Hi Aditya,

Thanks for your hint: I didn't know that subtelty about Lucida OT (and I don't know how to set it up when using Lucida OT).

That being said, actually what I would like to use is the kind of script font which is the attached document (those script fonts were widely used in higher mathematics textbooks in France). 
So when I use mkiv the result is the one I like and is attached to this message (test-scriptfonts-mkiv.pdf). However, thanks to your message I went to check, and noticed that lmtx does not give the same math script fonts, and I don't know what has changed between mkiv and lmtx regarding Asana Math, or the way in which fallback fonts are managed (please see the attached file test-scriptfonts-lmtx.pdf).

Thanks for your help: Otared
PS: this the the file test-scriptfonts.tex:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Some Font Definitions
\definefallbackfamily[myfont][math][Asana Math]
	[range={uppercasescript,lowercasescript}]

% lucida font
\definefontfamily[myfont][serif][Lucida Bright OT]
\definefontfamily[myfont][math][LucidaBrightMathOT]
\definefontfamily[myfont][sans][LucidaSansOT]
\definefontfamily[myfont][mono][LucidaSansTypewriterOT]

%\setupbodyfont[myfont,10pt]

%% End of Font Definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\starttext

\startbuffer[test]
Testing script fonts in maths
\startformula
x^2 + y^2 = z^2, \quad \sin(a)^2 + \cos(b)^2 = 1.
\stopformula
\startformula
\cal{A}, 
\quad \cal{B}, 
\quad \cal{C}, 
\quad \cal{D},
\quad \cal{E},
\quad \cal{F},
\quad \cal{G},
\quad \cal{H},
\quad \cal{K},
\quad \cal{L},
\quad \cal{M},
\quad \cal{P},
\quad \cal{S},
\quad \cal{T}
\stopformula
\hairline
\stopbuffer

\switchtobodyfont[lucidaot]
{\bf Lucida OT: }
\getbuffer[test]

\switchtobodyfont[myfont]
{\bf Lucida OT with Asana Math: }
\getbuffer[test]

\stoptext





> On 17 Oct 2019, at 08:00, Aditya Mahajan <adityam@umich.edu> wrote:
> 
> On Wed, 16 Oct 2019, Otared Kavian wrote:
> 
>> I use Lucida OT fonts for all my documents, but since I prefer the script fonts from another font I have the following setups for my font:
> 
> OT: Do you use this to get a less cursive script font?
> 
> Lucida (like many opentype math fonts) comes with two stylistic variants for script letters. The default is the cursive variant, but you can get the less cursive variant using ss04 stylistic set. See page 8 of
> https://tug.org/store/lucida/lucidaot.pdf
> 
> Aditya
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