Sane and insane temperaments: Difference between revisions
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Note that the GCD criterion above does not change no matter which mapping matrix (and hence, set of generators) you choose for the temperament. | Note that the GCD criterion above does not change no matter which mapping matrix (and hence, set of generators) you choose for the temperament. | ||
It turns out that an equivalent definition is that a temperament is insane iff its kernel is [[ | It turns out that an equivalent definition is that a temperament is insane iff its kernel is [[Mathematical theory of saturation|unsaturated]], when expressed as a subgroup of the full-limit. This is the same problem that would typically lead to torsion if tempered out of the full-limit. Torsion can be gotten rid of by restriction the temperament to a smaller subgroup, but if you do so, you are instead guaranteed to get an insane temperament. | ||
Some further examples: | Some further examples: | ||