**Linear Temperaments**

`A rank two temperament is a `__regular temperament__` with two generators. If it is possible for one of the generators to be an octave, such a temperament
is called a linear temperament (in the strict sense.) However, rank two temperaments in general are often called
linear. The most common choice for generators is for one generator to be an octave, or some nth part of an octave
for some integer n; in this case this generator is called the period and the other the generator.`

`A rank two temperament may be uniquely defined in various ways; one is by means of
the ``wedgie``, another by way of the ``comma sequence``, and still another by means of the mapping,
or ``icon``, for a reduced set of generators.
Here we are calling a pair of generators reduced if one generator is the period, and the other is the unique generator
greater than one and less than the square root of the period (or less than half the period in logarithmic terms)
which together with the period gives a generator pair for the temperament. This last definition depends on the
exact tuning, and hence in theory may not be uniquely determined; in practice this seldom matters but for this
and other reasons when working with temperaments using computer programs the wedgie is preferable as a means of
defining the temperament. The icon, or tuning map, for the reduced generator pair, listing the period first and
the generator second, we may call the standard icon.`

`Here is a list of seven-limit linear temperaments.`

Listed below are some of the important families of linear temperaments.