Tolkien created many languages. Is there any list of all the languages he invented?
Ardalambion, a fansite dedicated to analyzing Tolkien's invented languages, has asked this very question; according to him the answer is somewhere between 2 and 20, depending on how permissive you are when defining a language (emphasis his):
If we consider the "historical" versions of the tongues that are relevant for the classical form of the Arda mythos, Tolkien developed 2 languages that are vaguely "usable" (in the sense that you can compose long texts by deliberately avoiding the gaps in our knowledge), named roughly 8-10 other languages that have a minimum of actual substance but are in no way usable, provided mere fragments of at least 4 other languages, and alluded to numerous other languages that are either entirely fictitious or have a known vocabulary of only one or a very few actual words.
The entire list given is:
Languages with real meat:
Some substance, but not usable languages:
- Ikorin, which may or may not be just an extension of Doriathrin
- Khuzdul. Although Tolkien only wrote a small number of words, he revealed in notes that he had planned it out somewhat more extensively
- Taliska reportedly has a grammar, but it is as yet unpublished
- Black Speech
Here, Ardalambion may or may not be counting Oromëan, Aulëan, and Melkian, the three known dialects of Valarin; assuming he does certainly makes the numbers more sensible.
- Various dialects of Orcish
- the language of Harad
This list evidently differs from the one discussed in the question; the discrepancy can be made up by incorporating "intermediate" forms of the Elvish languages, which Tolkien revised extensively on the way towards his "finished" Quenya and Sindarin, as well as some Mannish languages that never had a decent vocabulary or grammar, but just some rendered names. These include:
- Primitive Quendian
- Common Eldarin
- Goldogrin (which would become Noldorin)
- The language of Dale, which had a few names rendered in it
- The language of Rhovanion, which likewise had a few rendered names
And there are a few others that are mentioned, but exist only in name:
- Mithrim, which largely survived in Ilkorin
- The language of Haleth (which had a single word: drûg, their name for the Drúedain)
The list in the book may also be including some languages Tolkien invented as a boy, or which weren't connected to the legendarium:
Which language is the "fourteenth" by the measure of the writer of that excerpt will depend on precisely what definition is used, which is not remotely clear. I have contacted the Tolkien Literary Estate directly, and will update when/if I get a reply.