I’m looking into an existing score and notating some bars for learning purposes.
Dorico marks notated C#5 with natural harmonics as unplayable (red note), but nevertheless that’s how the score is written.
What could I be missing - since I’m completely new to working with harmonics?
How can the composer ask the cello player to play a C# with natural harmonics?
The part is written in treble clef in this staff/this page.
C#5 is indeed unplayable with natural harmonics, but a professional cello player knows that and plays the note with artificial harmonics.
Ha ha ok, funny 
So actually it’s a notation error?
Hi, cellist here!
That natural harmonic, when played at pitch, that is a major 3rd above the middle of the A string is playable, even if a bit feeble and unstable—sorry @Vadian for contradicting you.
The closest option is to touch the F# a perfect fifth below which will give you that resulting pitch. That node, though, is not currently supported by Dorico.
Playing that with artificial harmonics is of course possible but you need to work out where it is.
Would any of these work using artificial harmonics instead? If I wanted the same pitch and “helping” the cellist?
No problem, but doing so sounds an octave higher.
You see often this notation which means “play this pitch with harmonics regardless natural or artificial”. For example Ravel writes a diamond notehead when he means “touch the string on this pitch”.
The top one, octave harmonic, gives a resulting pitch of C#6 (one octave above).
The middle one, fourth on C#5, gives C#7! (two octaves above).
The bottom one, fourth on C#4, gives C#6 (one octave above).
From this chart, you can see what natural harmonics are possible in the first half of the string of violin, viola, cello, double bass (ignore anything after page 1):
Strings Natural Harmonics Chart.pdf (29.6 KB)
In this, you can see the respective formulas.
String Harmonics Formulas.rtf.zip (1019 Bytes)
In this XIX century method you can see all natural harmonics on the upper half of the cello A string. Only the ones with square notehead are considered stable and usable:
More resources:
No, it doesn’t
See my last reply.
99% of composers don’t bother with doing the job for us, they just write the resulting pitch they want to ear.
Yes, but that’s valid only for natural harmonics from the nut to the middle of the string and for the touched note of the artificial harmonics!
Sorry, again, I’m a bit of a nerd in this 
!
Mmm … you’re right. I need to get back to working on this!
So, now, given my good deal of confusion, hopefully only caused by the unbearable heat around me, let’s try to find a way to obtain that C#5 as a natural (or less natural harmonic).
It seems that it is not possible to obtain a C#5 on the cello with a 100% natural harmonic. Also, the sources I quoted above seem to disagree on the sound produced by the minor third above the middle of the string.
In this document you will find every possible way with artificial harmonics (I hope my calculations are correct, but the playback seems to be):
How to obtain a C#5.dorico (472.9 KB)
Never mind! 
Although I played cello a few years I’m not a cellist, I’m a conductor.
When I conducted Ravel’s “L’heure espagnole” – which is full of natural harmonics – the first time 30 years ago it took almost a whole day to calculate all harmonics and I learned a lot…
In Svizzera fa caldo come in Italia 
(In Switzerland it’s just as hot as in Italy)
I sold my cello a long time ago, but I’m guessing if you place your thumb (since it would be well into thumb position) at the point on the A string where C#5 would be fingered, and instead of pressing the string into the fingerboard, simply played it as a natural harmonic, a C#5 might sound.
A bassist might know better than I, since they regularly use such tricks and use more varied harmonics.
There is no natural harmonic sounding C#5 on the cello A string, no matter what finger you put anywhere. The partials are A3 (fundamental), A4, E5, A5, C#6, E6, ~G6, A6, B6, C#7 etc. The higher, the more nodes you can choose from.
Sorry, can’t notate it on my phone…
Composers do make mistakes…
For a sounding C#5 harmonic the only option is an artificial (touch-fourth) with a thumb (or a 1-4 stretch) on C#3, on the G string (or theoretically, on the C string, but it’s harder to produce a clear sound there).
