Ok, diving into this a bit further …
I think it is fair to say the 32nd note beaming looks particularly odd in my example and in your second measure because Dorico is slanting the beams one space, for an interval comprising a half space. Normal Ted Ross beaming for this interval at these staff positions with one or two beams should be straddle-hang for 1/4 space and look like this as shown on pages 105 and 107, which is in fact what I’m getting in Dorico with my defaults:
So far, so good. With the addition of a third beam, the rules change a bit and everything gets more complicated. Gould’s own advice is a bit contradictory here as well. On page 21 she states, “With the addition of a third beam, the beams must slant a whole stave-space.” Previously on page 18 she states the outer beam must hang for upstems and sit for downstems. I think this is what Dorico is doing in my example anyway. Outermost beams hang (even though first isn’t really visible without a ledger line), and a slant of one space. She doesn’t address the issue of what to do when the interval between the notes is less than one space as we have here, but she does go on to say on page 21, “In the past, to ensure both ends of all beams are attached to stave-lines, some editions have slightly widened the distance between beams to allow for an angle of less that a stave-space. This is a good compromise: [example follows]” The example she gives then shows hang-sit for a beam angle of a half space, so clearly her decree that the beams “must slant a whole stave-space” isn’t set in stone and in fact isn’t even the preferred outcome when adjusting the spacing between staves is possible.
Moving on to Ross …
On page 125 where he discusses Triple Beams, Ross says, “If the beam slant calls for less than a one space slant, normal spacing between the beams in no longer used since this would not permit the ends of the beams to hang, sit or straddle the staff lines … Beam cannot start or end in a space … The spaces between beams are opened and altered in such a manner that the ends of each beam make contact with a staff line. (When at least one of the beams is outside the staff lines normal spacing is used.)” The beam slant in Vaughn’s example here does in fact call for a slant less than one space so the widening principle should apply here according to both Ross and Gould’s compromise solution. I didn’t have Engraving Options/Beams/32nd note beams/Widen gap between beams turned on because I didn’t really like the look of it, but if I turn that on here’s what I get:
I think widening them that much looks a little goofy, but it definitely looks strange immediately following the first which is not widened. I assume the first isn’t widened because Ross’s rule if “one of the beams is outside the staff lines normal spacing is used,” has been applied here, but the as “whole stave-space” rule seems to override the normal angle, the contrast is pretty noticeable. There’s no manual control over beam spacing in Properties, correct? This would be a nice feature to have in this situation, as widening the beam distance would probably make the contrast not quite so jarring. Being able to tweak the positioning of the inner beams would definitely be desirable as there isn’t any way to override the defaults (I think). Dorico generally does a better job than the default version of Finale with all things related to beaming, but the Patterson Beams plug-in is really excellent and I’ve used it on every file for years. I think the Finale example with Patterson Beams applied below is much preferable to Dorico’s solution using Vaughn’s example.
With the beam spacing slightly widened and an slant of 1/4 space, there are no wedges created. The outermost beams straddle-hang, the innermost sit-straddle, and the middle beams have a somewhat odd partial straddle configuration, but I think the overall result is more preferable, at least to my eye. I’m not exactly sure what rules Robert Patterson is applying here, but it does follow the Ross rule that “the ends of each beam make contact with a staff line” and the end result is a consistent clean look. Maybe someone will change my mind, but I would like to see an option to do something like this within Dorico. (There’s no way to exactly replicate this beaming in Dorico now, correct?)
Back to Vaughn’s original example, maybe Dorico is applying the when “one of the beams is outside the staff lines normal spacing is used” rule, and that is what is causing the inconsistency? I’m not sure what setting I have that would prevent me from getting the same result though.
