Many modern books and web sites that examine Tolkien’s Elvish languages take care to distinguish between Tolkien’s languages as he described them (Quenya and Sindarin) from fan-based reconstructions and extensions of his languages (Neo-Quenya and Neo-Sindarin). The distinction between Tolkien’s Elvish versus fan-based Neo-Elvish can confuse new students of the languages. People who approach the languages for the first time usually want to use them just as Tolkien did, and avoid fan-based reconstructions. However, these fan-based Neo-Elvish reconstructions can be both good and necessary for the introduction of the language to new students.
The simple fact of the matter is that Tolkien never “finished” his languages. He did not create a formal Elvish dictionary for either Quenya or Sindarin, and his grammatical discussions of the languages exist only in fragments. He invented Elvish for his own use and amusement. He constantly experimented with new forms and structures, and only formalized them to the extent that he needed to in order to incorporate them as names, poems and phrases in his published stories. He was both surprised and pleased at the degree of interest others took in his invented languages, but never had the time (and probably not even the inclination) to formalize them to a degree that would allow others to use them.
Therefore, in order to use Tolkien’s languages for the purposes of new writing and communication, some degree of reconstruction is required. This kind of linguistic reconstruction is nothing new or special, and even occurs for some real-world languages. Many ancient human languages, such as Ancient Egyptian, are known only in incomplete and fragmentary forms. The tools of modern linguistics are used to study such lost languages and extrapolate patterns from limited data to reconstruct various aspects of those languages.
The best approaches to Neo-Elvish treat Tolkien’s languages as if they were such “lost tongues”, and use similar linguistic tools to reconstruct them from the fragmentary evidence. For example, we know of the existence of the Sindarin verb echad- “to make”, but we don’t know its imperative form (the form used for commands). We do, however, know that pedo is the imperative of the verb ped- “to speak” from the phrase pedo mellon “speak friend”, and that noro is the imperative of the verb nor- “to run” from the phrase noro lim Asfaloth “run swift Asfaloth”. Thus, it makes sense to reconstruct echado “make [it]!” as the imperative of echad-. Strictly speaking, however, echado is Neo-Sindarin, since Tolkien never wrote down this imperative and we don’t know for certain whether he would have treated it as some kind of special case.
The imperative is a well-accepted aspect of Neo-Sindarin, since its formation is pretty straightforward and we have numerous examples of its use. For other aspects of Tolkien’s languages, however, the available information is more fragmentary and contradictory. Although we have a fair number of examples of the Sindarin past tense, there seem to be a large number of special cases and irregularities, so that Neo-Sindarin reconstructions of the past tense are more tenuous. To reconstruct the Sindarin past tense, we need a deep understanding of the phonological history of the Sindarin language, which itself is extremely complicated and not fully understood.
For these more difficult questions, our understanding of Tolkien’s languages can change over time. In much the same way that new information can occasionally be discovered about ancient human languages when archeologists unearth new texts, additional information about Tolkien’s languages is periodically published in various academic journals, which can further enhance our understanding of Neo-Elvish reconstructions. If you asked someone who was knowledgeable about Sindarin in the 1990s or early 2000s how to form its past tense, you would likely have gotten different answers than what we would give today, simply because more information about Sindarin past tense has been published over the intervening decades.
Another issue with Neo-Elvish comes from the use of the term within the history of Elvish fandom itself. A decade or two ago, “Neo-Elvish” was mostly used as a derogatory term for weak and improper reconstructions of Tolkien’s languages. The term was also used as a way to separate such reconstructions from the “real study” of Tolkien’s languages as a purely academic exercise. More recently, however, some parts of Elvish fandom have embraced Neo-Quenya and Neo-Sindarin as a useful terms to identify their own reconstructions and extrapolations of Tolkien’s linguistic material. Elvish educational courses that properly designate what is “Neo-Quenya” or “Neo-Sindarin” reconstruction tend to be of higher quality than those that don’t.
Both for teaching and learning Elvish, it is important to properly distinguish words and grammatical structures that come directly from Tolkien versus those that are extrapolations. Courses that fail to make these distinctions tend be either older with more dated material, or they are simply less exacting in how they treat Tolkien’s languages. Some people try to avoid these problems by using only “pure Elvish” as created exclusively by Tolkien himself. But even in this limited case, the mere act of juxtaposing such Tolkien-created words to form new sentences is enough of a creative act to leave the realm of “Quenya and Sindarin” and enter the realm of “Neo-Quenya and Neo-Sindarin”.
Part of the reason for this conflict is that the Elvish languages did not spring fully formed from Tolkien’s mind like Athena from the head of Zeus. Rather, they evolved over many decades as Tolkien explored various avenues and refined his ideas for how his languages worked. The Elvish languages that Tolkien imagined as a young man were quite different from those he used decades later when writing the Lord of the Rings. Even within the time period during and after the publication of the Lord of the Rings (1950s and 1960s), Tolkien kept changing his mind about how various elements of the Elvish languages worked. Even if you limited yourself to sources from the 1950s and 1960s, you would still be forced to make creative decisions about which elements of his languages you would use.
The depth of knowledge required to work through all this complexity can be daunting, especially for beginners. There are now thousands of pages of dense linguistic material describing Tolkien’s thoughts on his languages, and even more that remain unpublished. For this reason, some more knowledgeable fans of Tolkien’s languages have put together introductory courses as a gateway for beginners who want to access his languages for the first time. These introductory courses are forced to extrapolate and reconstruct elements of Tolkien’s language from the incomplete source material. The best of these courses acknowledge this fact, either by explaining their methodology or acknowledging in some way that they are Neo-Quenya or Neo-Sindarin extensions of what Tolkien wrote.
The terms “Neo-Quenya” and “Neo-Sindarin” have therefore become shorthand in Elvish fandom for those who acknowledge the complexity of Tolkien’s languages but still want to present them in a way that others could learn them in a reasonable amount of time. There is nothing inherently wrong with such reconstructions, and they are in fact necessary if you want to use Sindarin or Quenya as functional languages. Furthermore, this process of reconstruction is not yet complete, since Tolkien’s languages are still being studied, new information is still being unearthed, and new source material is being published on a regular basis. One of the beauties of Tolkien’s languages is that they are sufficiently rich and complex that such study is possible, and the tools of modern linguistics can be used to reason about the languages and extrapolate new information from them.
Therefore, if you encounter an author who makes it clear they are presenting reconstructed languages, either using terms like “Neo-Quenya” and “Neo-Sindarin” directly or by otherwise indicating they are extrapolating from Tolkien’s work, this is generally a good sign of the quality of the course material. On the other hand, if the authors of an Elvish language course claim that they are presenting “true Elvish” exactly as Tolkien wrote it, you should be suspicious of their approach, especially if they don’t explain the methods they used to arrive at the grammatical rules and vocabulary they describe.