Re: Slanted Beams thickness
On Thu, Mar 24, 2022 at 6:46 PM Valentin Petzel wrote: > Hello, > > Lilypond handles slanted Beams in a geometrically weird way, that is, the > thickness is not measured as the shortest distance between the opposing > sides > of the boundary, but as vertical distance. This results in Beams getting > optically thinner and closer the higher the slope is. But we can very > easily > factor this out by adjusting the thickness to the slope. In fact if we > want to > achieve a real thickness theta the adjusted thickness would need to be > theta·sqrt(1 + slope²). See attached an experimental example. > I was looking through the lilypond-devel archives trying to find discussions that I thought were held on this subject previously, but I couldn't find them. I did, however, find this post that indicates that the beam thickness and the blot diameter interact when determining the angle of the beam as defined by its centerline: https://lists.gnu.org/archive/html/lilypond-devel/2019-06/msg00023.html I found the attached .png to be quite interesting. Thanks, Carl
Re: Slanted Beams thickness
On Fri, Mar 25, 2022 at 7:47 AM Valentin Petzel wrote: > Are you sure about this? It is incredibly hard to cut diagonal lines with > a > chisel. As I mentioned half an hour ago this would have hardly any effect > in > the common cases anyway. > No, I'm not sure about this. It was my understanding, but my understanding could be wrong. > > And my intent is not to propose a new default, but to initiate some > discussion. This should not affect common notation practise (unless you > want to > reproduce a style with very little distance between the Beam, in which > case > reasonable slopes do cause bad results), but might be relevant for some > more > modern stuff. > > I think having options is good. And it may be that there is a difference between a single beam and multiple beams. If there is a single beam that's exceptionally steep, only one end will be on the staff, and we can fudge the location of the beam (make it a straddle beam). We don't have to worry about what happens with adjacent beams. If we have multiple beams, we have to make the inter-beam spacing work, which may be a substantial challenge. I think (especially in the case of multiple beams) there's much more to properly changing the optical weight of a steep beam than just changing the beam's thickness. Thanks, Carl
Re: Slanted Beams thickness
On 2022-03-25 01:44, Valentin Petzel wrote: Subject: Slanted Beams thickness From: Valentin Petzel [1] Date: 2022-03-25 01:44 To: [2]lilypond-devel@gnu.org Hello, Lilypond handles slanted Beams in a geometrically weird way, that is, the thickness is not measured as the shortest distance between the opposing sides of the boundary, but as vertical distance. This results in Beams getting optically thinner and closer the higher the slope is. But we can very easily factor this out by adjusting the thickness to the slope. In fact if we want to achieve a real thickness theta the adjusted thickness would need to be theta·sqrt(1 + slope²). See attached an experimental example. Cheers, Valentin A couple of points, on top of what has already been brought up. As has already been said, you will hardly notice any difference unless the slope is very high, which is a situation that you anyway try to avoid as much as possible, which also makes it hard to find examples in typeset scores. After all, that's one of the main reasons to use kneed beams. My gut feeling is that a mathematically exact solution is not likely to provide the most pleasing effect to the eye. There are already a number of optical corrections applied in LilyPond to handle other such discrepancies between the mathematically most obvious solution and the visually most pleasing solution. Something in between the current and the newly proposed approach is likely to look best. Even though a general guiding approach for Lilypond's layout decisions is to imitate old hand engraved scores, we shouldn't necessarily copy layout decisions that were caused by technical limitations in the hand engraving process, if we have a general agreement that something else looks better. /Mats References 1. mailto:valen...@petzel.at 2. mailto:lilypond-devel@gnu.org
Re: Slanted Beams thickness
