Database on tone rows and tropes -- Operation on a tone row

Operation on a tone row

An arbitrary element of 𝔄₁₂ is of the form (TⁱI^jQ^k ,S^m Rⁿ F^r) o P^s with i,m∈ {0,1,…,11}, j,k,n,r,s∈ {0,1}. In order to compute

(TⁱI^jQ^k ,S^m Rⁿ F^r) o P^s * f= Tⁱ o I^j o Q^k o P^s o f o F^r o Rⁿ o S^-m^._.

of a tone row, input f in numeric form and the values of the exponents i,j,k,m,n,r,s. According to the definition of this group action the sequence of S^m Rⁿ F^r acting on the domain of f must be reversed and the exponent m must be replaced by -m. Since r,n∈ {0,1} the minus can be omitted in front of r or n.

Database on tone rows and tropes
harald.fripertinger "at" uni-graz.at
January 2, 2019