Composing for everyone

Real-time composition tool, to test several operations for voices using editor.

Composing for everyone

(Text is a short version of a corresponding TEDx talk, helt at TH-Brandenburg on the 6th of December 2019.)

We can cope in the world because we possess inner models of its manifold subject areas. Some of them, like orientation in space, we learn as toddlers. Others, like mathematics, we often learn with great difficulty at school.

Why not use the knowledge and skills that are already there instead of laboriously learning something new? - It is precisely in using existing concepts that the approach presented here is for a compositional technique that is easy to learn.

Arithmetic in particular, i.e. the handling of arithmetic operations such as plus, minus, multiply and division by, forms the essential basis of this composition technique.

These operations are applied to the natural numbers.

These are understood here as a temporal sequence.

But what does this sequence have in itself that it could somehow provide a suitable basis for a musical composition?

Those are the divisors of each individual number in the sequence of natural numbers and the way in which these divisors rhythmically repeat themselves over the continuous sequence members.

Here you can see for the first prime factors 2,3,5 and 7 how often they occur in every single number in sequence.

Preferably such small prime numbers have a meaning for our understanding of rhythms and harmonies in music. Therefore only these first four are used here for the development of a composition method, but no larger prime numbers.

A first step on the way to the composition process now consists in realizing an adequate sonic realization of the natural numbers. For this, not the entire number, which is currently the element of the sequence, is taken, but only its parts of 2s, 3s, 5s and 7s. And also these parts are not used directly, but they are taken as divisors of another constant number, which I call the base number. Finally, the result of this division is interpreted as frequency and translated musically. The base number in the numerator consists only of the prime factors 2,3,5 and 7 in different but once fixed frequency.

Only if this division is possible without remainder and the result lies in the frequency range of the used musical instrument, also a tone sounds.

The actual composition process is comparable to the sound generation of synthesizers: Here, several filters are applied one after the other to a fundamental oscillation in order to obtain new sound variants.

In the composition process, the role of the fundamental takes on the sequence of the natural numbers. Arithmetic and related operations serve as filters.

An addition, for example, ensures that a sound event is brought forward in time.

An addition of 3 turns 0,1,2,3,4,5 into 3,4,5,6,7,8. If I enter +3 for one voice and +6 for the other into the editor above, this results in a kind of two-part canon of imitation.

In another experiment I perform a division by 2. Compared to the unchanged voice, the new voice is two times slower. This corresponds to the musical form of an augmentation canon. Another central operation does not come from arithmetic, but plays a central role in the compositional process, because it forms the sound events more strongly than the former. We are talking about the Modulo or Rest-Division.

Three more operations complete the sequence of available operations.

The inverting arrows indicate that here the assignment of the frequencies to the respective prime factors is inverted depending on the argument. Finally, with the rotating arrow, a cyclic place exchange of the same assignment is carried out.

The following applies:

The first operation entered is applied to the sequence of natural numbers,

the following on the result of the preceding and so on.

The result of each operation is converted into sounds as a divisor of a base number, as described above, even if other operations follow.