Normal forms: Difference between revisions
Changed a wrong calculation (13 is correct which was written as -13) |
m →Normal forms for commas: adopt template. Tenney height -> Tenney norm |
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=== Minimal form === | === Minimal form === | ||
The ''minimal form'', or ''reduced form'' shows the simplest comma list sufficient to define the temperament, where the commas are rated by a complexity measure such as the [[Tenney | The ''minimal form'', or ''reduced form'' shows the simplest comma list sufficient to define the temperament, where the commas are rated by a complexity measure such as the [[Tenney norm]], in which case it is called the ''Tenney-minimal form''. It is obvious why this form is useful, but unfortunately, it is not easy to find since it is equivalent to the ''shortest basis problem'', an NP-hard problem. The [[LLL reduction]] algorithm gives a good approximation. Otherwise, it is typically solved heuristically by hand. | ||
{{Note| This is the form shown in the "comma lists" of each temperament on this wiki. }} | |||
=== Antitransposed defactored Hermite form === | === Antitransposed defactored Hermite form === | ||