Violet DSP Evolution - an Open Baffle Project

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First off, this project is dedicated to the memory of Henry Darger, an American writer.

From wikipedia:

"In the Realms of the Unreal includes The Story of the Vivian Girls, in What is Known as the Realms of the Unreal, of the Glandeco-Angelinian War Storm Caused by the Child Slave Rebellion, and extends over 15 immense, densely-typed volumes of 15,145 total pages. The text is accompanied by three bound volumes of several hundred illustrations, scroll-like watercolor paintings on paper, the work of six decades, derived from magazines and coloring books."

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Violet is one of the Vivian Girls, after which this project is named. Digital signal processing (DSP) plays a central part to this also - hence Violet DSP. Its got a nice ring to it.

This project started several years ago - really though, it is the evolution of my interest in sound reproduction. Before I describe the goals and current results of this project, I'll share a little about how I got here.


I was originally turned on to the 'hi-fi' world by a friend taking me to a fancy gear shop one day. I think we were listening to Muddy Waters on electrostats, IIRC. Definitely kind of mind-blowing. I knew I could do the same on my own, DIY, and luckily I eventually found diyAudio.

I initially bought a pair of Acoustic Energy Aegis 1 loudspeakers. They weren't too bad really. Small, budget, and limited speakers, but focused on doing the midrange justice.

I then bought a used pair of original Advent speakers - they were interesting, but nothing extraordinary. I didn't know what I was looking for, I guess.

Somehow, then, I got lucky and stumbled on SL's Plutos. They are omni speakers, and in them I found I think what others have - that the polar radiation pattern matters, a lot. I think I really appreciated Linkwitz's down to earth practicality combined with his extensive technical knowledge. I don't use the Plutos much these days, mostly because I feel they were superseded in many ways by my more recent speakers - but I don't know if any speaker so far has the same super smooth presentation, all due to a very very regular polar pattern, IMO. I actually haven't updated the EQ to version 2.1, which might make all the difference to my using them more. I hope to sometime soon. The comparison then should be very interesting. One thing I think though, is that omni may present more ambient information than I like - too high a ratio of reflected to direct sound. We'll see - but I currently feel dipoles have the right balance for me.

One thing though, is that the Plutos have relativity complicated electronics driving them. I wanted to see what was capable at the other end of the spectrum, so I built single driver, no crossover Zigmahornets with DCA4 drivers. They were interesting, educational, but ultimately, unlistenable. Very precise imaging, but nothing going on below 200Hz, and seriously irregular highs. I sold them eventually.

At the same time, I wanted to see what a 'classic' design could do - a boxed speaker, with a well done crossover, good bass, good mids, good highs. I chose Zaph's BAMTMs, and made the floorstanding version. These were also very educational, and I still enjoy listening to them. They are very well done speakers, but the mild off axis irregularity in the mid-treble region becomes easily recognizable compared to something like the Pluto. Similarly, their 'box sound' is very obvious compared to omni and dipole speakers. They are still for sale, if anyone in SoCal is interested. So after having a number of different speakers, it was becoming obvious what was important (to me) - especially, how audible off axis radiation is.

I then dove into my first open baffle (OB) speaker. I wanted to keep it simple, and bought a pair of Visaton B200 8" drivers. I definitely didn't know what physical parameters matter in OB systems, but the B200 were regarded as very good full range, OB speakers. And they are (were). After all these different speakers, and endless tweaking I did, using B200s OB was the first time my girlfriend (now wife) said she liked what she heard, and thought it was an improvement. A good sign. I too, liked what I heard.

In hindsight, after learning a lot more about OB speaker systems, I can say that there is a lot 'wrong' with using just a single, 8" driver (no bass, beaming highs, good midrange, but not fully regular off axis response, power/displacement limitations). Not long after getting the B200s up and running, I decided to dive into an OB woofer - and selected MJK's Alpha15a H-frame design. Here is a picture of a very early version of the pairing - note the centered, circular, cardboard baffle for the B200. A no-no now. I was just beginning to develop my measurement setup, which was an invaluable step to learning what is going on with audio, speakers, etc. Here are some more interesting tidbits on the Alpha15a H-frame.

