Technical exercise and advice requested

[Mayla]

Hello, I am currently working on Rachmaninov's Prelude in b minor, Op 32 no 10.   I need any technical suggestions people could give me; perhaps you know of a technical excerise that would help me ?

In measure 48, we begin a fioritura group of notes, and my RH has been having problems in getting tense when using the fingering provided in my score, so I went ahead and changed it to what felt more comfortable to me and made much more sense to me (considering the passage work that comes before it). 

Let me tell you what I came up with :

                         f#b  ebef#  ef# bf#
RH (ascending) -- 3  5  3134   13  14

After hearing so many people rave about exercises and technical development in general, I went back to the books.  I slowly played through scales, arpeggios, octaves, thirds, sixths, chromatic scales, Pischna, Hanon, Schmitt, Czerny vol I and II of his selected piano studies, and then also Czerny's School of velocity, Op 299, various other people's works who are less known (why not ?) and then Brahms 51 exercises.  I also decided to play through some Bach just to see if I could find this precise figuration and fingering to go with it, but I just couldn't -- I couldn't find it anywhere except for in this precise piece and in this precise place within the piece, and to fit my specific hand and personal needs, too.

Am I missing something ?     What should I do ?  I mean, I could just practice that specific place in the Rach's music, but I feel pretty naughty doing that since I have obviously missed the boat somewhere else  .

Any help you can give me is greatly appreciated .

[dnephi]

I'll look into this and get back to you.

[Mayla]

Okay, thanks  .

[michael_langlois]

If you'll pardon my audacity in replying without having tested the fingering myself at the piano, it seems to me that the fingering that is in (my) score, 235 123 123532 521 321, actually facilitates the passage by grouping the the ascent into three sub-gestures, the first and third of which require a subtle, efficient supination of the wrist (à la Chopin 10-1). 

Perhaps once the positions are found, it would be helpful to rehearse the shifts (and rotation on the last pair) between F#3, B3, E4, and F#5, each with their corresponding finger from the above system.

Hopefully I have not retraced steps you have already taken.

Best,

Michael

[ramseytheii]

Hello, I am currently working on Rachmaninov's Prelude in b minor, Op 32 no 10.   I need any technical suggestions people could give me; perhaps you know of a technical excerise that would help me ?

In measure 48, we begin a fioritura group of notes, and my RH has been having problems in getting tense when using the fingering provided in my score, so I went ahead and changed it to what felt more comfortable to me and made much more sense to me (considering the passage work that comes before it). 

Let me tell you what I came up with :

                         f#b  ebef#  ef# bf#
RH (ascending) -- 3  5  3134   13  14

Yikes.  I think as a basic principle of fingering, apply Occam's Razor: the less movement, the better.  This one is jumping all over the place and seems unrelated to the musical phrase totally.  No offense but Yikes!

At the tempo, you can't reasonably expect 3 to leap over 5, especially at the interval of a fourth.  Also, the stretch from F# to B with 3 and 5 creates tension.  Then the thumb is being used way too many times for such a fast passage.  Let's try and consolidate more notes into fewer hand positions.

His fingering is written technically for large hands, but it also fits those with small hands who have long reaches between the fingers.  I met a girl with tiny hands, who could stretch from C to A with the second and third fingers.  3 to 4 could comfortably stretch a fourth, and uncomfortably a fifth.  To put it in perspective, I have large hands, but 3 to 4 for me is comfortable though I never use it only for a third, and my 2 to 3 can comfortably, though I never use it, stretch a fourth.  She has tiny hands with a big stretch.

So I don't know what kind of stretch you have, but you can use the thumb more economically if you happen to have a small stretch for instance:
1 2 5 1 2 3 1 2 3 5
OR
1 2 5 1 2 3 1 2 1 5
though it is dangerous with more thumbs.  I suppose you could try:
1 2 5 1 2 3 2 1 2 5
but it will make the delineation of the phrase more difficult (because you aren't starting each wave with the thumb).

I recommend practicing Rachmaninoff's fingering in creative ways until it feels comfortable, it is really the best for this passage.

Walter Ramsey

After hearing so many people rave about exercises and technical development in general, I went back to the books.  I slowly played through scales, arpeggios, octaves, thirds, sixths, chromatic scales, Pischna, Hanon, Schmitt, Czerny vol I and II of his selected piano studies, and then also Czerny's School of velocity, Op 299, various other people's works who are less known (why not ?) and then Brahms 51 exercises. 