Are you sure about this? It is incredibly hard to cut diagonal lines with a chisel. As I mentioned half an hour ago this would have hardly any effect in the common cases anyway. And my intent is not to propose a new default, but to initiate some discussion. This should not affect common notation practise (unless you want to reproduce a style with very little distance between the Beam, in which case reasonable slopes do cause bad results), but might be relevant for some more modern stuff. Cheers, Valentin Am Freitag, 25. März 2022, 13:52:14 CET schrieb Carl Sorensen: > On Thu, Mar 24, 2022 at 6:46 PM Valentin Petzel wrote: > > Hello, > > > > Lilypond handles slanted Beams in a geometrically weird way, that is, the > > thickness is not measured as the shortest distance between the opposing > > sides > > of the boundary, but as vertical distance. This results in Beams getting > > optically thinner and closer the higher the slope is. But we can very > > easily > > factor this out by adjusting the thickness to the slope. In fact if we > > want to > > achieve a real thickness theta the adjusted thickness would need to be > > theta·sqrt(1 + slope²). See attached an experimental example. > > I think LilyPond handles beams not in a geometrically weird way, but in a > geometrically correct way. > > If I understand correctly, I think that the slanted beams are defined not > by the perpendicular thickness, but by the vertical "thickness", and that > this is intentional. > > When the end of a beam sits on a staff, it should take up a fixed > percentage of the staff space, which we call the beam thickness. In > actuality, it is not the perpendicular thickness of the beam (the dimension > perpendicular to the beam center line) but the vertical thickness (the > dimension perpendicular to the staff lines. Of course, this does lead to a > reduced perpendicular thickness, which might be considered the optical > thickness. > > This models hand engraving, where chisels of a fixed width were used, and > the chisels were always held with the ends perpendicular to the staff > lines, so that the ends of the beams were vertical. > > If we want to have a setting to change that, I'm fine. But I don't think > we should change the default, without strong evidence from good > hand-engraved scores that this is the proper way to do it. > > The same is true of beam spacing. Beam spacing needs to match the vertical > staff spacing, not the perpendicular spacing. Lilypond uses beam quanting > to make sure that the beams interact properly with the staff lines. > > I note that Dorico offers "optical beaming" for slanted beams, but can't > find any discussion of it. > > Thanks, > > Carl signature.asc Description: This is a digitally signed message part.
Re: Slanted Beams thickness
Hi Simon, none of these slopes are extreme enough to really make a difference. Am Freitag, 25. März 2022, 14:21:12 CET schrieb Simon Albrecht: > Hi everyone, > > On 25/03/2022 01:44, Valentin Petzel wrote: > > Hello, > > > > Lilypond handles slanted Beams in a geometrically weird way, that is, the > > thickness is not measured as the shortest distance between the opposing > > sides of the boundary, but as vertical distance. This results in Beams > > getting optically thinner and closer the higher the slope is. But we can > > very easily factor this out by adjusting the thickness to the slope. In > > fact if we want to achieve a real thickness theta the adjusted thickness > > would need to be theta·sqrt(1 + slope²). See attached an experimental > > example. > > > > Cheers, > > Valentin > > I think this is a great idea. IMO, the way to think about it should be: > slanted beams shouldn’t appear any less weighty than horizontal ones. > It’s not easy to find very obvious examples, but I attach four versions > of a bar from Grieg in which both beams seem equally thick. > > I agree with others that the distances between multiple beams don’t seem > good in your mockup. It’s certainly important to preserve the qualities > of the beam quanting that Lily does, but I don’t know how the > intricacies of that would play out. > > Best, Simon signature.asc Description: This is a digitally signed message part.
Re: Slanted Beams thickness
Carl, If you look at the video I posted, could you explain how you see using that instrument non along its tooling direction? (Like, "diagonally" wrt cutting edge at the tip) seemd to me it would be very hard to get a straight line doing so... L On Fri, 25 Mar 2022, 13:52 Carl Sorensen, wrote: > On Thu, Mar 24, 2022 at 6:46 PM Valentin Petzel > wrote: > > > Hello, > > > > Lilypond handles slanted Beams in a geometrically weird way, that is, the > > thickness is not measured as the shortest distance between the opposing > > sides > > of the boundary, but as vertical distance. This results in Beams getting > > optically thinner and closer the higher the slope is. But we can very > > easily > > factor this out by adjusting the thickness to the slope. In fact if we > > want to > > achieve a real thickness theta the adjusted thickness would need to be > > theta·sqrt(1 + slope²). See attached an experimental example. > > > > I think LilyPond handles beams not in a geometrically weird way, but in a > geometrically correct way. > > If I understand correctly, I think that the slanted beams are defined not > by the perpendicular thickness, but by the vertical "thickness", and that > this is intentional. > > When the end of a beam sits on a staff, it should take up a