Next I added a tweeter (a single, forward firing Dayton ND20FB), combined with a 10" rectangular baffle, similar to early Linkwitz Orion designs. The addition of a woofer and tweeter definitely took things to a more serious level - a truly fullrange speaker system. I was doing all XO and EQ in the computer at this point, using various software, and doing all my own measurements (which were fairly flawed, but still very necessary). I might add that the various pieces software I was using at the time were a serious PITA - nothing wanted to work together in a complicated chain of bits and pieces. Later, I'll write up what I use now, which is a million times easier, and way more powerful. It was also around this time that I spent a week living with a pair of SL's Orions, which was wonderful.

By this time, I was using my speakers as monitors for my audio recording hobby - I lived with a lot of musicians, and recorded a lot of their music - from acoustic ensembles to full blown, loud rock. One of the serious benefits of this was having heard the live event, and then trying to reproduce it as faithfully, and as engagingly over my speakers. But speaking of blown, one day my (expensive) B200 drives blew when listening to live drum recordings at live levels (b200s are only rated for 30W - definitely not enough). I then replaced them with Dayton RS225 drivers, but I was still learning. I soon abandoned these drivers, after figuring out they were also power limited, and also had polar regularity issues. They were replaced with Eminence Alpha6a drivers (a 6", very good driver IME), and then with smaller 4" drivers, ultimately the TangBand W4-1320sj.

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At the same time, I discovered the Neo3PDR dipole tweeter - and soon realized that this driver was way way better than either a single, forward firing tweeter, or back to back tweeters. I was continuing to discover the benefits of a regular polar response - in both the Neo3, and in the value of minimal baffle (aka none at all). In a recent thread, I've documented what it has taken for me to achieve a very regular off axis response in the midrange and treble, with regards to open baffle, dipole radiation.

Not long after adding the Neo3PDR tweeters, I designed a new woofer system - for lack of a better name, I call it the GWx4. I wanted something smaller to replace the bulky, low SAF, H-frame - so my goals for it were smaller size, inexpensive, higher SPL output, and possibly increased LF extension. I feel I met those goals, and retired the Alpha15a.

It was also around this time I read Floyd Toole's book, Sound Reproduction. Only someone with a large companies' resources could have conducted such an in depth study of what matters when it comes to quality sound reproduction. It is a must read! It very much stresses the importance of the off axis response, among many other invaluable studies.

That brings us up to the current time.
 
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So here it is, not done, but pretty darn close.

Starting at the top, is a Neo3PDR dipole tweeter, with a thin (.5") open cell foam surround, which helps smooth the already good off axis response. The rear chamber has been removed. Meniscus is another (good) source for the Neo3 if PE is out of them, as they have been for months now. The mid is a TB W4-1320sj. It is a 4" driver, and yes, small, particularly for dipole duty, which tends to require both a lot of power handling and volume displacement. But a 4" driver is required to avoid beaming and basket/magent issues, both which degrade off axis performance. The woofers are 10", high QTS Goldwood drivers GW-210/8. The total cost for the drivers is about $400 dollars.

The crossover points are 275Hz and 1700Hz. In both cases, each driver is at its comfortable limit, one way or another, mostly in terms of being displacement limited or directivity limited. The slopes are all LR4 acoustic responses. All crossover and EQing is done in a computer, and each driver has its own power amp. I will post the EQ settings soon, and will eventually develop an analog equivalent, so there won't be any computer necessary (ya!).

It isn't physically possible to get a full range (20-20kHz) polar response without a true anechoic chamber, so we'll have to be satisfied with breaking it down to multiple plots. Here are the polars for mid/treble section, and then woofer section (whoops, lost the polars, on axis only now, I guess. Notice the nice SoundEasy target overlay of a LR4 low pass at 275Hz - very helpful!):

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All measurements were taken outdoors, with the mic at the listening position (6'). The mid/treble section was 9' off the ground, and the gate time was about 12mS, which gives a resolution of 80Hz. I'm going to post a full write up of my measurement procedure, and my computer setup at a later time. My interest in writing all this up is to help people learn how to do it themselves. DIY!

My goals for this project are fairly well developed by now.

1) A full range, open baffle, dipole speaker. This ended up being about 30Hz to 20kHz. It seem that below 30Hz is not dipole territory - monopoles and dipoles seem to have the same response, with monopoles much easier to pull off. A sub is still an option for this design, but definitely not necessary for music, IMO.