I think that when - or if - you study technical exercises, you should not do it willy-nilly, but try and categorize them so you can refer to specific exercises for specific passages.  For this one, I would recommend Brahms 51 exercises nos. 8a and 8b, because they are specifically for stretching in between the fingers.

Walter Ramsey

[Mayla]

If you'll pardon my audacity in replying without having tested the fingering myself at the piano, it seems to me that the fingering that is in (my) score, 235 123 123532 521 321, actually facilitates the passage by grouping the the ascent into three sub-gestures, the first and third of which require a subtle, efficient supination of the wrist (à la Chopin 10-1). 

Perhaps once the positions are found, it would be helpful to rehearse the shifts (and rotation on the last pair) between F#3, B3, E4, and F#5, each with their corresponding finger from the above system.

Hopefully I have not retraced steps you have already taken.

Best,

Michael

Thanks, Michael.  Well, I had been using this very fingering, actually, for about 3-4 years, and this one passage just never came for me.  It was very hit and miss and I did practice as you recommended, actually, but it's the tightness between the 2nd and 3rd fingers from f# to b in both octaves that always did me in.

I consulted with a wonderful teacher just recently who advised a special movement from the finger number 2 to 3 that did help to relieve the tightness, but in the upper octave, when I would do the same movement --except reach to the F# above with finger number 5, vs just to the "E" in the octave below-- it just didn't work for me.

So, I decided to stick with what I posted above, because that particular fingering never once causes tension for me (and it doesn't force my hand out of a more relaxed and natural position) if I use forearm rotations, or supination of the wrist, as you suggest.

I took this piece to a masterclass one time, and the master actually suggested that I completely skip one of the notes altogether and just go to the next (in order to avoid this tension).  Well, I just wasn't willing to do that in this case (I have been willing to do that in select chords if I can't reach all the notes, but this is different).  So, I guess it's a bit of a difficult passage.

Did you happen to listen to my recording attached to the original post ?  If so, how does it sound to you ?

Thanks .
Mayla

[Mayla]

Yikes.  I think as a basic principle of fingering, apply Occam's Razor: the less movement, the better.  This one is jumping all over the place and seems unrelated to the musical phrase totally.  No offense but Yikes!


Walter Ramsey

hee hee... yeah, I realize it seems a bit absurd  , but I think it works, actually.  It's not a fingering-type I have ever come up with in my life before, but I think it's rather .... charming, actually  .  The problem with starting with my thumb on the f# is that I can't easily achieve this considering the passage just before it -- so the thumb is kinda not quite an option in this scenario.  In this case I decided over sheer physical comfort rather than worrying about how much movement I was doing (just as long as it wasn't actually inhibiting me in any way).

Did you happen to listen to the recording attached to the bottom of the initial post ?  What do you think about the phrasing ?

Thanks for the suggestions and thanks for the exercise recommendations, I will take a look at them .

[lostinidlewonder]

The passage in question is actually measure 49, in Boosey+Hawkes edition anyway. and it is as Ramsey suggested. It is an arpeggio pattern and should feel like it with an open hand nice flattened fingers.

Mayla your fingering offered: 3531341314 has too many jump movements for the passage in my opinion. 353  the last 3 is a jump ok this is acceptable but being followed by another one I believe that the 14 is pushing it too far. I would love to actually see your hands play it with that fingering it would be a mystery !

[Mayla]

I would love to actually see your hands play it with that fingering it would be a mystery !

Well, you know lostinidle, I would love that, too  .  And, of course, I am a mysterious woman  .  Okay, but seriously.  I did feel a bit unorthodox when I first decided to change everyhting around, but I was genuinely frustrated and decided to completely wipe the slate clean and treat this passage as though I were a complete beginner with no preconcieved ideas whatsoever, only aiming for comfort and ease.  Nobody came here, knocked down my door and arrested me as it turns out, so the fingering stuck  .

That brought up a few issues in my mind, actually, most of which I won't expound on at the time.  But, I did think -- what makes it 'too many jumps' if it sounds and works better than ever before ?  I realize that it seems like it's not the most efficient use of my hand, however, it is !  I am spending a lot less energy, actually, doing it this way.  So, I thought, if it's easy for me and it sounds good -- who from the audience is really going to know that passage well enough to know what I am doing ?  Who will even notice ?  I suppose that would depend on who the audience is, to some extent.  But, if it came off cleanly and beautifully in a performance, why would anybody take issue with it ?

