Aberrismic theory: Difference between revisions
| Line 73: | Line 73: | ||
|} | |} | ||
Mathematically, this difference corresponds to choices of <math>\mathbb{Z}</math>-linear maps | Mathematically, this difference corresponds to choices of <math>\mathbb{Z}</math>-linear maps | ||
<math>\alpha : \mathbb{Z}^3\langle\mathbf{L}, \mathbf{m}, \mathbf{s}\rangle \to \mathrm{JI}( 2, p_1, ..., p_s )/\mathrm{ker}(T)</math> (here | <math>\alpha : \mathbb{Z}^3\langle\mathbf{L}, \mathbf{m}, \mathbf{s}\rangle \to \mathrm{JI}( 2, p_1, ..., p_s )/\mathrm{ker}(T)</math> (here <math>T</math> is a temperament map defined on the 2.p<sub>1</sub>....p<sub>s</sub> subgroup), determined by differing choices of <math>\alpha(\mathbf{L}), \alpha(\mathbf{m}), \alpha(\mathbf{s})</math> and subject to the constraint that <math>5\alpha(\mathbf{L}) + 2\alpha(\mathbf{m}) + 3\alpha(\mathbf{s}) = T(2).</math> | ||
== Musical open problems == | == Musical open problems == | ||