The 2011 Richard C. Heyser Memorial Lecture: "Where Did the Negative Frequencies Go?" Case Study 1: Recording

Case Study 1: Recording

Back in 1987, the AES published the anthology pictured above of historic papers on "Stereo." It includes a document (celebrating its 80th anniversary this year) that pretty much defined the whole field of stereo reproduction, including the 45°/45° stereo groove and the moving-magnet stereo cartridge. That document, a 1931 British Patent Application written by the English engineer Alan Dower Blumlein, is worth quoting at length:

"The fundamental object of the invention is to provide a sound recording, reproducing and/or transmission system whereby there is conveyed to the listener a realistic impression that the intelligence is being communicated to him over two acoustic paths in the same manner as he experiences in listening to everyday acoustic intercourse and this object embraces also the idea of conveying to the listener a true directional impression. . . . An observer in the room is listening with two ears, so that echoes reach him with the directional significance which he associates with the music performed in such a room. . . . When the music is reproduced through a single channel the echoes arrive from the same direction as the direct sound so that confusion results. It is a subsidiary object of this invention so to give directional significance to the sounds that when reproduced the echoes are perceived as such."

In other words, if you can record not only a sound but the direction in space it comes from, and can do so for every sound wave making up the soundstage, including all the reflected sound waves (the reverberation or "echoes"), then you will be able to reproduce a facsimile of the original soundstage, accurate in every detail. In addition, because the spatial relationship between the direct and the reflected sounds will be preserved, that reproduced soundstage will give a realistic illusion of depth.

Incidentally, I mentioned earlier Hermann Bondi, one of Hoyle's collaborators on the Static Universe Hypothesis. Like Blumlein, Bondi had worked on the British development of radar in World War II. When I worked in the research lab developing LEDs, in a corner office was a charming elderly gentleman, Dr. Henry Boot. Only years later did I learn that Henry was one of the people who invented the cavity magnetron, which was fundamental to the British development of radar. I suppose you could therefore say that there are just two degrees of separation between me and Alan Dower Blumlein.

The Blumlein Patent Application mentions that, when recording for playback over headphones, the simplest way of carrying out the preservation of the soundstage is to use two microphones spaced as far apart as the average pair of human ears: the "binaural" technique. This, however, makes headphone listening mandatory; until recently, headphones have been about as popular as a head cold for relaxed, social listening. Blumlein was concerned with a system for playback over loudspeakers, and proposed a method of recording directional information as a ratio of amplitude differences between the two signal channels.

The ear/brain, of course, uses more than amplitude information to determine the direction of sound sources. It uses the amplitude difference between the signals reaching the two ears above about 2kHz, but below about 700Hz, it determines direction by looking at the phase difference between the signals; ie, it uses time-of-arrival information. (Both frequencies are proportional to the head size, so there will be a spread among individuals.)

Things get a bit ambiguous between those two frequencies, but there are two other mechanisms also at work: first, the frequency-response modifications due to the shape of the pinnae differ according to the direction of the perceived sound; and second, the head is in continual lateral motion, sharpening up all the mechanisms by introducing second-order (rate-of-change) information. The result is that human beings—and animals—are very good at determining where sounds come from (unless they happen to consist of pure tones in the "forbidden" region between 700 and 2000Hz, which is why birds, for example, use such tones as warning signals).

Blumlein's genius lay in the fact that he realized that the low-frequency phase information can be replaced by corresponding amplitude information. If you have two independent information channels, each feeding its own loudspeaker, then the ratio of the signal amplitudes between those two loudspeakers will define the position of a virtual sound source for a centrally placed listener equidistant from them. For any ratio of the sound levels of the two speakers, this virtual source occupies a dimensionless point somewhere on the line joining their acoustic centers. The continuum of these points, from that represented by maximum-left/zero-right to that represented by zero-left/maximum-right, makes up the conventional stereo image. If there is no reverberant information, then the brain will place the virtual image of the sound source in the plane of the speakers; if there is reverberation recorded with the correct spatial relationship to the corresponding direct sound—that is, if it is "coherent"—then the brain places the virtual image behind the speakers, the exact distance depending on the ratio of recorded direct sound to recorded reverberant sound.