I don't know -- it's just stuff worth pondering, in my opinion, since that would completely over-haul my entire piano-playing-attitude.  I mean, what if I ONLY did what was easy and didn't waste time trying to adopt conventional methods of doing things when/if I have tried them and they didn't actually work for me, or if what I thought of came more easily for me ?  Why limit myself when nobody else is going to come play the piano for me ?

Thanks for the comments and for the measure number correction -- I was not sure if mine were entirely accurate or not (but I went back and checked and they are accurate according to me) -- or maybe Boosey (and Hawkes, too  ) is counting the pickup measure as meaure number one ?  I didn't.  In any event, I guess we all found our way .

So, I may experiment some more -- but I may just end up doing exactly what I am doing currently.  Once our computer becomes capable, I will see if I can't post a video  .

[cmg]

I, too, have the Boosey & Hawkes edition.  The groupings of 235 123 123 seem to be the most rational and effortless way to play this passage.  I really don't understand your problem with it, unless it's tension. 

Use a flat, open, relaxed position and the notes fall right into place.  It's very pianistic, actually.  In practicing, isolate each grouping.  Feel that position in your hand.  Freeze-frame and relax. Then shift to the next.  And so on.  With good rotational technique you can easily connect the groupings as the tempo is increased.  Plus, you have the damper pedal to help you out. 

I wonder why you intellectualize technical issues so much.  This passage is really not that challenging, particularly compared to other repertoire you say you play.  How do you manage Chopin if this gives you so much trouble?  Stop thinking and let your hand/body tell you the answer.  Be mindful of the tension in your hand.  If it's there, stop.  Release it.  See if your fingering is taxing your hand to the degree that tension is creeping in.  Most tension arises from attempting wide stretches the hand can't accommodate.  You'll usually feel this tension in your thumb initially.  See what you can do about re-fingering the passage.  There's ALWAYS a workable solution for any hand.  That's why God gave us "rotation technique."

And, the best "exercises" you'll ever find are in Chopin Op. 10 & 25.  If I were you, I'd dedicate my time to mastering them.  Every problem and its solution is posed there.  Just practice slowly without tension for months and months and Chopin will show you the way.   

[Mayla]

Well, yes, tension is precisely the problem as I mentioned earlier. 

I have decided to take a couple of photos, which looks more relaxed to you ?

1.  Suggested fingering (with a "nice, open, flat hand position") :



2.  My magical fingering (with a truly relaxed and natural hand position) :



Okay, granted, I am not actually sitting at my piano, but the idea is similar.  How can I possibly, truly "relax" within that first position ? It's actually not physically possible.  As I said, there was a way that somebody showed me to be able to use the same fingering while remaining more relaxed, but I still find what I wrote up above to work better for me.

[Mayla]

This passage is really not that challenging, particularly compared to other repertoire you say you play.

Oh, like what ?   

[henry_v]

Mayla,

I think your are using, unfortunately, a wrong approach to solve this problem. I can hardly imagine this fingering being usefull in a very fast tempo (still being able to hear all intonations clearly and with a natural dynamic phrase), I am sorry.
After reading your post I've studied this passage for 10 min. to see what the problem is. I think there are several options regarding fingering, the one being written in my score (2 3 5 1 2 3 1 2 3 5) seems to be at the end, the most natural. Problem is, this fingering needs a rather complex movement of hand/arm (it's mainly about rotation and a kind of circular movement of the hand) in order to play it easy or effortless.
In the beginning it seems to be far more easier to play it with your fingering, because it doesn't need any kind of flexibel movement of the hand, just changing of positions. Unfortunatly your fingering will limit in speed, accuracy, quality of tone etc.
I can think of one other option: 2 3/4 5 1 2 3 2 3 1 3/4/5, but still being inferior to the first one.

You talk alot about playing with comfort/ease in general. Of course, this is one of our goals we want to achieve, and it's necessary for natural playing and it's the ultimate test case to see if one has truly mastered a passage. But don't confuse playing comfortably with using tricks and thus avoiding the problem.
It's also not true that if one can play a passage with ease at a slow tempo that one can play it at any tempo. This is only true if one uses the right technique to play the passage (at any speed). You can be playing with 'great ease' (or at least the feeling of ease) at slow tempo using a wrong technique. 