2) As regular an off-axis response as possible, after taking care of the on-axis response. This goal has taken a lot of the attention, as achieving off-axis regularity requires looking at a number of different issues. I define an ideal dipole response as -1dB at 30deg off axis, -3dB at 45deg, and -6dB at 60deg. 90degs should be about -20dB down.

3) Being a 'budget' design. I suppose $400 isn't actually considered 'budget' but for a full range dipole speaker, that is the best I can do so far. I think the driver cost for the Orion's is something like $2500.

I think a quick, partial comparison with Linkwitz's Orions is appropriate. First off, I feel he really pioneered a lot of OB territory, and taught me most of what I know. But, something to consider is that he designed the Orions about 10 years ago - driver technology and our general understanding of what matters the most for quality sound reproduction has changed. We currently have way more resources, knowledge and good drivers available , and all the while I've been designing these speakers, I've been keeping in mind what the Orions are capable of, and where there is room for improvement. In terms of improvements, I see two main areas, and I've addressed them here.

First off, Linkwitz went to great lengths to select the highest quality drivers, particularly in terms of non-linear distortion and stored energy - and as a result, each driver costs in the neighborhood of $250 (and there are ten drivers total!). In Floyd Toole's book, he addresses a growing consensus that non-linear distortion (NLD) is only audible above a certain relative levels. I had a chance to speak with Linkwitz about a year ago, and his said he generally agreed - that NLD was not as important as he once thought. So the lesson is that the drivers used don't have to be as top notch as once thought, and hence can be less expensive. I have measured NLD on the Violets, and so far, it looks to be well below audible levels.

Second, Linkwitz didn't take off axis regularity as far as he could have in the Orion's design - for the midrange/treble, he uses a 11" baffle (or so), which then introduces a dipole peak at about 700Hz - above that, the off axis response becomes irregular, and doesn't stick closely to an ideal dipole response. I don't have polars for the Orions, but physics is physics. I've addressed this in my design by using no baffle at all - and it should be obvious in the above polars that regularity has been achieved.

One thing that the Orions have that I compromised on is maximum SPL output - particularly for the midrange in the Violet. I think the Orion's are rated for 108dB SPL. I haven't pushed the TB mid yet, but it won't be that high. OTOH, I'm guessing that it won't have any trouble with 'live' levels, which for me is more important. If this turns up to be an issue, the Alpha6a should be a very capable driver for high output levels. Another thing to note is that 'maximum spl output' is a fairly ambiguous term, and has a lot to do with what music you listen to, and at what average level - even 100dB SPL at 1m average is very loud. 108dB SPL at 1m is definitely not necessary for most people.

Next installment coming soon.
 
Thanks for sharing your design again Cuibono, and more importantly the iterations and philosophy behind them. Until today I think the Orion is still something that I lust after, yet I have not even heard them. So reading from someone who had lived with them and *then* build his own is quite an interesting read.

From this presentation, the target SPL of Orion is 115db, so that's very high and domes may just be the right choice and compromising polar response.

I listen to levels far below those numbers so small drivers suffice
 
Thanks - being part of an inspiring community is what its all about for me.

115dB is really really loud. Even 105dB SPL/1m is definite neighbor complaint fodder. Its all about compromises I guess - but being aware of what compromises you're making is the more difficult part.

Trying to rate the maximum output of a speaker is problematic too - are we talking about a swept sine wave at 1xxdB SPL at 1m? Tone bursts? White or pink noise? Music, which has a highly variable content? Is the maximum output limited by a maximum % of NLD, or as the point where a certain % of driver unit's voice coils fail? Is it measured or calculated? All of these things have to be specified to have real meaning. In the case of the Violet, so far all I can say is that it plays loud. That may have to suffice, and even if a voice coil burns, its replaced for $50. Not too bad.

Thanks for the link to that presentation!
 
So here I'd like to present my EQ settings and a little about the computer end of things.

After trying various software schemes, mostly really complicated and seriously frustrating (usually involving Thuneau's Allocator), I finally got a simple, solid setup going. My computer is an 8 year old Compaq desktop running Windows, and it doesn't max out, so I'm not replacing it. The point is that it doesn't take fancy hardware or software.