Thus, by recording and playing back just the amplitude information in a two-channel system, we can create a virtual soundstage between and behind the loudspeakers (footnote 6). And if, instead of capturing an original event, we record many individual sounds in mono and assign each one a lateral position in the stereo image with a panpot (along with any added reverberation or echo), when we mix down to stereo, again we have a true amplitude-stereo recording. It is fair to say that 99.99% of all recordings are made in this way. It is so fundamental to how recordings are now made that I doubt if anyone thinks about the fact that it is based on psychoacoustic sleight of hand: the substitution of amplitude ratios for time-of-arrival differences in the midrange and bass.

For many years, I was a hard-line Blumlein purist when it came to classical recording. I was attracted by the theoretical elegance of the M-S technique—a sideways-facing microphone with a cosine or figure-8 pickup pattern is spatially coincident with a forward-facing mike; sum-and-differencing the mike outputs gives you true amplitude stereo—and of two figure-8 microphones horizontally coincident at 90°, each positioned at 45° to the forward direction. Of all the "simple" techniques used to capture live acoustic music, these two, in all their ramifications, are the only ones to produce real stereo imaging from loudspeakers.

I used to dismiss with a snort recordings made with spaced microphones. After all, if the microphones are separated in space by a distance larger than the wavelength of most of the musical sounds—10', say—unless an instrument or voice is exactly halfway between the two microphones, there will be, in addition to the amplitude information, a time delay introduced between the electrical signal that voice or instrument produces in one channel and the signal it produces in the other. Such time information pulls the image of the source farther toward the nearest speaker, resulting in an instability of central imaging and a tendency for sources to "clump" around the speakers. Add to that the fact that the interchannel amplitude differences produced by spaced microphones do not have a linear relationship with the angular directions of the sound sources, and it is hard to see how a pair of spaced microphones can produce any image at all.

Yet . . .

In 1992, we were recording two concerts for Stereophile featuring classical pianist Robert Silverman.

The main pickup was with a single stereo microphone, but I had put up a pair of omnis that I fed to a separate recorder. After the concert, it became apparent that the stereo mike had failed, so I was forced to use the spaced-omni recording for the CD release. Here is a short track from that album, Schubert's Moment Musicaux No.3:

[Play Schubert Moment Musicaux No.3, from Concert CD, Stereophile STPH005-2 (1994)]

There are two things intriguing about this recording. For this lecture, one minute in, I flipped the right channel's polarity. I doubt that anyone noticed—there is so much time disparity between the two channels that it cannot be considered a stereo recording at all; rather, it is two different recordings of the same performance that happen to be played back simultaneously. The second thing is that, despite that theoretical imperfection—for which I was duly castigated on Usenet—the CD sold quite well. People liked the sound.

I wasn't too surprised by that. Theoretically perfect amplitude stereo has served us well, but when I played people some of my classical recordings made in the appropriately purist manner, they often described the sound as "thin" or "cold" or "lacking bloom."

As I said earlier, when people say they like or dislike something, you should take notice. And in this instance, the late Michael Gerzon had discussed the matter in a paper he gave to the London AES Convention in 1987. Specifically, he had postulated that Blumlein's substitution of amplitude for phase differences at low frequencies is inadequate, that people prefer the sound when there is some time-difference information between the channels, presumably because the information their brains use to synthesize a model of the stereo image now has more in common with what they would have heard at the original event.

Gerzon had floated the idea of using two pairs of microphones to capture all the information the brain requires: spaced omnis below 1kHz; coincident figure-8s above, with a crossover between the two. I tried that, with disappointing results. However, after 1992, I used a similar miking technique with which I thought I could get the best of both worlds: the good amplitude stereo from coincident or quasi-coincident mikes, and the lower-frequency bloom from spaced omnis. Both mike pairs were used more or less full-range; the only EQ was a touch of top-octave rolloff on the omnis, and some first-order low-frequency boost on the cardioids to compensate for their premature bass rolloff when used distant from the source.

It was the acquisition of a Sonic Solutions Digital Audio Workstation in 1993 that allowed me to fine-tune this technique, because it became apparent that the two pairs of mikes needed to be time-aligned for the resultant stereo image to lock into place. This time alignment of mikes had been used by Denon and was described in an early 1990s AES convention paper, but I had no way of easily implementing this until I could slide individual tracks backward and forward in time to get the required synchronization.