In this case, you can play perfectly the passage with the fingering written in the score (even if you have smaller hands). I've seen  the photo's of your hands you posted. There you play it like a chord. It's not about that, because when I play the second note with my 3rd finger, my second finger isn't in contact with the F#, because of rotation of my hand in order to put my 5th finger at the right place (on the E).  This way, it will be much easier playing the passage, using a the most logical fingering.
Unfornately, to truly understand the movement, someone (probably a good teacher) has to show it to you.

I hope all this is not too confusing. Hope it will help you.

                                             

[Mayla]

Mayla,

Unfornately, to truly understand the movement, someone (probably a good teacher) has to show it to you.

Thanks for posting in, henry.  I have figured that a truly good teacher would just be able to point me to an exercise that would fix the problem (probably Hanon ?), since all problems can be solved and are found through exercises.  So, I thought, why bother my teacher at all ?  Why not just ask for the specific exercise that many people must have gone through and remember in their exercise training ?

I think the problem is that what is most "logical" for one person is not necessarily logical at all for another.  And what is logical in one context is not necessarily logical in another.  If the problem is that I am caused tension when trying to go from 2 to 3, even if I am not touching them at the same time (and, at tempo I have little time to "relax" between them and actually MUST stay "stretched"), then perhaps I ought to stop doing that ?  In this case, yes, I will avoid the tension because it's not something I am willing to try to get used to anymore -- I have spent enough time doing that and it's not gotten me hardly anywhere as far as I am concerned.

In the first photo above, I was simply displaying what my hand looks like when/if I follow what was most logical for another person :  "nice, open, flat hand" -- it isn't logical for me, and apparently it's not logical for you, either.

I still consider myself to be exploring.

[cmg]

Well, yes, tension is precisely the problem as I mentioned earlier. 

I have decided to take a couple of photos, which looks more relaxed to you ?

1.  Suggested fingering (with a "nice, open, flat hand position") :



2.  My magical fingering (with a truly relaxed and natural hand position) :



Okay, granted, I am not actually sitting at my piano, but the idea is similar.  How can I possibly, truly "relax" within that first position ? It's actually not physically possible.  As I said, there was a way that somebody showed me to be able to use the same fingering while remaining more relaxed, but I still find what I wrote up above to work better for me.

Okay, first you have terrific hands, m'lady.

But, you're missing the point on tension.  I think DannyElfboy wrote extensively on this some many months ago, explaining that you must "contract" muscles -- as in your spread-finger photo -- to make the fingers do their work.  But as soon as that particular, specific job is done, you must let go of the contraction and snatch a miliisecond of non-contracted "relaxation."  If you hang on to that contraction, you get tension.  Yes, that odious word and condition.

So, with the passage in question, you must realize that any contracton to initially set the hand to depress the keys, is a mini-burst of tension.  Right?  Play a chord and you need firm fingers, but the instant you strike the keys with that perfect shot, you let the hand "relax," but not so much that it collapses like a rag doll's hand.  Just enough to rid yourself of the initial muscle contraction.  Then, almost instantaneously, you let the weight of the hand/arm/shoulder/butt/legs/flip-flops move into the keyboard.  In other words, relax.

Now, use this notion on each of those Rach Prelude note groupings.  Not all of them make you extend your hand so fully, so the next group is where you let the contraction/tension dissipate.  Look, Miss Mayla, try Opus 10/1 (Chopin) for a few minutes at the keyboard.  The principle you need to explore is embodied in every bloody measure of that Etude.  And the secret to making the big stretches as tension-free as possible, is ROTATION.

Well, this is meant to be helpful, but re-reading it, I sound like a lunatic.  Sorry.  Good intentions nonetheless.  

[cmg]

p.s. that spread-finger photo of your hand wouldn't look that locked and rigid if you had shown us a video.  You see, that spread position is part of a rotational movment.  In the photo, you've frozen the worst aspect of it.  In movement, you wouldn't be locked into the torturous grasp in that way.  It would be a fluid, flow-through of a rotational gesture over a rather large span.  Not locked into position like some arpeggio-machine thingie.