My soundcard is an Asus Xonar D2 soundcard, which I got on sale for about $120. It has insane noise floor and distortion specs, and is perfect with 2 channels in and 8 out. The only thing is that it isn't a prosumer type card, but geared to gamers, so it has all sorts of superfluous software garbage. Also, Asus needs to put more work into their drivers - they were problematic at first, but since sorting it out, it has been solid. The only warning is that, because of the extra software garbage, it adds delays to different channels, as one would do with a surround processor. I haven't found any way to defeat the delays, and talking with Asus about it was like talking to a cardboard box. Anyway, the delays are easily compensated for. I can post the exact delays on each channel sometime if someone needs them.

The crown jewel of all this setup is Cocko's Reaper - a digital audio workstation - Reaper started as a community project (IIRC), and is now 'commercial' but only $60 for a personal license, or you an use it totally free without limitations. It comes with a lot of effects, of which we are interested in the EQ and time delay. I can't say enough good things about this software - learn to use it, and it is seriously powerful. And I've never had a single technical issue with it (well, one tiny one, but thats it). I also use this software for mixing, and sometimes recording (my recording rig is a 4 channel stand alone field unit).

The other bit of important software is my EQ plugin - I don't use Reapers free plugins, although I could - I've just always used 'Ultrafunk Sonitus:fx' plugins, particularly the EQ (it is a bundle of different plugins). I suppose one could use any EQ plugin, and there really are many - the only thing is that I've found different manufactures use different ways of defining "Q" - so a Q value in Sonitus would not be equal to a Q value in Reapers EQ. Annoying, important to be aware of, but not too big a deal.

Anyways, I highly suggest this software setup. I can't tell you how many hours I've wasted and hated trying to get different pieces of software to talk to each other and hand off information smoothly - it just isn't worth it. So my computer is basically a black box - you plug your source into the stereo input, and you can get up to 4 stereo channels of EQ'd and XO'd signal out. There is a bit of a time delay (about 350mS in my setup), so that is an issue with syncing to video - but a faster computer should be able to get that down to a few mS, which is unnoticeable. I used to have it working that way, but its a pain to maintain. I'm content with a slight delay. The only thing is that the computer running Reaper can't also be the source (like for all our digtal music) - it just won't work! Or, at least, I can't get it too in any simple fashion.

So here are my current EQ settings - THESE ARE NOT FINAL! They result in a flat anechoic response with my mounting setup - but not a flat in-room response. Any change in the driver mounting would necessitate a change in EQ. My next step will be doing some final in room, ungated measurement to deal with room modes, and a 'house curve' - the highs can use a dB or 2 of roll off, but that is very room dependent, and subject to taste. First, here is a picture of my Reaper main screen - the awesome thing is, all I have to do is start my computer, and start Reaper, and it is rolling - Reaper opens where you left it, so you don't even have to click 'play' or anything.

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Let me give a little description - there are four stereo tracks. The first is the line in - and it received the signal from the analog input of the soundcard. It is here I control the volume, and where I can apply EQ to the whole signal. From here, the signal is routed to three other tracks - where it is cut up into the bass, mid and treble signals. EQ and XO is done in these tracks, as is the time delay to compensate for the soundcard's weird behavior. These tracks are then routed out to the individual soundcard's outputs - viola, a 3 way digital crossover! (An astute observer will notice that the tracks are in parallel - but for optimum phase performance, they should be in series, according to Linkwitz. I'll deal with that later...)

So here are my EQ settings. First the bass -

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The mid requires two instances of the plugin to get all the EQ'ing it needs (notice the 12dB boost):

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The treble is pretty simple too:

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Thats it for now. Eventually, I will make an analog equivalent of my final EQ/XO circuit. I feel the computer is sonically benign, but it just make the electronic end of things a lot more complicated - and probably harms my noise floor a bit.
 
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Cuibono,

do you think adding another W4 above (or below, as in TMM) would help with SPL limitations in mids ? That could add another 6dB of headroom, whether that is enough I'm not sure but it might be significant. It shouldn't affect the polars much ...

Great progress BTW. Truly inspirational. I can't wait to see the passive version (I guess semi-passive would also work, with in-line filter for the bass amp to get the "losless" dipole correction, that is without large/expensive/power eating inductor).
 
so do you feel well with the asus analog to digital conversion? what sampling rate do you use? and why don't you use the pc for the source? there should be ways of routing the input to several dsp... also thing like the newborn miniDSP would be a nice way inbetween passive and pc-based x-over... with 2 of them one can make it three way plus 2 channels to drive sealed sub as you suggested...

i don't get the mid equing... i'll try to figure out tomorrow with the sun :)

inspiring work and great explanation too. thanks!
 
