- a problem or a question that motivates the experiment,
- a program whose behaviour can help to better understand or even solve the
problem or to answer the question,
- musical data that are used as input data for the program.
While the original motivation – to find out something about the problem – may be a
special task from a larger music-theoretical context, the experiment itself splits into
subtasks that are not directly connected with that context. If a suitable program and/or
corresponding data are not available to the experimenter, he (or she) has to prepare the
experiment first by writing a program and/or encoding data. An individual
music-theorist may do so whenever an experiment comes to his mind. He will consider
these subtasks as necessary steps within the organisation of his work. He will reuse
programs or data whenever possible, but ideally he would not change his motivating
question just because of problems with a program or with lacking data. The
motivation for the experiment governs all subsequent intentions. The experiment is
sucessfull, if an answer or some new insight into the problem has been gained. From
this local perspective, there is no reason to invest time and energy into the
managment of further single experiments of the same kind, unless they are necessary
in the same concrete music-theoretical context in which the experimenter is
involved.
The growing practice of making computer-aided experiments, the existence of already
written programs and encoded data provides two other directions of possible scientific
activity:
- reuse of programs in similar experiments with varying data,
- reuse of data in other experiments with varying questions.
But the hermeneutic interest of an analyst has its own dynamics – depending on findings
in a specific situation. Thus one has typically a tension between intended experminents
and immediate practicability. The challenge of the RUBATO concept consists in its
support capability to flexible analytic experiments including the possibility of a division
of labour among several researchers. See also Jörg Garbers contribution to this volume
([3]). With regard to mathematical modelling this is related to another field that
attracts scientific interest, namely the ongoing process of systematization within
Mathematical Music Theory. The development of software integration techniques
includes two roles of mathematical models, namely data models and models for
music theoretical objects, which come in close interaction, but must not be
confused.
3. Metalanguage
Already in his first book Mazzola (cf. [5]) suggested a theoretical framework comprizing
all of his concrete music-theoretical models. In his most recent book (cf. [9])
this aspect plays a central role and led to an extended meta theory. Hence the
attempts of localizing specific mathematical models within the framework of a