1edo

1 equal division of the octave (1edo) is the tuning system that contains a single note and the octaves above and below that note.

Theory

One note repeated in octaves is an example of a trivial temperament, it is even a system that demonstrates trivial examples of telicity. That said, it is actually useful in some cases from a musical standpoint, particularly as a subset of larger EDOs.

The first piece of Musica ricercata by György Ligeti simulates 1edo by playing only one pitch class (A) throughout different octaves on the piano, though the piano is not itself tuned to 1edo. The last chord of the piece uses another pitch class (D), breaking the pattern.