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cuibono, about your woofers only

Is there a reason fore that very special woofer design ?

Hard to figure out how it really works
And whether it actually is more effective with 4 woofers, rather than with 2 woofers

Crossed relatively high, a woofer sounds different whether you listen to its back or front
But might actually be of advantage, if they sound just slightly different
 
Thanks for your complements!

Bratislav - yes, a second W4 could be added, I had considered that. It may have a small detrimental effect on the vertical polar response, but that might not be audible. The main reason I haven't so far is that I'm not sure the mid section needs more output yet. If so, there are several options..

human.bit - so far, I have no qualms with the Asus sound quality - it has really exceptional specs - way beyond what I consider minimum. I would love to find a way to route audio into Reaper from inside the computer, but like I've said, I can't find a way that is simple and reliable. I think I use 24/96 quality, but I'm of the camp that there is no audible difference compared to 16/44 in a high quality chain - if you haven't, read this article. It is the most comprehensive comparison I know of. I would enjoy trying a simple self contained DSP system, but so far haven't seen one that is capable of what I need, in a simple and affordable package.

The mid EQ is fairly simple - there are two bands of 2nd order HP (at 100 and 275Hz), and two bands of 2nd order LP (at 1700Hz), a shelf at 690Hz to compensate for the dipole roll off, and dip to take care of the dipole peak at 2000Hz, and then a little EQ for a peak at 1600Hz. Actually, not much EQ beyond what any bandpass dipole would need for a flat response. I don't know if there will ever be a true passive version, although it is possible I guess - dipoles just inherently have a very sloped response. Maybe we are confusing passive, wrt a normal XO that comes after the power amps, and an analog, line-level circuit that comes before the power amp - what I would call an ASP?
 
Hi Tinitus - there is a link above to the write up I did for the woofers, it might have some answers. The main reason for using 4 woofers is greater volume displacement (aka, SPL). It works because the wavelength in the bass frequencies is much larger than the distance separating the drivers - so they acoustically appear as one below a certain frequency range. Using 4 drivers adds 5dB output compared to 2 - I measured (6dB would be the calculated value, so it isn't perfect). There isn't any difference between front and back radiation, due to the multiple reversed drivers and the large wavelengths involved.

I wonder if anyone will try building them - they were designed to be fairly high performance while fairly inexpensive...
 
I wonder if anyone will try building them - they were designed to be fairly high performance while fairly inexpensive...

the complexity of the PC based xo will probably prohibit many of us from building

once you start w/ the passive route...i think there'll be interest for sure


btw...i might be interested in your BAMTM set in the near future if you don't have a buyer for them. I built a set for my friend and he thoroughly enjoys it. Another friend of mine wants one too. :dodgy:
 
Another couple of notes.

I forgot to add that the Neo3PDR drivers have a series capacitor to protect them from undue abuse (I've already killed a pair). I currently am using a 22uF 35V Panasonic FC electolytic - sometime I'll try a film cap, but I'm not expecting much return on the $40.

there should be ways of routing the input to several dsp...

Oh, I forgot, I already have a way to route stuff through the computer - I set it up a while ago, and haven't been using it much lately - it involves 'Jack', and audio routing/patching program. It actually works okay, I just dislike it because it was finicky to originally setup, and whenever I want to use it, it still requires a bunch of setup - starting various programs, and then linking them together. I don't know what it does with the sample rates, it leaves a tiny space between songs, :soapbox: :soapbox: :soapbox:. Its just not my favorite, but it works.
 
Listening Impressions...

I'm a little surprised no one has asked "Hows it sound?", but I guess that is a good thing. My evaluation probably isn't worth too much, full of bias, we all know. But I'll throw a few tidbits out there - I'm currently doing production ceramics, so I have the speakers set up where I work, and listen to them about 6 hours a day.

I tend to get caught up in technical stuff - hows the bass extension? Is it even? Can I hear a, b or c?... But after just listening for a couple of days, I stopped thinking about that stuff - and today I found myself thinking how beautiful everything sounded. Every recording sounds different, and some of course have issues - but even recordings that I didn't like in the past don't sound offensive anymore - they just have a certain 'character'. They are all involving, very open and clear sounding, and all very enjoyable to listen to. They also are all convincingly realistic, even poor/amateur recordings.

