User:Inthar/Style guide

This page documents my xen math notation and its differences from conventional xen notation or conventional math notation.

Variables

• Capital italicized Latin letters may denote scales written cumulatively.
  • S(n) = 100n cents
• Lowercase italicized Latin letters may denote (rotational equivalence classes of) scales written as steps, or abstract scale words. For example:
  • s(a, b, c) = abacaba
  • [math]\displaystyle{ \sum_{n=a}^{b-1}s(n) = S(b)-S(a) \ \text{if} \ s(n) := S(n+1)-S(n) }[/math]
• Bolded variables denote interval sizes (especially letters of scale words) and elements of lattices.
  • 5L 2s
• Sans serif function names are scale constructions, or more generally functions named more verbosely than in conventional math notation.
  • [math]\displaystyle{ \mathsf{MOS}(5,2;6)(\mathbf{L}, \mathbf{s}) = \mathbf{LLLsLLs} }[/math]
  • Blackdye is [math]\displaystyle{ \mathsf{Fl}(\mathrm{Pyth}[5]; 10/9) }[/math]

Algebraic structures

• [math]\displaystyle{ \mathrm{JI}\langle p_1, ..., p_r \rangle }[/math] is the p₁.[...].p_r subgroup, the subgroup of [math]\displaystyle{ (\mathbb{Q}_{\gt 0}, \cdot) }[/math] generated by rationals [math]\displaystyle{ p_1, ..., p_r. }[/math]
• If R is a commutative ring with 1, [math]\displaystyle{ R^r\langle a_1, ..., a_r\rangle }[/math] is the rank-r free R-module generated by basis elements [math]\displaystyle{ a_1, ..., a_r. }[/math] Ordered tuples in such modules are assumed to be in the given basis. Example: [math]\displaystyle{ (0,1,3) \in \mathbb{Z}^3\langle \mathbf{L}, \mathbf{m}, \mathbf{s}\rangle }[/math]

Discrete sets

• For [math]\displaystyle{ k \in \mathbb{R} }[/math] and [math]\displaystyle{ n\in \mathbb{Z}_{\gt 0}, }[/math] [math]\displaystyle{ [n]_k }[/math] denotes [math]\displaystyle{ \{k, k+1, ..., k+n-1\}. }[/math] I may also use [math]\displaystyle{ [i:j] }[/math] for [math]\displaystyle{ [j-i]_i. }[/math]

Miscellaneous

• [math]\displaystyle{ \log }[/math] is base e.
• Temperament names are.capitalized.