Standard music notation represents notes without regard to
how sharp or flat the different intervals are tuned, and the same notation
can be used for all the different tunings that have prevailed
at different times in western music, as well as for such esoteric
tunings as those in which the octave is divided into 17, 19, or 31
equal intervals. The rationale for the naming of notes emerges
if one takes a particular note as reference point and identifies
the notes that one reaches by going up or down from that note
by multiples of a fifth. One obtains a diatonic scale if one goes
down a fifth from the reference note and goes up from it by
five successive increments of a fifth, and transposes the seven
notes thus obtained by octaves into the span of a single octave: