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
- 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
- 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,
- 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.
- 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
- the occurrence of the input structure in the interval-structure
of a tone row in normal form,
- but also in its retrograde,
- or in its inversion,
- or in its cyclic shifts. E.g. the interval-structure
11,3,1,1
is found in a tone row with interval structure
1,1,2,7,9,7,2,2,11,4,11,3
even though the four intervals occur at the end and the beginning
of this sequence.
Database on tone rows and tropes
harald.fripertinger "at" uni-graz.at
January 2, 2019