How to input an interval-structure

Let f: {1,…,12}→ Z12 be a tone row, then its interval structure is the vector (f(2)-f(1),f(3)-f(2),…,f(12)-f(11),f(1)-f(12)). All intervals are encoded as elements of Z12*={1,2,…,11}. E.g., the interval from i to i+1, i ∈ Z12, is equal to 1 (one step up), whereas the interval from i to i-1 is equal to 11 (one step down is the same as 11 steps up).

In order to input the interval structure of a tone row

  1. either a comma-separated list of 11 intervals from the set {1,2,…,11} must be input, if the alphabets A1 or A2 are chosen, or a sequence (without commas) of 11 intervals from the set {1,2,…,9,A,B} if the alphabet A3 is considered. E.g.
    1,1,2,7,9,7,2,2,11,4,11,3 or 11279722B4B3
  2. or a part of the interval-structure of a tone row must be input, e.g.
    1,1,2,7 or 1127
    which is an interval-structure of length 4,
  3. or a blank-separated list of parts of an interval-structure must be input. E.g.
    1,2,7 7,2,2 9,7,2 or 127 722 972
    which consists in this case of three structures all of length three. Using AND demands that all the different parts must simultaneously occur in the interval structure of a tone row, whereas using OR at least one of these parts must occur in in the interval structure of a tone row.
  4. It is also possible to replace the occurrence of an arbitrary interval by a dot ., of arbitrary many intervals by .* which includes also the situation of no intervals, of at least one interval by .+, or of at most one interval by .?. E.g., in order to search for an interval structure where there is exactly one digit between two intervals 6 enter
    6,.,6 or 6.6.

Searching for an interval-structure finds


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