to answer the technical aspects of your question. I run a PS Audio stack using the MKII DAC. Still in search of my forever mains. EPOS an English manufacturer that design's and produces their own drivers in house has been my go to for a number of years now...Looking to next level my system with the GR NX-Studio kit. Still using twin Martin Logan Dynamo 400 for the bottom end. Rel performance for half the price. Take care Ed.

  • @edmaster3147

    @edmaster3147

    Жыл бұрын

    @@lexicon612 That sounds like a nice path in the hobby, enjoy!

  • @NoEgg4u
    @NoEgg4u Жыл бұрын

    If you do not have room for adding a sub-woofer box, then consider Vandersteen's Quatro speakers (or a higher model, budget permitting), because their powered bass section includes an 11-band potentiometer. That will allow you to smooth out bumps, and fill in gaps, in bass frequency surpluses and deficiencies. Even with separate subs, it is unlikely that you will have a location where the full range of that sub will deliver all of its bass frequencies uniformly. There will still be bumps and valleys in nearly every room that affects what you hear from subs. So it helps with subs (whether built-in to speakers or with separates) to be able to dial in the amount of boost for its frequency range. When you get the bass right, the sonic image becomes more cohesive.

  • @PSA78

    @PSA78

    Жыл бұрын

    You can never fill in gaps as increasing 'positive wave' will increase 'negative wave' by the same magnitude, bumps (two 'positive') can however be brought down. 🙂

  • @NoEgg4u

    @NoEgg4u

    Жыл бұрын

    @@PSA78 The next time I get together with Richard Vandersteen, I will tell him about his engineering flaw in his reference speakers, the Model Seven. Richard has had powered subs in his Quatro model speakers, since 2006, and it seems that no one has told him what you have identified, and it has been 17 years.

  • @PSA78

    @PSA78

    Жыл бұрын

    @@NoEgg4u I feel sorry for him if he doesn't understand how physics works, maybe he should open a book or watch a few of Pauls videos, it's not that complicated.

  • @gerritgovaerts8443

    @gerritgovaerts8443

    Жыл бұрын

    You can achieve a flat bass response over the frequency range that your subs cover if you have at least 4 of them and place them strategically . Two is already a lot better than 1 , but definitely not enough to get a flat response throughout the room.

  • @PSA78

    @PSA78

    Жыл бұрын

    @@gerritgovaerts8443 Exactly, "place them strategically", that way it's possible to counteract how the rooms dimensions work against (or for) the wave lengths. That's not possible when they are located in the speakers themselves, like Paul says.

  • @johannkrist
    @johannkrist Жыл бұрын

    When I got my new speakers that go down to 30hz I sold my sub, I tried it with the speakers for some time, tried to fiddle with settings and placement, tried to turn it off for some time and then after around two weeks turned it on again, two days later I turned it off again and sold it.

  • @JonAnderhub
    @JonAnderhub Жыл бұрын

    Why on earth would someone spend $30,000 on a pair of speakers only to have to buy more speakers to make up for the deficiencies in the design of the $30,000 speakers? 1:42 "...yet in many rooms you won't hear a whole lot of deep bass (from the Aspen FR 30s) that is because where I have to set the Aspens speakers in the room to get the best Imaging, to get my best sound stage and top end is not necessarily and in fact probably not where the best position would be to get great bass." Well, that sounds like a design flaw! Because for $30,000, the bass in the speakers is virtually useless and a person has to buy additional speakers to make up for this design flaw? Why on earth would somebody do that?

  • @davidfromamerica1871

    @davidfromamerica1871

    Жыл бұрын

    Those are my same thoughts as well. If the FR 30’s go down to 20 as we are told they do, the only reason one would need a subwoofer is if they need bass below 20. Secondly, we are also told to make the subwoofer disappear in addition to the above along with the FR 30’s. None of this makes any sense whatsoever unless one is a die hard bass head. That would mean you would not want your subwoofer to disappear. That is why one has to take all this with a product sales pitch. They prey on gullible people. It’s called drinking the Kool-Aid.

  • @MrPeeBeeDeeBee

    @MrPeeBeeDeeBee

    Жыл бұрын

    It is no secret that many mains speakers go down to 30 and below hz, however, they almost always do this at minus dbs of at least 10hz. So while the low bass is being produced it is quieter than having a dedicated sub that you can tune for your bass needs. Also bigger subs move more air which in turn means more realistic levels of bass.

  • @worthingtonmodelrailway8628
    @worthingtonmodelrailway8628 Жыл бұрын

    So Paul, why would I buy an expensive sub-woofer rather than a less expensive one, if it's just so we feel the bass and don't really hear it?

  • @nomorokay

    @nomorokay

    Жыл бұрын

    The more expensive sub will go lower, and yes, you will hear the difference. A really cheap sub might not reach 30 Hz, while a better one may get below 25 Hz, and an even better one may get below 20 Hz. Keep in mind that those specs refer to the absolute limit of the subs' capabilities, where their response may not be linear. To accurately hear the lowest note on a 5-string bass guitar, which is at 30 Hz, you'd want a sub that can reach at least 25 Hz, so that it can accurately sound like what the musician is playing.