Since then, I have made all my classical recordings in this manner. Here is a typical example: Minnesotan male-voice choir Cantus singing Eric Whitacre's Lux Aurumque in the glorious acoustic of Sauder Hall, at Goshen College, in Indiana. You can see the two pairs of mikes in this photograph.

Not shown in the photo is a third pair of mikes, omnis on a Jecklin disc, farther away from the singers, which I used in case it turned out that the main pickup was too dry. (When you are on location and the clock is ticking away your money, you cover your bases.)

[Play Cantus: Eric Whitacre, Lux Aurumque (excerpt), from While You Are Alive CD, Cantus CTS-1208 (2008)]

If you listen critically to this recording, you will hear that acoustic objects get a little larger, the farther away they are from the center of the stage. However, their spatial positions in the image are correct.

I tell this tale because it illustrates one of my points: that thinking you are right about something in audio doesn't mean you are right. No matter how much you think you know, there will always be new things that upset your world view. Einstein, for example, would be astonished to find that his "biggest blunder," the Cosmological Constant, turns out to be real—that we now are aware that something completely unknown to science is causing the expansion of the universe to accelerate. Physicists call it "Dark Energy," but that's just scientific shorthand for "We have no idea what it is."



Footnote 6: this creation of a virtual soundstage only works for soundsources to the front of the listener and a two-channel system. However, when the mixing engineer requires a virtual image to be placed to the listener's side in multichannel audio, it fails for the simple reason that we do not have a pair of ears on the front and back of our heads.
Share | |
Comments
bernardperu's picture
Why would you read Stereophile anyway?

JhonnyR

 

If Stereophile has the principle of not doing DBT and for you doing so is a matter of principle why oh earth would you even care to read Stereophile? Your statement above suggests you have very extensive knowledge of the content of Stereophile's articles. So you keep reading stereophile's reviews knowing they are irremediably flawed?? How perverse is this?

 

The real question lies on your double blind tested hatred. 

 

Whatever your answer is I will have to assume that your hatred is a broken record and it will just go on.

GeorgeHolland's picture
He probably reads them as I

He probably reads them as I do for the laughs.smiley

JohnnyR's picture
You Didn't Comment..........

......on your error filled post above so why should I comment on your assumptions? If you wish to worship Fearless Leader then by all means bow down and do so. I myself prefer to ask questions and be skeptical about his "methods" and the reason "why" he doesn't test ALL items under review.

John Atkinson's picture
You're Welcome

Andreasmaaan wrote:
It's a pity that some proponents of DBT as the only valid methodology have used the comments thread here to launch personal attacks against JA.

Indeed. I am not sure why I have become a lightning rod for these audio skeptics. Perhaps it is because it is a matter of religious belief on their part - having had extensive experience of blind testing, I rejected it and thus became a heretic in their eyes. Or perhaps it is just our courtesy in allowing them the space on this website to express themselves.

Andreasmaaan wrote:
JA does measure every piece of gear his reviewers review - a practice which ensures that the opinions of the reviewers are grounded in objective data, or otherwise as the case may be.

As my reviewers do not see the measurements until after they have written the review, I take my hat off to them.

Andreasmaaan wrote:
To cut what is risking becoming a lengthy expression of indignation short: thank-you JA for a wise and thought-provoking read.

You're welcome and my thanks to everyone else who appreciated the preprint. It was an honor to have been invited by the Audio Engineering Society to give this lecture - it's not often that you get the opportunity to look back over a 4-decade career!

A Happy New Year to everyone who surfs this site.

John Atkinson

Editor, Stereophile

JohnnyR's picture
Ahhhhhhhhhh Typical Atkinson Answers

You ignore the errors and just plow along blissfully gobbling up the unwarranted praise.

"JA does measure every piece of gear his reviewers review"

As I pointed out above, along with other errors on the part of Andreasmaaan,you do NOT test every piece of gear your reviewers review, but then you pretended that you do in your response. Only certain items are tested by you. Please get your own facts straight if that's even possible for you to do so.

Regadude's picture
Johnny brand speakers

Johnny, I wish you a great new year 2013, in which you sell 10 times more of your home made speakers than in 2012. 

Since you sold zero of your speakers in 2012, you need to sell 10 X 0=0 speakers in 2013 to meet this objective. Maybe you can hire George Holland as your director of marketing and sales... 

Get cracking, you have only got 364 days left to sell your quota...