fixed > percentage of the staff space, which we call the beam thickness. In > actuality, it is not the perpendicular thickness of the beam (the dimension > perpendicular to the beam center line) but the vertical thickness (the > dimension perpendicular to the staff lines. Of course, this does lead to a > reduced perpendicular thickness, which might be considered the optical > thickness. > > This models hand engraving, where chisels of a fixed width were used, and > the chisels were always held with the ends perpendicular to the staff > lines, so that the ends of the beams were vertical. > > If we want to have a setting to change that, I'm fine. But I don't think > we should change the default, without strong evidence from good > hand-engraved scores that this is the proper way to do it. > > The same is true of beam spacing. Beam spacing needs to match the vertical > staff spacing, not the perpendicular spacing. Lilypond uses beam quanting > to make sure that the beams interact properly with the staff lines. > > I note that Dorico offers "optical beaming" for slanted beams, but can't > find any discussion of it. > > Thanks, > > Carl >
Re: Slanted Beams thickness
Hi everyone, On 25/03/2022 01:44, Valentin Petzel wrote: Hello, Lilypond handles slanted Beams in a geometrically weird way, that is, the thickness is not measured as the shortest distance between the opposing sides of the boundary, but as vertical distance. This results in Beams getting optically thinner and closer the higher the slope is. But we can very easily factor this out by adjusting the thickness to the slope. In fact if we want to achieve a real thickness theta the adjusted thickness would need to be theta·sqrt(1 + slope²). See attached an experimental example. Cheers, Valentin I think this is a great idea. IMO, the way to think about it should be: slanted beams shouldn’t appear any less weighty than horizontal ones. It’s not easy to find very obvious examples, but I attach four versions of a bar from Grieg in which both beams seem equally thick. I agree with others that the distances between multiple beams don’t seem good in your mockup. It’s certainly important to preserve the qualities of the beam quanting that Lily does, but I don’t know how the intricacies of that would play out. Best, Simon
Re: Slanted Beams thickness
... which is what Valentin also just said. Sorry Valentin for the double up! L On Fri, 25 Mar 2022, 13:43 Luca Fascione, wrote: > Yes but look at the took and how it's held in the hand: you won't ever get > a clean line from it holding is slanted to the direction of motion, that > thing is meant to be pushed straight ahead... > > > > On Fri, 25 Mar 2022, 13:19 Dan Eble, wrote: > >> On Mar 25, 2022, at 04:35, Luca Fascione wrote: >> > >> > This video shows Hans Kuehner at work >> > >> > https://www.youtube.com/watch?v=BvyoKdW-Big >> > >> > at 4m36 shows beams being engraved, he appears to keep the instrument >> > orthogonal to the line direction, >> >> It's fascinating, but those beams are nearly horizontal and Valentin's >> concern is about steep beams. >> — >> Dan >> >>
Re: Slanted Beams thickness
On Thu, Mar 24, 2022 at 6:46 PM Valentin Petzel wrote: > Hello, > > Lilypond handles slanted Beams in a geometrically weird way, that is, the > thickness is not measured as the shortest distance between the opposing > sides > of the boundary, but as vertical distance. This results in Beams getting > optically thinner and closer the higher the slope is. But we can very > easily > factor this out by adjusting the thickness to the slope. In fact if we > want to > achieve a real thickness theta the adjusted thickness would need to be > theta·sqrt(1 + slope²). See attached an experimental example. > I think LilyPond handles beams not in a geometrically weird way, but in a geometrically correct way. If I understand correctly, I think that the slanted beams are defined not by the perpendicular thickness, but by the vertical "thickness", and that this is intentional. When the end of a beam sits on a staff, it should take up a fixed percentage of the staff space, which we call the beam thickness. In actuality, it is not the perpendicular thickness of the beam (the dimension perpendicular to the beam center line) but the vertical thickness (the dimension perpendicular to the staff lines. Of course, this does lead to a reduced perpendicular thickness, which might be considered the optical thickness. This models hand engraving, where chisels of a fixed width were used, and the chisels were always held with the ends perpendicular to the staff lines, so that the ends of the beams were vertical. If we want to have a setting to change that, I'm fine. But I don't think we should change the default, without strong evidence from good hand-engraved scores that this is the proper way to do it. The same is true of beam spacing. Beam spacing needs to match the vertical staff spacing, not the perpendicular spacing. Lilypond uses beam quanting to make sure that the beams interact properly with the staff lines. I note that Dorico offers "optical beaming" for slanted beams, but can't find any discussion of it. Thanks, Carl
