Well, I wouldn't say "on syntax", I'd say "on code" - and code only contains symbols, not "references to variables in a specific scope"; scope is determined by context - the surrounding code, which the macro can't alter: you can't substitute code into other code while retaining the same surrounding code, that's a contradiction in terms! But this is just terminology.
The old MIT Scheme macro system seems interesting from what you say - is there any place I could go to find an implementation which has this behavior? Or at least examples of code which use it? It seems like it lets code do precisely what I said it couldn't above: contain "references to variables in a specific scope", which is pretty cool. I don't think you'd need to implement environments as first-class run-time objects, merely second-class compile-time objects, with this technique, unless you also allow macros themselves to be first-class.
Okay, I think I'm starting to see. There is quite a big difference between the way Lisp people think of macros and the way Scheme people think of them.
From the documentation, I think that the current version of MIT scheme has this behavior, so look at http://groups.csail.mit.edu/mac/projects/scheme/. (By the way, in case you run Ubuntu, the version of MIT Scheme in the repositories is broken for me.) Look in the documentation for macros (under "Special Forms"), and it's their non-standard low-level macro system. If you're interested in stuff like that, you should also check out syntax-case, which I don't know much about, but I understand is the new, cool way to write Scheme macros. It includes hygienic and unhygienic functionality. Google search for "syntax case" and you'll get some documentation.
The more I look at it, though, the more I think that Scheme macros solve a different problem than Lisp macros. I don't know what it is yet, but it would be interesting to know.
I think you've hit the nail on the head. Hygenic macros and unhygenic macros are very different things (unlike dynamic vs lexical scoping, which are just different ways to create a function). Lisp macros are 'true' macros (Wikipedia: "Macro: a set of instructions that is represented in an abbreviated format"). Hygenic macros are more like a new abstraction that was inspired by Lisp macros.
Well, I'd rather not argue about what 'true' macros are, but I would point out that your definition is basically data compression for programs (which, by the way, I think is an interesting approach to take to programming language design). I'm pretty sure both types of macros and normal functions would all fall under it.
As for the hygienic vs. unhygienic difference, unhygienic macros are certainly easier to define: they rearrange source code into other source code.
The one thing I can think of that hygienic macros can do that unhygienic ones can't is that while they are rearranging source code, hygienic macros can insert references to things that aren't bound to any variable in the expansion scope. The common example I've seen for this is that it lets you protect against people redefining your variables weirdly. For instance, if you insert a reference to 'car', it means whatever 'car' meant where you defined your hygienic macro, even if 'car' has been redefined to be something crazy in the place where your macro is used. The Scheme hygienic macro system also has a way to break hygiene if you want to, so it can do everything other Lisp macros can do.
I guess the question then is, is it useful to be able to do that?
And if you decide you want to be able to do that, are Scheme-style hygienic macros the right way to go about it?
(One option would be to just let you insert objects straight into forms, instead of symbols that you think should reference those objects. This would be fine unless you wanted to be able to set those things later, in which case you'd need some way to get at the actual underlying variable boxes.)