  • @worthingtonmodelrailway8628

    @worthingtonmodelrailway8628

    Жыл бұрын

    @@nomorokay I can hear acoustic bass perfectly defined with my speakers with their 8” woofers which with a bass reflex design go to 20Hz and a 32’ organ pipe will shake the room so in some ways I question the need for a sub period.

  • @nomorokay

    @nomorokay

    Жыл бұрын

    @@worthingtonmodelrailway8628 It sounds like your system does want you want and need it to do. Congratulations! It’s rare that a system like the one you describe performs the way you describe, but I’m not doubting you in any way. If the speakers and the room enjoy a rare synergy that allows it to perform that well, that’s great. However, with most stereos in most rooms, subwoofers do complement the main speakers very effectively. My system is based around modded and bi-amped Klipsch La Scala IIs. Where they excel is in the midrange and upper bass, where they have a big and realistic sound. However, due to their “portable” size (in movie theatre or travelling sound reinforcement terms), their bass horns are not long enough to go very deep. In my tests, I found that they start to roll off at 100 Hz and by 50 Hz, not much is happening. Accordingly, a sub or two is called for. Why two? Because a powerful subwoofer can create a very uneven sound field, with peaks and nulls in surprising places in the room. Accordingly, the second sub is not for more power, it’s to even out the sound field. To correct for the added power, both subs have to be turned down by 3 dB. The result is effortless and understated bass that seems to be coming from the main speakers, allowing you to hear every instrument in a natural and realistic way.

  • @sebastiantomita5956
    @sebastiantomita5956 Жыл бұрын

    Then why bother with a speaker that expensive and not just go for standmounts with external subwoofers?

  • @davidfromamerica1871
    @davidfromamerica1871 Жыл бұрын

    Other combination of. 😀😀😀😀😀😀😀 😂😂😂😂😂😂😂 🙄🙄🙄🙄🙄🙄🙄 🤔🤔🤔🤔🤔🤔🤔

  • @1TruePatriot
    @1TruePatriot Жыл бұрын

    Paul, Absolutely love your videos! But you imply that COVID is over, when in fact it is FAR from over. While I know you did not mean to spread misinformation, I hope you will issue a correction, as there's already too much misinformation about COVID being thrown around carelessly, and even worse, in some cases, intentionally. But thank you for the video on subwoofers!

  • @PetraKann
    @PetraKann Жыл бұрын

    Disagree with this answer. A 26hz sound frequency has a wavelength of over 13 metres (342/26). Most rooms are smaller than 13m in any given dimension so stereo imaging is not relevant. Hide your subwoofer wherever you like. Notice how there are never sub-woofer pairs installed in a domestic room.

  • @NoEgg4u

    @NoEgg4u

    Жыл бұрын

    "Notice how there are never sub-woofer pairs installed in a domestic room." Vandersteen's System Nine grouping includes a pair of sub-woofers. That sub-woofer pair can also be purchased separately. They are state-of-the-art, and they are used in domestic rooms.

  • @slode1693

    @slode1693

    Жыл бұрын

    Sub location isn't about stereo imaging. low frequency waves have very apparent areas where the waves cancel each other out or build on each other. Sub location in regard to seating area, regardless of room size has a huge impact on that. Every room is different, and each will have a best location for the sub/s. And yes, there are many hi fi setups in domestic rooms running multiple subs to reduce or eliminate those high and low spots to cover multiple seating areas. (It's not for stereo imaging). When you see two subs setup symmetrically next to the mains it's likely someone who doesn't know what they are doing to achieve good sound. In rooms with multiple subs and good bass the sub locations are usually kind of awkward.

  • @jeremiahchamberlin4499

    @jeremiahchamberlin4499

    Жыл бұрын

    I agree with your disagreement. The nulls and ‘boomy’ spots in a room produced by the standing waves of the too-long lower frequencies will vary with sub placement; using more than one sub is an effort to fill in the nulls and level the ‘boomy’ spots. Paul explains himself well, but the room will have an effect on bass regardless.

  • @PetraKann

    @PetraKann

    Жыл бұрын

    @@NoEgg4u A waste of money if your room is if a standard size. Stereo imaging is not physically possible at those low frequencies and high wavelengths. If you hid a subwoofer in a room and played say low frequencies below 50Hz (~6 metres wavelength) you would not be able to discern where the sound is actually coming from using your ears alone. You could if the subwoofers were placed at least 12m apart and you positioned yourself in the centre. Preferably further apart. It’s the reason multiple sub woofers are used in large auditoriums and stadiums. If you’re sitting 50m from the stage you can distinguish low frequency direction/imaging. Waste of money in a home environment imo

  • @PetraKann

    @PetraKann

    Жыл бұрын

    @@slode1693 If the wavelength is 13m for a 26Hz frequency explain how constructive and destructive inference works or how standing waves form within a room dimension that is less than half of 13m