Bsrgvty

I would like to know which instruments of a modern orchestra are not able to play a full chromatic run?

I know that the harp for example is in a certain key and you have to use the pedals to change the key you're in. So a fast run wouldn't be possible, because you can't change the pedals that quickly.

The modern Timpani is as far as I know also already able to play a chromatic scale, but how fast can you actually change the pitch with the pedal?

Are there any other instruments which requires certain actions to play outside of a specific scale, or are there even instruments which aren't able to play a chromatic scale?

In a modern western orchestra, that's about it. Unless you're foolish enough to try to write precise pitches for flexatone or slide whistle, and then try to write a chromatic scale.

Playing a chromatic scale on timpani is definitely dubious. Besides the speed and accuracy needed, you would be re-tuning the same drum as you played it, which would cause a slide between every note. Basically it would turn into a glissando, which is a real thing for timpani, but it's an effect, not a scale. I would expect a competent timpanist to have no problem playing a slow chromatic scale, say one note per second. It would be weird and probably something they've never done, but ultimately not unreasonable. Twice that fast would be impractical, and I'm not sure where the transition is.

I don't know what kind of music you're trying to write, but all woodwinds and brass have particular spots where playing chromatically is difficult. Modern woodwinds have enough keywork that all half step and whole step trills are playable, but some are more awkward than others. Brass instruments have some impossible trills.

Instruments capable of chromatic runs over their whole range at high speed^[1]:

• 
  Keyboard:
  
  
  • Piano
  
  
  • Harpsichord
  
  
  • Organ
  
  
  • Accordion
  
  
  • Ondes Martenot (also full-range glissando)
  
  
  • Synthesizer
  
  
  • Celesta
  
  


• 
  Strings:
  
  
  • Violin
  
  
  • Viola
  
  
  • Cello
  
  
  • Double Bass
  
  
  • Guitar
  
  
  • Mandolin
  
  
  • Banjo
  
  
  • Hurdy-Gurdy
  
  


• 
  Brass:
  
  
  • Horn (modern valved)
  
  
  • Trumpet
  
  
  • Trombone
  
  
  • Tuba
  
  


• 
  Woodwinds:
  
  
  • Flute
  
  
  • Oboe
  
  
  • Clarinet
  
  
  • Bassoon
  
  
  • Saxophone
  
  


• 
  Percussion:
  
  
  • Vibraphone
  
  
  • Marimba
  
  
  • Glockenspiel
  
  
  • Tubular Bells
  
  
  • Crotales
  
  
  • Steel Pan
  
  


• 
  Others:
  
  
  • Chromatic Harmonica
  
  
  • Theremin (also full-range glissando)
  
  

Instruments with limited capability for chromatic runs^[2]:

• 
  Keyboard:
  
  
  • ?
  
  


• 
  Strings:
  
  
  • Harp (retunable to different keys using pedals)
  
  



• Brass:



• 
  

  Woodwinds:

  
  
  
  • Recorder
  
  


• 
  Percussion:
  
  
  • Timpani (retunable using pedals, would be slow and cause glissando)
  
  
  • Crystal wine glasses (in quantity, slowly)
  
  
  • Handbells (in quantity)
  
  
  • Rototoms (in quantity)
  
  
  • Tuned gongs (in quantity)
  
  
  • Whirlies (in quantity, slowly)
  
  

Instruments not capable of chromatic runs:

• 
  Keyboard:
  
  
  • ?
  
  


• 
  Strings:
  
  
  • ?
  
  


• 
  Brass:
  
  
  • ?
  
  


• 
  Woodwinds:
  
  
  • Bagpipes (not chromatic)
  
  
  • Tin Whistle, Low Whistle, Diatonic Flute (not chromatic)
  
  


• 
  Percussion:
  
  
  • Bell Tree, Chime Tree (pitched, but untuned)
  
  
  • Flexatone (unreasonable to tune)
  
  

¹ Playing several notes per second and not having to do anything (like retune) that you would normally only do while you're not playing and that would slow you down or force you to leave a pause between some notes.

² Capable of playing a chromatic run only at slow speed, with pauses, or in part of its range.

(Please feel free to edit this answer to add instruments or details.)

There are some compositions that require the Orchestra to use Natural Horns or early versions of the instrument. I suspect that most modern orchestras will have the modern horn players fill the parts, but you wouldn't be able to do a chromatic run on the original instruments. For example the bugle and or the hunting horn are sometimes used, and I believe Bach wrote parts for the Shepard's Horn in one piece.