How to input a tone row in normal form

Consider a group G acting on the set of all tone rows. Then the normal form of a tone row f is the lexicographic smallest element in the orbit G(f) of f. For more details see Section 3.2 and Remark 3.2 of [1].

In order to input the normal form, first the alphabet must be chosen. According to this choice

  1. either a complete normal form of a tone row must be input in numeric version (where each symbol of the chosen alphabet must appear exactly once). E.g. the chromatic scale using numbers from 1 to 12 is input as
    1,2,3,4,5,6,7,8,9,10,11,12

    If a tone row is input which is not the normal form of its orbit it will not be found in the database. E.g. the sequence
    2,3,4,5,6,7,8,9,10,11,12,1
    also describes the chromatic scale, but is not contained in the database.

    In order to obtain the normal form of an arbitrary tone row the link D12 × D12-normal form of a tone row or Normal forms of a tone row in the 12-scale can be used.

  2. or a part (a subsequence) of the normal form of a tone row must be input, e.g.
    10,11 or 1,3,4 (for the alphabet {1,…,12}) or
    9,10 or 0,2,3 (for the alphabet {0,…,11}) or
    9A or 023 (for the alphabet {0,…,9,A,B}),
  3. or a blank-separated list of parts of tone rows must be input, e.g.
    4,5 2,7 (for the alphabet {1,…,12}) or
    3,4 1,6 (for the alphabet {0,…,11}) or
    34 16 (for the alphabet {0,…,9,A,B}).
    Using AND demands that all the different parts must simultaneously occur in one tone row, whereas using OR at least one of these parts must occur in one tone row.
  4. It is also possible to insert a dot . for exactly one single value, dot plus .+ for at least one single value, or dot star .* for no or anay number of values.

    In order to look for a tone row where there is a gap of exactly two pitch classes between 4 and 6 type
    4,.,.,6 (for the alphabet {1,…,12}) or
    3,.,.,5 (for the alphabet {0,…,11}) or
    3..5 (for the alphabet {0,…,9,A,B}).
    In order to look for a tone row where there is a gap of at least one pitch class between 10 and 12 type
    10,.+,12 (for the alphabet {1,…,12}) or
    9,.+,11 (for the alphabet {0,…,11}) or
    9.+B (for the alphabet {0,…,9,A,B}).

    Take care: Searching in the alphabet {1,…,12} for 4,..,6 seaches for tone rows where there is a 2-digit number between 4 and 6, thus for 4,10,6, or 4,11,6 or 4,12,6, whereas in the alphabet {0,…,11} it searches for tone rows of the form 4,10,6, or 4,11,6. Finally in the alphabet {0,…,9,A,B} searching for 4..6 finds those tone rows where there are two pitchclasses between 4 and 6.

The software will find a tone row if and only if the input pattern occurs in a normal form of a tone row.
Database on tone rows and tropes
harald.fripertinger "at" uni-graz.at
January 2, 2019