JohnnyR's picture
Happy 2013 Raghead

[flames deleted by John Atkinson]

Unlike yourself Raghead, I will be DESIGNING and BUILDING my own speakers and learning. You do know that word "learning"? Hmmmm maybe you stopped after age 10. You on the other hand will be on here *yawning* and acting the fool and spending your money on Stereophile reviewed crapola.yes

Regadude's picture
So only your speakers are good?

So according to you Johnny, everything Stereophile reviews is crapola?! There is not one good piece of equipment that has been reviewed by Stereophile? Hundreds of reviews, not one good product?

But you, in your basement, build quality speakers... 

I have challenged you before (as well as George) to name your gear. What kind of gear merits the Johnny seal of approval? 

As always, you always ignore my challenge (George chickened out to). It seems you can only complain, but cannot even provide a list of your gear. 

I guess ever seeing pictures of your "famous" speakers is also out of the question. 

All talk and no action. 

Regadude's picture
Johnny the pussy

So Johnny, where are your speakers pics and specs?

In your imagination.... [flame deleted by JA]

GeorgeHolland's picture
Johnny never offered to show

Johnny never offered to show you anything other than his backside which I think is approriate considering the childish actions of yourself.What does it matter what our audio components are? Anything we mention would be ridiculed by yourself no doubt. Sorry but I'm not playing your silly game. Good God grow up and act like a man for once will you? angry

John Atkinson's picture
Getting Facts Straight

JohnnyR wrote:
As I pointed out above . . . you do NOT test every piece of gear your reviewers review, but then you pretended that you do in your response. Only certain items are tested by you. Please get your own facts straight if that's even possible for you to do so.

Out of morbid curiosity, I looked at the past 15 issues of Stereophile - we published 98 full reviews and follow-up reviews. Of those 98 reviews, 83 were accompanied with a full set of measurements, or 84.5%. So even if not every review includes measurements, the vast majority do, which supports Andreasmaaan's point.

I have explained to you before, in other comment threads, why we do not publish measurements of analog playback components, which is due to lack of resources. I have also explained to you why we do not publish measurements of tweaks, which is that it it is difficult to determine exactly what to measure. I don't see any reason to reopen those discussions, but that you continue to be fixated on these two issues and continue to raise them is sad.

And, as I have warned you, JohnnyR, I am continuing to delete comments from you, and others, that are nothing more than flames aimed at other readers.

John Atkinson

Editor, Stereophile

JohnnyR's picture
Get Out Your Dictionary

"Reviews" means just that, any item reviewed by your staff. If you think "tweaks" don't qualify then they should be labled as "Opinions" not a review.angle All of those full reviews you speak of were what speakers, amps, preamps, cd transposrts and the like?

Yeah I know why you don't test tweaks, that would involve you using those horrible SBT or DBT. That's a really nice system you have set up. "We don't believe in DBTs or do them or can't afford to do them"......"We don't know what to test on the tweaks"..........add the two up and you get "We don't have to show that tweaks actually do anything other than what our "reviewer" subjectivly alludes to in their sighted biased listening using their golden ears"......EXCUSES Mr Atkinson plain and simple. no

Once more I ask you to read and comment about this link:

http://forums.audioholics.com/forums/loudspeakers/83412-diy-loudspeakers...

You seem to think DIY can't do anything right in your previous post in answer to Raghead. Insulting intelligent people that actually build better speakers than the status quo can produce is beyond being pompus in your case.THAT is what's SAD.

Don't you have some real work to be doing instead of being on the forums? I thought that was Ariel's job. Let him earn his pay.

ChrisS's picture
Circle Game

JRusskie,

Look up "fixation" and "perseveration" in your dictionary. "Absolute truths" regarding audio products seems to exist only in your basement and in your head.

John Atkinson's picture
What?

JohnnyR wrote:
John Atkinson wrote:
I looked at the past 15 issues of Stereophile - we published 98 full reviews and follow-up reviews. Of those 98 reviews, 83 were accompanied with a full set of measurements, or 84.5%. So even if not every review includes measurements, the vast majority do, which supports Andreasmaaan's point.

"Reviews" means just that, any item reviewed by your staff. If you think "tweaks" don't qualify then they should be labled as "Opinions" not a review.angle

I am not sure what you mean. You were objecting to Andreasmaan's statement that Stereophile accompanies its reviews with measurements as not being true. I offered the analysis above to show that he was correct.

