It is difficult to say who actually invented the first functional chromatic harmonica.
John Broecker quotes (reply #5):
“The first known patent for a slide chromatic harmonica
was a British patent #2716 from 1862, patent owner’s name unknown.
The reed placement system used is unknown. “
It is difficult to verify that quote. I could only find the following additional info on a German site: “1862 – Eine chromatische Mundharmonika wird in Großbritannien patentiert. ”
 Persönliche Mitteilung von Otto Becker unter Berufung auf das Deutsche Harmonika-Museum, Trossingen und auf Pat Missin.
Pat Missin wrote in a response when asking him about patent# 2716 :
“The patent does not cover a slide chromatic, it doesn’t even cover a harmonica. It is for a chromatic pitch pipe, granted to one William Chesterton Burden. “
The patent# DE19331A from 1882 by Adolf Glass Junior shows a harmonica that certainly could have been played chromatically (as much as the previously mentioned Johan Richter harmonica could have been). It does not explicitly mention that, though.
Another patent of another candidate comes form the same year, 1892. It was Johann Wilhelm Schunk (not clear if he was related to Johann Erdman Schunk, the founder of the Schunk harmonica factory ) who patented (patent# DE19222) his idea of a harmonica with a slider that allows switching between the top and the lower reed plates. He writes “this will allow to switch between different scales”. He does not exclusively mention it would allow to play chromatically.
The museum also features a 1884 patent# DE25587A granted to Seydel. An
article about that patent was written by the “Freie Presse” newspaper. It states the patent was issued to Seydel and that it is the first known chromatic harmonica patent. The patent does not exclusively mention “playing chromatically”. It just describes another way to switch between reed plates. Therefore, in my opinion this article was not really accurate.
Coming back to the Carl Essbach harmonica, I have not seen anybody operate or play that harmonica. Based on the description of the patent, the assumption is that the wooden mouthpiece can be moved vertically by pushing down the two buttons (located on the top left and right corners). That way, the player has either access to the upper, or when pushing down the two buttons, the lower reed plate and is therefore able to play different scales.
Update: I recently visited the Klingenthal-Zwota harmonica museum and was able to operate the Essbach harmonica. When pushing down the two buttons the inner body moves down and when releasing up again (via two bendable metal plates residing inside the comb at the right and left side -> see patent# DE25587A) Therefore, it is not the mouth piece that moves but rather the harmonica comb. This is a very interesting mechanism. I wish I would have had more time to explore that.
Essbach harmonica: how the mechanism works
Hohner prototype of movable harmonica body, courtesy Joel Andersson
The first time a chromatically tuned harmonica was mentioned in a patent (at least as far as I could find) was in 1896. The patent# DE95610A issued to Christian Weiss explicitly mentioned the name “chromatic harmonica”. The harmonica described is not a slide chromatic. It has only two reed plates. The blow reeds can be used to play a c-major scale. The draw reeds will fill in the missing notes in order to play fully chromatic.
At that time, Hohner did not seem to have filed for any patent regarding some sort of chromatic harmonica; however, I could find these drawings of two prototypes in the book “100 years of Hohner”. The description states: these two harmonicas can be seen as predecessors of today’s Chromonica.
The second harmonica in the above drawing actually exists. I saw it in a video produced by the Norwegian television (starts at about 6:12). The famous harmonica soloist Tommy Reilly is trying it out. He plays a couple of notes and also turns the button to play different notes. Difficult to say if the tuning is actually chromatic.
Harmonica prototype from the old Hohner museum (see also
image above) with a round knob to change between different scales
Update: I found this link to a video directed by Chris Morphet and made available by Roger Trobridge “Visit to Hohner Factory in 1972”. At about 4:40 Manfred Haug (one of Hohner’s former directors) mentions that the above harmonica is a Hohner chromatic harmonica prototype from 1910.
While recently visiting the Museum of music and winter sports in Klingenthal, I discovered these Seydel and Bohm chromatic harmonicas.
Update: this year I was able to go back to the museum to uncover at least some parts of the mystery regarding the Seydel and Bohm chromatic harmonicas. I especially want to thank the museum to give me the opportunity to inspect the below harmonicas and provide additional information. Both harmonicas must have been manufactured before 1920, because that year they were donated to the “Music instrument making and craft school Klingenthal” (Gewerbeschule Klingenthal).
As previously thought, the hinge on the right side moves the harmonica body down and up similar to the above video by Joel Andersson showing a Hohner chromatic prototype.
Bohm “Chromatic” harmonica from the music and winter sports museum, the manufacturing date must have been before 1920
After some closer inspection, it was clear that some parts are missing. My assumption is that in order to play chromatically either the top or bottom channels must have been covered somehow. The principle could be similar to the Adolf Glass Junior harmonica from 1882, patent# DE19331A (see picture above).
Another thought: the “Meine Mandoline” harmonica, manufactured by Bohm around the same time could have been used as a reference. Even though in that case the purpose of the slider was to create some sort of vibrato effect, a similar slider could have been used to cover some of the channels in order to play chromatic.
Bohm “Meine Mandoline” from around 1920, from my collection