Re: Slanted Beams thickness
Yes but look at the took and how it's held in the hand: you won't ever get a clean line from it holding is slanted to the direction of motion, that thing is meant to be pushed straight ahead... On Fri, 25 Mar 2022, 13:19 Dan Eble, wrote: > On Mar 25, 2022, at 04:35, Luca Fascione wrote: > > > > This video shows Hans Kuehner at work > > > > https://www.youtube.com/watch?v=BvyoKdW-Big > > > > at 4m36 shows beams being engraved, he appears to keep the instrument > > orthogonal to the line direction, > > It's fascinating, but those beams are nearly horizontal and Valentin's > concern is about steep beams. > — > Dan > >
Re: Slanted Beams thickness
Hello all, @Abraham: In fact this is not done at scheme level here, but at C++ level. There reason is that we do not want to change the value of the thickness, but for Lilypond to think about this thickness in a more natural way. Also this example already handles the beam distance. For some reason the slanted beam are just slightly thicker than they should be, I’ll still need to look into why this is the case. @Werner: In fact it is a bit too thick on slanted Beams. I just did not yet find out the exact reason for why this is, as mathematically they should be the same. I do not think it is a problem with calculation of the root, so I suppose is in some way related to the way lilypond draws these Beams. @Jeam: I’ve stumpled upon a post in the Dorico dev blog which also mentions this Beam thing, which got me to look into this. One has to remember that in the old days Beams would have been cut into the pewter using special chisels. But these things cannot really cut diagonally, so you need to keep the chisel in line with the Beam, resulting in a constant Beam width regardless of slope. So this is something you will find in all old hand engraved scores. Furthermore if you look at the examples you must see that the way this is handles just look bad with high slopes. I don’t think you’ll find engraving literature stating that Beam thickness should apply to the actual thickness of the Beam and not the size of the vertical intersection as this does seem to be the more reasonable thing, but I think the other points make a strong case for why this is a legitimate claim. Anyway, I do not think this is really intentional behaviour. The current approach as a big advantage for aligning Beams to Staff lines (which arguably is not that much of an issue for Beams with very high slope), but I guess the main reason for this is that it has little effect on the most common slopes you’d assume to find. Even with an 50% slope (which would be quite a high slope you’d find very seldomly) we’d need only about 11% more thickness. With a 25% slope (which is much more realistic) we’d be at around 3%. So while you’d notice a slight difference between these it would be hardly noticeable. Cheers, Valentin signature.asc Description: This is a digitally signed message part.
Re: Slanted Beams thickness
On Mar 25, 2022, at 04:35, Luca Fascione wrote: > > This video shows Hans Kuehner at work > > https://www.youtube.com/watch?v=BvyoKdW-Big > > at 4m36 shows beams being engraved, he appears to keep the instrument > orthogonal to the line direction, It's fascinating, but those beams are nearly horizontal and Valentin's concern is about steep beams. — Dan
Re: Slanted Beams thickness
Sorry, forgot to say: instead of correcting with 1/cos(\theta) I wonder if correcting with 1/cos(\theta/2) would be an idea? sl2 = sl / (1+sqrt(1+sl*sl)) // tan(\theta/2) th *= sqrt(1+sl2*sl2) HTH L On Fri, Mar 25, 2022 at 9:35 AM Luca Fascione wrote: > This video shows Hans Kuehner at work > > https://www.youtube.com/watch?v=BvyoKdW-Big > > at 4m36 shows beams being engraved, he appears to keep the instrument > orthogonal to the line direction, > which makes Valentin's formula appropriate to capture this process. > > (I love it when it goes "What happens when you make mistakes?" -> "I > _don't_ make mistakes!" (7m59 or so) ) > > As Werner said, I'd have expected something more of a halfwayhouse, > because in my mind I was expecting more or a nib > pen feel to this, but even looking at photography based processes > there seems to be no evidence that any of that technique > would influence this. > > I feel that for more organic looking fonts (such as lilyjazz) this might > want to change, but I guess that's a somewhat different > topic. > > L > > On Fri, Mar 25, 2022 at 8:10 AM Jean Abou Samra > wrote: > >> Le 25/03/2022 à 01:44, Valentin Petzel a écrit : >> > Hello, >> > >> > Lilypond handles slanted Beams in a geometrically weird way, that is, >> the >> > thickness is not measured as the shortest distance between the opposing >> sides >> > of the boundary, but as vertical distance. This results in Beams getting >> > optically thinner and closer the higher the slope is. But we can very >> easily >> > factor this out by adjusting the thickness to the slope. In fact if we >> want to >> > achieve a real thickness theta the adjusted thickness would need to be >> > theta·sqrt(1 + slope²). See attached an experimental example. >> >> >> >> Did you look into engraving literature to back this up? >> Given the amount of effort put by Han-Wen & Jan in beam >> formatting, I have trouble imagining this being just >> an oversight. >> >> Jean >> >> >>