JohnnyR wrote:
Once more I ask you to read and comment about this link:

http://forums.audioholics.com/forums/loudspeakers/83412-diy-loudspeakers...

You need to consult with your fellow traveler GeorgeHolland, who criticized me about linking to other sites :-)

JohnnyR wrote:
You seem to think DIY can't do anything right in your previous post in answer to [Regadude.] Insulting intelligent people that actually build better speakers than the status quo can produce is beyond being pompus in your case.THAT is what's SAD.

With respect, you are arguing with the voices in your head here. I haven't written anything about DIY speaker designers not being able to do "anything right." What I have said is that a DIY designer, like yourself, doesn't subject his loudpeakers to the scrutiny of a disinterested marketplace, something professional designers do as a matter of course. So the question whether or not DIY designs are superior to commercial designs isn't put under independent scrutiny. It remains unsupported conjecture, as far as I am concerned.

John Atkinson

Editor, Stereophile

GeorgeHolland's picture
Mr Atkinson, you could 

Mr Atkinson, you could  compare DIY against manufactured speakers but of course you won't. Might upset those that can't make good speakers and I'm not talking about the DIY cheeky

Johnny plainly stated that "tweaks" are reviewed in your magazine and online yet they aren't tested, hence you don't test every component under review. You have a reading comprehension problem? How many components reviewed by Jason Serinus have been tested? uh huh, right.

So now you wuss out about commenting on links? That proves you had nothing to say in the first place about it so you shouldn't have opened your mouth.Cop out time for Mr Atkinson.

The only unsupported conjecture on here are your abilities to print honest reviews. Your ability to avoid testing  alot of audio components is well known by now. Very impressive spinning you do on here.wink

John Atkinson's picture
Reading Comprehension

GeorgeHolland wrote:
Mr Atkinson, you could  compare DIY against manufactured speakers but of course you won't. Might upset those that can't make good speakers and I'm not talking about the DIY cheeky

Back in the early 1990s, Stereophile's Corey Greenberg was one of the judges for a DIY loudpeaker competition in San Francisco. There were 2 winning designs and as part of the prize, those 2 speakers were subject to a full set of measurements in Stereophile, published in the March 1992 issue. The speakers' measured performance was good but not great and certainly didn't embarass professional designers.

GeorgeHolland wrote:
Johnny plainly stated that "tweaks" are reviewed in your magazine and online yet they aren't tested, hence you don't test every component under review. You have a reading comprehension problem?

I don't believe so. JohnnyR was wrong, in that we very rarely publish full reviews of tweak products. Of the 98 reviews published in the magazine January 2012 through March 2013, there was just one review of a "tweak," Robert Deutsch on the HiFi Tuning Supreme Fuses in May 2012. ( I don't count the AudioQuest power strip reviewed by Kal Rubinson's review in December 2012 as Kal didn't make any comment on its sound quality, only on its utllity.)

GeorgeHolland wrote:
How many components reviewed by Jason Serinus have been tested? uh huh, right.

The correct answer is none. But that doesn't support JohnnyR's case either, as Jason's reviews are published on the website Secrets of Home Theater and High Fidelity, which has no connection with Stereophile. I hardly believe I am obliged to support reviews of products in competing publications with measurements in Stereophile.

John Atkinson

Editor, Stereophile

JohnnyR's picture
Wow Nostalgia Time Kids

"Back in the early 1990s, Stereophile's Corey Greenberg was one of the judges for a DIY loudpeaker competition in San Francisco. There were 2 winning designs and as part of the prize, those 2 speakers were subject to a full set of measurements in Stereophile, published in the March 1992 issue. The speakers' measured performance was good but not great and certainly didn't embarass professional designers."

Golly "only" 20 years ago and as we all know, nothing new has happened since then to make speaker design any better (Insert BIG sarcasm face here) cheeky Talk about a lame example Atkinson.

Yeah yeah, "full reviews" whatever, Plenty of "little revews" though all the freakin time and all they are , are OPINIONS but you know what? You let your reviewers get away with murdering the intergrity of the audio world with their stupid banter about  "blacker backgrounds,lifted veils and HUGE improvements in the sound" without them having to justify their claims, Pretty slick there pal.

Oh and Jason Serinus "reviews" as posted about the recent RMAF isn't connected to Stereophile? Give us all a break, Your EXCUSES are even lamer this time than usual.

