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There's very sketchy background information about tenor guitars on the World Wide Web, and as a result, this page is one of hago.org.uk's most visited. Welcome!
And here's where the confusion really breaks out - pick any other instrument from menu on the left and there's a common thread - 6 strings tuned in fourths with strings 2 and 3 a major third apart. Even the Guitarron or Guitarrone fits the pattern, though its body makes it, according to one site we visited, akin to holding a bath on your lap...
The tenor, however, breaks the mould. Or not. According to which school of thought you come from!
A number of classical guitarists call the Niibori prime guitar a "Tenor Guitar" on the grounds that it sits in pitch between the alto and the bass. And this does have a nice feeling of closure and symmetry about it.
But elsewhere, the name is taken for a 4-string guitar, with a scale length of 23" (585mm) - about the same as a Terz Guitar. But the guitar is tuned in fifths - C G D A - like the tenor banjo or the cello. Indeed it is generally accepted that the tenor guitar was created to allow a tenor banjo player to follow the fashion as it evolved from from Dixieland Jazz towards the more progressive Jazz that featured guitar. It allows a tenor banjo player to provide a guitar-based rhythm section with nothing to learn.
Elsewhere, a small minority of players close-tuned the instrument to D G B E to produce a deep instrument that could be played with the 4-note chord shapes found on the top 4 strings of the guitar or ukulele. But actually, though, the deep pitch warrants the wide-spaced chords that the banjo tuning permits, and the close-tuned tenor does not have the same full, clear sound.