Re: Slanted Beams thickness
This video shows Hans Kuehner at work https://www.youtube.com/watch?v=BvyoKdW-Big at 4m36 shows beams being engraved, he appears to keep the instrument orthogonal to the line direction, which makes Valentin's formula appropriate to capture this process. (I love it when it goes "What happens when you make mistakes?" -> "I _don't_ make mistakes!" (7m59 or so) ) As Werner said, I'd have expected something more of a halfwayhouse, because in my mind I was expecting more or a nib pen feel to this, but even looking at photography based processes there seems to be no evidence that any of that technique would influence this. I feel that for more organic looking fonts (such as lilyjazz) this might want to change, but I guess that's a somewhat different topic. L On Fri, Mar 25, 2022 at 8:10 AM Jean Abou Samra wrote: > Le 25/03/2022 à 01:44, Valentin Petzel a écrit : > > Hello, > > > > Lilypond handles slanted Beams in a geometrically weird way, that is, the > > thickness is not measured as the shortest distance between the opposing > sides > > of the boundary, but as vertical distance. This results in Beams getting > > optically thinner and closer the higher the slope is. But we can very > easily > > factor this out by adjusting the thickness to the slope. In fact if we > want to > > achieve a real thickness theta the adjusted thickness would need to be > > theta·sqrt(1 + slope²). See attached an experimental example. > > > > Did you look into engraving literature to back this up? > Given the amount of effort put by Han-Wen & Jan in beam > formatting, I have trouble imagining this being just > an oversight. > > Jean > > >
Re: Slanted Beams thickness
Le 25/03/2022 à 01:44, Valentin Petzel a écrit : Hello, Lilypond handles slanted Beams in a geometrically weird way, that is, the thickness is not measured as the shortest distance between the opposing sides of the boundary, but as vertical distance. This results in Beams getting optically thinner and closer the higher the slope is. But we can very easily factor this out by adjusting the thickness to the slope. In fact if we want to achieve a real thickness theta the adjusted thickness would need to be theta·sqrt(1 + slope²). See attached an experimental example. Did you look into engraving literature to back this up? Given the amount of effort put by Han-Wen & Jan in beam formatting, I have trouble imagining this being just an oversight. Jean
Re: Slanted Beams thickness,Slanted Beams thickness
> Lilypond handles slanted Beams in a geometrically weird way, that > is, the thickness is not measured as the shortest distance between > the opposing sides of the boundary, but as vertical distance. This > results in Beams getting optically thinner and closer the higher the > slope is. But we can very easily factor this out by adjusting the > thickness to the slope. In fact if we want to achieve a real > thickness theta the adjusted thickness would need to be > theta·sqrt(1 + slope²). See attached an experimental example. Looks good! However, I don't fully agree with the thickness values in your experimental example. For very steep angles the beam appears a little bit too thick IMHO; I think there should be a correction factor. Werner
Re: Slanted Beams thickness
Hey, Valentin! On Thu, Mar 24, 2022 at 6:46 PM Valentin Petzel wrote: > Hello, > > Lilypond handles slanted Beams in a geometrically weird way, that is, the > thickness is not measured as the shortest distance between the opposing > sides > of the boundary, but as vertical distance. This results in Beams getting > optically thinner and closer the higher the slope is. But we can very > easily > factor this out by adjusting the thickness to the slope. In fact if we > want to > achieve a real thickness theta the adjusted thickness would need to be > theta·sqrt(1 + slope²). See attached an experimental example. > > Cheers, > Valentin I attempted to do this some years ago, but with my limited Scheme abilities, I dropped it. In addition to the beam thickness correction, it would probably be prudent to have the beam spacing corrected as well so the white space between beams stays the same. Maybe? Just a thought. Best, Abraham