I think that is about all I'd describe them as - very enjoyable to listen to.

I was trying to push the volume today - and I couldn't push it enough! Particularly, I was listening to Vivaldi's Four Seasons, a piece I like a lot. I maxed out my computer before I maxed out the speakers or amps - the signals going through were on the verge of clipping, and represented 15-20dB louder than I would usually listen at. I haven't measured SPL yet (which is difficult to do meaningfully), but I can say the music was at what I would guess are live levels. It was pretty loud. I would expect, if someone were there with me, they would have to shout from a few feet away. And how did it sound? AWESOME!! Loud is GOOD! There was no hints of stress, congestion, or loss of coherency - if anything, things were easier to follow, more well defined, more powerful, and way more enjoyable to listen to. I really want to keep turning it up! I'll have to see what I can do... I think my ears were ringing a little afterward. My heart and foot were definitely beating!

Anyway, I enjoyed it.

I've been thinking a little more about the analog active version - the cost in part is going to be in the $350-$425 range (about the same as the Orion and Pluto ASP boards). It is pretty easy to put together a good, small computer for that price. I'm not sure going with the ASP is worth it - for the same money, one can have a much more flexible platform. Similarly, a computer would allow one to do phase linearization, which is something I'll look into before too long. I think the only reason to avoid the computer (which could be a headless unit), would be to be an analog purist about things (digital is bad!:witch:). I guess computers add a degree of instability, but my turntable isn't even close to working these days. I guess there isn't a lot to be gained in going analog. (Similarly, analog active boards with lots of opamps can have high noise floors.) Pick your poison, I guess.
 
....

AWESOME!! Loud is GOOD! There was no hints of stress, congestion, or loss of coherency - if anything, things were easier to follow, more well defined, more powerful, and way more enjoyable to listen to. I really want to keep turning it up!
...

:D Congratulations :D

It's a perfect evidence that you've done a great job in putting them all together. :)

------------

I've been enjoying loud music myself, too, but in these years I found myself trapped in a miserable situation. I always worry about disturbing the neighbors. Such conflict makes it a 'forbidden' pleasure :( Just like driving.

I drive fast, with all caution and concentration I can have. But even so, I can't enjoy the speed because the worry of speeding tickets. Sigh~
 
Good point - I forget that not everyone wants to deal with computer headaches.

The EQ for the woofer section could be pretty easily done passive or analog, line level active - I just haven't bothered.

Are you in California sqlkev?



yes...i'm in southern california :)



hmmm...sound like you've got quite good extension and spl w/ those woofers
i built myself a set of LR's Thor dipole woofers but they weren't loud enough for my taste. Looks like I'll be trying out the woofers you're using soon. :cool:
 
Every recording sounds different, and some of course have issues - but even recordings that I didn't like in the past don't sound offensive anymore - they just have a certain 'character'.

cuibono,

what you are writing is very indicative to me that you must really have a very nice system. Your description reminds me of some of my own experiences of lately.

When I got into loudspeakers in earnest, it was all about differentiation: Extended treble with less distortion, contoured bass instead of boom boom and improved imaging, which separeted individual instruments/voices from one another. That was the time, when "bad" recordings became unlistenable. Annoying hiss, ping pong stereo, missing stage - all those things.

Not long ago things started to change:
More and more I got interested in integration or - better phrased - 'balance'. A certain degree of differentiation had become a matter of course in my system, but it did not all fall together harmoniously and with ease. This has improved. I very much ascribe it to my better understanding of room related matters like power response, directivity and early reflections. As of now I have achieved a much better integration of the musical performance in front of me. And - lo and behold - many of those 'bad' recordings have become listenable again. Of course they have not changed in quality, but they don't annoy any longer.

I'm wondering if this is some end of the journey or what will come next.
Thank you for giving us such a significant insight into the 'sound' of your system.

Rudolf
 
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Interesting what you say there Rudolf, and I have the same experience with my new dipoles: "bad" recordings are revealed as "bad" to an even greater extent, but they are much less annoying, and the music in the recording is let through much more than before.

A stereo system that needs good recordings to sound nice is not really a good system in my opinion.
 
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