I think trombone might be a good candidate for this.
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Kazoo?
Any instrument where the pitch is not quantized into steps by design.
Guitars do this with frets, though there are of course fretless guitars but the problem is the quantization of pitch/fretted strength length that frets provides allows complex chords to be played in tune. This is functionally impossible to do on a fretless stringed instrument and is why violin type instruments mostly play single notes or two paired notes.
A classic church organ is the bridge between the world of quantized pitch instruments and instruments where pitch is constructed as part of each note. Each pipe produces a sine wave at a determined pitch.
Yes
It's true for any string instrument without frets or wind instrument without valves.
Of course, even with keys on the trumpet, you need to sound the correct harmonic interval using breath. Otherwise how could you get so many notes from three buttons!
I'm not sure what your question is about exactly. A slide whistle is the simplest version, I suppose?
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Stringed instruments with a fingerboard require the player to develop the skill we call "intonation", unless the fingerboard has frets.
Brass instruments require the player to develop intonation via their embouchure. They literally buzz the notes with their lips.
Reed and woodwind instruments require embouchure but the embouchure stays consistent across notes (although some changes can bend, overblow, or change octaves). That said, the player can change the pitch a little with their voicing, but the real note changes are discrete valves (like keys on a piano).
Modular synthesisers
Often you're trying to wrangle an analogue voltage into something musical
While it's not to the same degree as a string instrument, a lot of brass instruments require the player to create the pitch. They might have 3 keys with which to play all their notes, so the sounds aren't predetermined, they need to be pitched by the player.
And to an even lesser degree all instruments require the player to pitch them properly, because even with keys and buttons, they still need to be fine tuned while they are played. Many woodwinds get sharp as the scale rises, so the player needs to know to pitch down a little, or certain notes might always play flat, so the player needs to pitch up.
All brass require this, as the base pitch is created by the embouchure, and the player centers the pitch this way.
The keys just give them a greater range of pitches as (I believe) an integral of the pitch they're currently playing.
Voice is not exactly an instrument, but I'd say it qualifies too.
Guitar if played with a slide.