How to input non-rhythmic passages in which different instruments are playing at different speeds

The pdf file indicates what I would like represented in the Dorico project version. I have no idea how to do this. I have tried using the “open meter” option, but that won’t allow me to superimpose different instruments playing different ad lib passages simultaneously, which is what the manuscript calls for. Unfortunately, the Dorico project file is too large in size to upload here. If you can see what is needed from the jpeg picture, you could tell me what steps I need to follow to achieve this look. Or perhaps you could tell me another way to notate this. The pianist is improvising his passages, while the strings are doing their own thing—all unmetered. Thanks in advance for your help with this.

I would notate everything except the strings straightforward in 2/4, 3/4, 4/4 and 5/4 meter. Then notate the strings in the 5/4 bit each as a (hidden) tuplet.

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What kind of hidden tuplet? And who is it hidden from? What about the improvised passage in the piano R.H., over the repeated five tuplets in the left hand? I could not find a way to place them over top of one another.

basically you count the number of notes you want to put down. Then you choose the note value you want to notate (in this case crotchets / eight notes) and build a tuplet with the normal amount of crotchets related to the amount you want to put down.
You can then later hide the tuplet number and bracket.
It is worth having a look into the manual.

Thanks for the reply and suggestion. I find the manual is difficult to comprehend because it doesn’t respond directly to this issue of non-metric notes. And one cannot superimpose a set of non-metered passages over top of metered ones. If one could only “shut off” the rhythmic/metric automatic mechanism this issue wouldn’t occur. As a professional composer, I really don’t need an automatic function to figure out the rhythms in a given measure. I know how to do this myself. The further one goes with non-traditional notation, programs such as this one present all sorts of problems that become difficult to solve.

you can - f.e. by using hidden tuplets, see above…

if you find the explanations in the manuals difficult to understand, there are a few threads in this forum, where this issue has been successfully discussed.
It’s actually an area, where Dorico’s concept does shine and gives you necessary tools at hand. Your example above is actually one of the easy ones.
as I am with my phone only, I can’t offer you an example right now …

Music software has to have a way to organize and place the entries rhythmically, before anything else. If you’d rather just write notes wherever you want them to appear graphically, you’re better off with pencil and paper. Aleatoric boxes have been requested many times. I have no idea what it will take to make such a feature usable.

The boxes in the screenshot above appear to have only slightly differing spacing from each other. What does this spacing indicate? One brute-force way to do this is shift them one by one in Engrave mode, using the secondary circular handle:

Manual beat offset
NB. each note is shifted by a different amount.
And this would not affect the spacing in the parts.

I think this is also a good method if you just need them not to line up with each other, which is what your screenshot looks like to me. I would resort to hidden tuplets only if there are coherent rhythmic proportions.

Many thanks to kb and Mark Johnson for your suggestions. I will try these approaches and see if I can come up with something reasonable. Extracting parts, though, might prove problematic. I am pretty much finished with this 154-page score, except for these two measures that are holding things up. If I can’t achieve the desired results, I will have to go back to my old DOS-based SCORE program, which probably won’t have a problem with doing what I need. This method would allow me to create what I want on the given page, then convert the page first to an EPS file. then to a pdf file, and finally interpolate it into the Dorico master pdf file. At the end, I can print out the score simply from the pdf file.