Yep typical Fearless Leader goobley gook. Did you major in Universisty in the double speak of Orwell's 1984? If not then you are gulity of plagiarizing the concept.

John Atkinson's picture
Not making sense

JohnnyR wrote:
Golly "only" 20 years ago and as we all know, nothing new has happened since then to make speaker design any better...

Again you are arguing with the voices in your head, JohnnyR. Of course a lot has happened in the past 20 years, especially the advent of low-cost measuring equipment. But you're missing my point, which is, as I wrote earlier today, that a DIY designer doesn't subject his loudpeakers to the scrutiny of a disinterested marketplace, something professional designers do as a matter of course. You have repeatedy claimed that your speakers are as good as if not better than commercial designs. However, unlike engineers like Kevin Voecks, Paul Barton, Richard Vandersteen, Jeff Joseph, etc, your ability to pay your mortgage and feed your family doesn't depend on your skill as a speaker designer. Their's does, and it makes a difference.

Look, if you seriously believe your speaker designs are fully competitve with commercial designs, email me your measurements. I'll get back to you with my interpretation of what they mean, assuming they are as comprehensive as what I publish with every Stereophile speaker review. Put up or shut up.

JohnnyR wrote:
Yeah yeah, "full reviews" whatever, Plenty of "little revews" though all the freakin time and all they are , are OPINIONS but you know what? You let your reviewers get away with murdering the intergrity of the audio world with their stupid banter about  "blacker backgrounds,lifted veils and HUGE improvements in the sound" without them having to justify their claim...

You're not making sense. "Andreasmaaan" was discussing reviews in the magazine being accompanied by measurements. I was discussing reviews in the magazine being accompanied by measurements. You seem to be discussing something that exists only in your mind. And unlike Professor Dumbledore's quote, that doesn't mean it's real :-)

JohnnyR wrote:
Oh and Jason Serinus "reviews" as posted about the recent RMAF isn't connected to Stereophile?

That was a show report. No-one other than yourself equates a magazine's coverage of a show with its formal equipment reviews. Are you seriously suggesting that magazines shouldn't publish show reports without including a full set of measurement data for each room they report on? Really? There isn't an audio magazine or website that does that.

John Atkinson

Editor, Stereophile

JohnnyR's picture
BLAH BLAH BLAH

Go have another pink drink Fearless Leader.

Me let YOU interpet my frequency response? Don't make me LAUGH. You can't even interpept Wilson't ragged ass frequency response laugh

[usual flames deleted by John Atkinson]

John Atkinson's picture
Making my point

JohnnyR wrote:
John Atkinson wrote:

Look, if you seriously believe your speaker designs are fully competitve
with commercial designs, email me your measurements. I'll get back to
you with my interpretation of what they mean, assuming they are as
comprehensive as what I publish with every Stereophile speaker review.

Me let YOU interpet my frequency response? Don't make me LAUGH.

You make my point for me, JohnnyR. It was a serious offer on my part. Professional loudspeaker designers send out their products for review and for the public scrutiny of possible customers. Amateur speaker designers, such as yourself, are often afraid to let anyone else judge their work.

John Atkinson

Editor, Stereophilee

Regadude's picture
There you go

I have been challenging Johnny tp provide pictures and or the specs of his speakers. He has never met my challenge.

Now the editor of Stereophile offers to look over his data. Johnny again makes up excuses to avoid providing any information on his heavenly speakers.

Big talker...

bernardperu's picture
Contamination

Dear Jon,

What should have been an enlightening discussion of your great lecture has been contaminated by ill-conceived comments. Some individuals have posted comments that have created an environment of nastiness. 

I would seriously urge you to start deleting ill-conceived comments from now on, whether they use flamable language or not. Some people are just turned on by the flames, but others aren't. And those others would much rather focus on the joy of engaging in the music and exchanges related to it.

You do not run a state-owned site but a private one that is likely to become a lot less lucrative (in all senses) if such nasty comments are to become visible.

I am not even pointing out names and we all know who I am talking about.

I am just giving you feedback that comes from an avid reader of Stereophile online. 

Finally, the correction of my use of English was mentioned by one of these individuals. Please allow me to say that English is my second language and it is oxidized. Sorry about that. 

Thanks!

 

Site Map / Direct Links