There is NOTHING new under the sun,simply revisions & polishing of the same old tech..

Once there was. What happens ?

To answer the OP's question,  if you discount synthesizers and other electronic devices, I would have to say it was the saxophone, invented by the Belgian instrument maker Adolphe Sax in the early 1840s and was patented on 28 June 1846. A very serious instrument.  

The hi-hat (1930) changed drumming forever. 

The Moog synthesizer?

Pedal steel guitar, synths, electric piano, clavinet and Hammond/Leslie organ.

How about: "Generally, the invention of truly novel instruments has slowed down since the 20th century. However, there are still interesting developments:

Recent inventions:

• The steelpan: This unique percussion instrument, born in Trinidad and Tobago in the early 20th century, is considered the only widely used acoustic instrument invented in that timeframe.
• Electronic instruments: The rise of electronic music in the 20th and 21st centuries has led to a constant stream of new electronic instruments, like the synthesizer, the sampler, and various digital controllers. These are constantly evolving and pushing the boundaries of sound creation.
• Experimental instruments: Many composers and musicians are constantly experimenting with new ways to create sound, pushing the boundaries of what constitutes a "musical instrument." These can be unique combinations of existing instruments, modified versions, or entirely new designs.

Factors to consider:

• Adoption and widespread use: While new instruments are constantly being invented, not all gain widespread adoption and become "serious" instruments in the traditional sense.
• Evolution of existing instruments: Many "new" instruments are often variations or adaptations of existing ones, making it harder to pinpoint a specific invention date."

Here are a few.

Jimi Hendrix kinda did. a few others helped too. but Jimi did the heavy lifting.

I’d say the most exciting thing on the music horizon is AI. Who hasn’t wished for an app that could build a song around a riff or a few bars hummed from your mouth?

I have a collection of fragments that have magically appeared in my head over the years. I’d say, at least enough for an album if I had the skills to build songs around them. They’re just sitting there on my digital recorder waiting for the AI app.

The fact they appear once-or-twice a year is why I never considered trying to "monetize" them. I’m sure Paul Simon, Peter Gabriel, etc. get these inspirations weekly at least.

Here's something new:

Any instruments new or old, and there is an "uncountable "numbers of them , often not well known define music perception, because each one had his own "timbre"...

And the last discovery in acoustics demonstrated that this is  fundamental because "timbre" of instruments define  the way we will hear and understand music.

https://www.pnas.org/doi/full/10.1073/pnas.2308859121

https://phys.org/news/2024-02-pythagoras-wrong-universal-musical-harmonies.html

Now this very interesting documentary will illustrate what i want to say better than i could :

Çifteli: This microtonal instrument changed the way I think about music

To answer the OP questions there exist an incredible number of musical instruments all along mankind history...

This does not end....

"timbre" and "rythm" had no date no age and no programmed lifespan, they are meanings...

This Sumerian instrument sound anything save primitive...

Here two instruments separated by millenia played together :

As, I think, Nietzsche said - Without music life would be an error -.

It might still be an error but perhaps less so.

Dweller, this is an extremely cool machine, and it makes some music too !

Indeed, saxophone is a serious instrument.

AI coming..I don't know what to expect, makes me kind of nervous.

Composer Harry Patch was continually inventing new instruments throughout his life! 

Maybe/probably the harpejji:

@mikelavigne:::Hendrix did NOTHING NEW,he simply COPIED/Polished Link Wray's style!!!

Well... have you already seen/heard every instrument in this world? Why are you looking for new instruments? Go east, to the continent of Asia (especially) and you will find instruments (you’ve never heard of) that will blow your mind for many lifetimes...

Well, what makes you think we are not familiar with Middle Eastern, Indian and others instruments ? None of those by themselves exactly blow my mind.

The overall most impressive instrument is still human voice followed by, I think, piano.

I like Moog synthesizers a lot, by the way.

Tom Waits has some pretty strange instruments in his music at times. Not sure if it’s anything new though. 
 

Basically, I had nothing material to contribute, just felt the need to interact! 
 

Hope you all have a good Sunday evening!

The wish to interact is very 'material', that's, substantial.

I will take a look at Tom Waits' arrangements.

The Therman and the Melotron come to mind as newer instruments.

The electric guitar of all things. Invented in 1932. It’s based on an acoustic guitar, but it’s a completely different instrument.

Electric guitar is so important, it can do many things, even sing almost like a violin.

Trey Gunn used a Warr Guitar.  It will play bass, guitar and can sound like a synthesizer.  Chapman Stick is another example.  Tony Levin is a master playing that.

Just remembered,

The Harmonium was another newer instrument.

How long ago was the kazoo invented?  

The cowbell is an idiophone hand percussion instrument used in various styles of music, such as Latin and rock. It is named after the similar bell used by herdsmen to keep track of the whereabouts of cows. The instrument initially and traditionally has been metallic; however, contemporarily, some variants are made of synthetic materials.

All kinds of unique and interesting Eurorack modules coming out weekly.

Every new pipe organ is unique. 

Since electric guitar is two-component instrument, the Kemper profiler made guitar amps obsolete about 10 years ago. Other digital devices, by Neural and Fractal have expanded that transition. In live music almost no one uses a "real" amp anymore. In blind tests no one can tell the difference, although as in audiophilia there are some who stubbornly hold on to the belief they can despite their own failure in blind tests, but they will age out because almost all younger players have gone digital. I now play strictly through software and have sold my "real" amps.

If AI can be considered an instrument it is the newest, although it mimicks current instruments. But it will eventually replace musicians. Especially those who play instruments that can't shift pitch easily.

AI will replace musicians only if it also replaces us. In all other scenarios it will not.

However, this real computer revolution is coming, what we have now is child toys, the very beginning. I don't want to even think about it.

It's already happening. There are AI music generators like Soundraw, Loudly and Suno. All AI requires is a frequency and timbre generator. Timbre can be sampled from any existing sound. Composition will take a little longer. At first it will all sound similar, much like today's pop music. Being creative and composing different-sounding songs and genres will be more of a challenge because AI only uses existing data.

The Incredible String Band used anything they found lying around!

More on the AI front. I doubt if a new instrument will ever be invented. I've been going down the AI rabbit hole for a while, mostly for investment purposes but as a former software engineer I've gotten obsessed with the technology also, and I'm fully convinced music as a commercial endeavor for humans is dead. Apps like Udio and Suno are already capable of generating high-quality songs. Rick Beato, a former music professor, producer and guitarist with over 4 million YouTube subscribers says an AI-generated song will top the charts within 2-3 years and within 10 years 9 of the top 10 songs will be AI-generated. After what I've researched, I totally agree. So that leaves hobbyists to invent new instruments because there will be no money in it for businesses to do it. The only reason to play an instrument will be for a sense of accomplishment.

The more I learn about AI, the scarier and at the same time, amazing it becomes. Many "generative" jobs will disappear much quicker than people will imagine, like musicians, artists, writers and authors.