I'm familiar with the sword school material, as I've used their resources to teach myself Fiore. One of the first changes I had to make though was coming up with English names for the techniques, stances and footwork because (like many HEMA folk) they leave all these names in the original language even though it makes the arts nigh-impossible to learn for people who don't speak those languages.
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The moves in this book are all Fiore but the most important contribution I think I've made is making the material easy to learn for someone who speaks only English and has no prior martial art background -- which is who I think the average person interested in lightsaber combat often is. It's not 'pure' the way many HEMA folks seem to want things, but fortunately I'm not trying to recreate a historical style here but rather adopt the techniques for use in a modern sport style of saber fencing to be used for sparring and choreography.
Pragmatic approach and for clarification I have no objection for your choices. HEMA is HEMA and sabre dueling is sabre dueling. But for HEMA and HEMA purists, that depends on school and if practitioner is taking part in competitions. When competition is main focus, the techniques gets less "pure", reason being no sharp blades, no heavy armour, lighter and faster swords etc. Actually might come much closer to sabre dueling because of those restriction. Check out Helsinki Long Sword Open
gold match [nofollow] from last February. What always catches my eye in matches like these is that there are hardly never grabs on opponent's sword. And Fiore has many techniques that goes around grabbing swordblade. And if light sabres were real that'd be very, very bad idea.
On the opposite side of the coin is the historical recreation and all that preparing for competiotion goes out of window and books are taken off of their shelves. Many times it comes just repeating same thing and finetuning the grip, stance, movement of blades etc. until the stance one is looks more like the stance that is in manuscript. And more often than not it still looks weird or works weirdly.
Similarly I am looking to adopt some Japanese Jō staff techniques for use with the double-bladed saber as I think the way the staff is held in some techniques can be adapted for the unique handle design of the double-bladed saber.
Thought about this last night too. There isn't equivalent for two-bladed sabre in Fiore, so Japanese and perhaps some Chinese styles are logical step. Although, I started to think about spearlike lightweapon to implement for Fiore's spear. But that goes against many visual and style consepts in Star Wars universe so I'll propably leave it at that level.
From my understanding De Arte Gladiatoria Dimicandi is based on Fiori's Flos Duellatorum and the moves are essentially identical. Is that not so?
Yes and no. There is straight lineage from Fiore to Vadi, that is obvious. Many stances are same, same goes with strikes, but Vadi adds few of his own too. For example Vadi has high stances (sword above head) while Fiore has none. But biggest difference is sword length. For Fiore the sword should come around bottom of sternum when standing on it's tip. Vadi comes all the way to armpit. For me, 190cm/~6'4", my longsword for Fiore is 125cm/~4'2" (could be bit longer) and for Vadi I'd need a sword that is 155cm/~5'2". This makes the dynamics of the sword different. Ie. when you stand in Tutta Porto di Ferro with Fiore and take step forward you switch sword to Dente di Zenghiaro on your left side. For Vadi, Tutta Porto di Ferro is identical, but when taking step, the sword stays on your right side, can't remember the name of the stance, and only switches sides through strikes. And this is mainly because of the difference in sword length. I did have chance to try Vadi with my own sword and borrowed Vadi length sword. Doing plays with longer one made more sense that doing them with shorter. But setting details above aside, you are right, base is very similar in Vadi's book compared to any manuscript of Fiore's book. Vadi propably studied under some Fiore's students or perhaps even under Fiore himself. There is only about 50 years between Fior di Battaglia and De Arte Gladiatoria Dimicandi so either of above is possible.
And as last note on this post I do like that you are taking European art and implementing that when most sabre stuff so far have taken it's inspiration from Asian arts. And if you have any questions of Fiore or HEMA feel free to ask. I answer what I can.