Most of the posts so far on this topic have missed the point somewhat.
Gilles Chouinard was quite right saying, "Mixtures are not made to be
played solo all by themselves.  They are made to complement the palette
of other stops so they are used in conjunction with these."

However, although all Mixtures are multiple ranks of pipes (at least
more than one) there are basic differences between a true Mixture on
a classical organ and on a mechanical organ.

A classical organ Mixture comprises ranks of octave and double octave
ranks together with Quint (fifths) and/or tierce (thirds) ranks.  As
explained by Gilles, the composition of, for example, a 4-rank Mixture
with ranks of 15-19-22-26 (15 being two octaves above unison) might
break back to 12-15-19-22 at some point up the keyboard, and again to
8-12-15-19 further up.

Occasionally not all ranks break back at the same place, making
the composition of the set very complicated.  The reason for the
break-backs is to provide tonal brilliance in the bass and depth in
the treble, apart from the impracticability of making microscopically
small pipes.

It is usual that all ranks are made up of diapason-toned pipes.
There is no such thing as a "Mixture pipe", except that they are part
of a Mixture "stop", all brought in to play together by drawing one
stop.  Designing an effective Mixture is very complex with pitch and
scale considerations.

The main difference with a Mixture on a mechanical organ is that
(as far as I know) no Mixture ranks break back, but run consecutively
from the lowest note to the highest.  The pipes within a Mixture may
be any type, including reeds, e.g., "Clarinet Mixture" on a Gavioli
or Marenghi could include a sub-octave cello rank, two or more unison
violin ranks, stopped and open flute ranks, and a clarinet reed and
perhaps a trumpet, all coming on with one register.  Mixtures on German
organs such as Bruder and Ruth are mainly open flute pipes of very
high pitch with or without Quint ranks, but the ranks never break back
in pitch.

John Page, UK