Comprenez?

[Mayla]

But, that is the point, I have practiced it as you are talking about for years.  And, I am perfectly aware that there will be times when we must be firm in order to play, and then relax -- how many repetitions I wonder did I do like this ?  As it turns out, it actually takes very little weight or effort to depress the piano keys so I only use another "technique" when I have no other choice.

Anyway, in this case, I can do both ways slowly, but only one way quickly.  And, one of these ways I could probably do all day long (why fight that ?), while the other I can hardly do three times in a row (as is required) and it is much more labored (why force that ?).

So far I have not heard anybody actually complain about my recording.  There are actually things I might say about it, but either people are trying to be nice or they have nothing to say. 


btw -- I am glad that you like my hands 

[henry_v]

Thanks for posting in, henry.  I have figured that a truly good teacher would just be able to point me to an exercise that would fix the problem (probably Hanon ?), since all problems can be solved and are found through exercises.  So, I thought, why bother my teacher at all ?  Why not just ask for the specific exercise that many people must have gone through and remember in their exercise training ?

I think the problem is that what is most "logical" for one person is not necessarily logical at all for another.  And what is logical in one context is not necessarily logical in another.  If the problem is that I am caused tension when trying to go from 2 to 3, even if I am not touching them at the same time (and, at tempo I have little time to "relax" between them and actually MUST stay "stretched"), then perhaps I ought to stop doing that ?  In this case, yes, I will avoid the tension because it's not something I am willing to try to get used to anymore -- I have spent enough time doing that and it's not gotten me hardly anywhere as far as I am concerned.

In the first photo above, I was simply displaying what my hand looks like when/if I follow what was most logical for another person :  "nice, open, flat hand" -- it isn't logical for me, and apparently it's not logical for you, either.

I still consider myself to be exploring.

About exercises, I don't know how to answer that one, since I've never used them. I think that some Chopin etudes (op. 10 nr. 1 or 25 nr. 1 for example) will give you all the technique you need for this passage. However, I am quite sure that the 'secret' lies in the way moving (although as I said before, it's not simple, but rather complex and difficult to understand from writing).
You say that at tempo you have little time for relaxing between the two notes (F# and B). You need  a completely different sensation. To describe it I must go into detail and I am afraid it will be even more confusing. Anyway, why play strictly legato? why not more 'jump' from one note to another?
If it's still not working, I gave you my second  fingering option (inferior to the original one but still being more appropriate than yours I think).

And yes, I completely agree with you that what is logical for one person may be not for another person. With 'wrong approach to solve the problem' in my previous post' I was referring to the fingering you use, not to your question about exercises. You can use exercises for this problem, or better, making an exercise yourself out of this problem/passage.
I still think your first fingering will not get you there, the fingering written in the score will not give you any tension, unless you are doing something wrong.
If possible post a video, that will point out many things more clearly.

[cmg]

Your fiortura sounds fine!  A little notey, but you can play this!  I tried the passage myself (haven't played this in some time) and realized my hand instinctively did this:

124 123 123 532 521 432.  That way I'm prepared for the next round with the same fingering beginning 124, not 2.  I like, personally, the 124 because it sets up my rotational mechanism immediately.  My hand isn't big either.  Can play a 9th, just barely reach a 10th.

[cmg]

Anyway, why play strictly legato? why not more 'jump' from one note to another?

That's the ticket!  Forget the strictly legato part.  Look.  Try practicing the passage WITH pedalling.  Forget finger legato.  Let the pedal do the work.  Just relax with it.  You certainly have the technique to play this.  Your brain is getting in the way.  Be sloppy (pedal) and stupid for a few minutes, will you?

p.s. if you will note in Op 10/1 there are several bars that demand "jumping."  Don't think in such a Bachian technical way about technique here.  God gave you a pedal, now please experiment with it.

[Mayla]

Be sloppy (pedal) and stupid for a few minutes, will you?

hmmmm ..... well, only if there is chocolate icecream involved .

[cmg]

 

[Mayla]

 


(pssst ... *whispers* what are we looking at  )

[Mayla]

About exercises, I don't know how to answer that one, since I've never used them. I think that some Chopin etudes (op. 10 nr. 1 or 25 nr. 1 for example) will give you all the technique you need for this passage. However, I am quite sure that the 'secret' lies in the way moving (although as I said before, it's not simple, but rather complex and difficult to understand from writing).
You say that at tempo you have little time for relaxing between the two notes (F# and B). You need  a completely different sensation. To describe it I must go into detail and I am afraid it will be even more confusing. Anyway, why play strictly legato? why not more 'jump' from one note to another?
If it's still not working, I gave you my second  fingering option (inferior to the original one but still being more appropriate than yours I think).

And yes, I completely agree with you that what is logical for one person may be not for another person. With 'wrong approach to solve the problem' in my previous post' I was referring to the fingering you use, not to your question about exercises. You can use exercises for this problem, or better, making an exercise yourself out of this problem/passage.
I still think your first fingering will not get you there, the fingering written in the score will not give you any tension, unless you are doing something wrong.
If possible post a video, that will point out many things more clearly.

Yes, I tried to post a video, actually (which could only be done in slow-motion because it's just my webcam) but for some reason it doesn't come out.  Obviously the Chopin's etude would only apply if I used the original fingering.

btw -- what, exactly, makes a fingering inferior to another ?  The number of rotations involved ?  The tension felt ?  The sound produced ?

Please, feel free to describe in detail.  I think that it actually can be clear.

[henry_v]

So far I have not heard anybody actually complain about my recording.  There are actually things I might say about it, but either people are trying to be nice or they have nothing to say. 

It's difficult to judge your recording because you completely isolated the passage (in all aspects). However, to me, it sounds quite mechanical (partly the piano maybe, are you using a digital?) and irregular (both in tone quality and rhythm, even if you play on a digital), and at least didn't convince me that the fingering you use is a fine one. It may sound worse when you use the original fingering written in the score, therefore I think you are using a wrong technique/way of moving.

By the way, nobody is forcing you playing in a laboured way, on the contrary, I try to explain that this passage can be played in a very natural, fluid way, if you know how to do it.

But may I ask you, are you truly satisfied the you play it? If so, then, what's the problem?

[Mayla]

Where are my irregularities, exactly ?  I am not disagreeing, I just think that if they are there, they can be pinpointed (as a matter of fact, I can hear some myself -- but don't you think we would be hearing the same thing ?).  And, I am curious what you mean by mechanical AND irregular ?  That's a bit of an odd and normal description to me.

And, no, I am not *completely* satisfied with my playing, yet.  Nor was I before, which is why I changed.

[cmg]

Where are my irregularities, exactly ?  I am not disagreeing, I just think that if they are there, they can be pinpointed (as a matter of fact, I can hear some myself -- but don't you think we would be hearing the same thing ?).  And, I am curious what you mean by mechanical AND irregular ?  That's a bit of an odd and normal description to me.

And, no, I am not *completely* satisfied with my playing, yet.  Nor was I before, which is why I changed.

Oy vey . . . your turn at bat, Henry.  But I'd suggest insisting that our dear friend take a break from this Prelude, kick back and fix herself a nice chocolate sundae.  Then a cool bath.  Then a big martini.

[henry_v]

Yes, I tried to post a video, actually (which could only be done in slow-motion because it's just my webcam) but for some reason it doesn't come out.  Obviously the Chopin's etude would only apply if I used the original fingering.

btw -- what, exactly, makes a fingering inferior to another ?  The number of rotations involved ?  The tension felt ?  The sound produced ?

Please, feel free to describe in detail.  I think that it actually can be clear.

For the chopin studies, yes, try to use his fingering, then you will discover the kind of technique Chopin had in mind.

About fingering, what is important at the end, for me, is the sound. Well, talking about sound is a very, very complicated matter, and achieving a good sound or the best sound possible for a piece or passage will take a lifetime of study and is very difficult to talk about.
In this case, your fingering has many unnecessary jumps (from B-5 to E-3 and F#-3 to B-1) and involves much use of the thumb, very short one after another.
So, if you want to achieve fluidity, velocity and a legatissimo sound (what I think this passage is about, very shortly, and what btw also is indicated in the score), that fingering would make it very difficult and will not help you achieving it.
If one faces a technical problem or feels any kind of tension, sometimes using a different fingering can be a solution.
Anyway, I still think the meaning of the passage will dictate you the technique and in this case the fingering.

[Mayla]

Oh, okay.  I will switch to what you are talking about.  It's crystal clear to me now.  Thanks.