The example music piece for violin and vibraphone "AOGdogma#3" from this article is below at #11.

The system "THE FLIPPIN' POMPOMS" described in the article can be found in #5.

Meanwhile, the principle of "THE FLIPPIN' POMPOMS" has been transferred to a web-based program that allows distant users to interact with each other:

Arithmetic Operation Grammar (AOG) was presented for the first time at the CMMR 2019, see:

AOG takes the natural numbers as starting point as a time sequence. There are no explicitly formulated harmonic or contrapuntal rules in AOG. Instead, one assumes that the organization of the divisors within the natural numbers satisfies rules that are similarly good. Other pieces of music are now created by changing this basic element through the application of arithmetic operations and additionally by using the modulo division and finally -- to obtain a tone pitch -- by performing a kind of selective division (symbol //) in which from a so-called base number those powers of 2,3,5 and 7 are removed which are contained in the value resulting from the preceding operations for a specific formula at a specific tick t. Thus, in AOG, "composing" then means defining formulas according to which the basic element id(N) is modified. Several formulas can be used to generate several voices.

S E S S I O N 3

elegie

Sonification of a drone flight IV

M O D U L O

MY WAY TO WORK

ComposingWithImages

Sonification of a drone flight (3rd version)

Sonification of a drone flight

THE FLIPPIN' POMPOMs

ComposingWithSpheres

kaleidophone for vibraphone

A Feedback machanism aims to optimize the AOG generation formulas so that they would reproduce past sound events, including those of the user.

S E S S I O N 1

S E S S I O N 2

S E S S I O N 3

S E S S I O N 4

S E S S I O N 5

S E S S I O N 6

S E S S I O N 7

The following audio example shows the result of representing the canon Brother Jacques with AOG formulas. Once the motif is heard in all four voices, the voices diverge again as t progresses. The formulas and the starting point t0 were found using an optimization algorithm. Four formulas with 16 operations each provide the desired result.

ComposingForEveryone -- Processing library -- see processing.org

M O D U L O

groove

taichi

SHIMMER

AOGdogma#3 is for violin and vibraphone. Thus, it could not be rendered exactly by the processing script in ComposingForEveryone. There was made a variant sending midi commands to a physical modeling software.

The idea behind this presentation is to show the user not only a system that reacts in real time but also the symbolic representation of the sound generating system. This can even be designed by the user: Users can design the formula structure and listen in real time to what it will produce in terms of sound. Afterwards, they can define places that may be varied by the optimizer. Only then does the performance take place (see example below).

Thus, a musician can determine the character of the resulting accompaniment and to what extent it is automatically adapted to the current music-making. The basic problem with "Arithmetic Operation Grammar" is that the formula writing is very powerful and it is very easy to create convincing compositions, but the connection between the resulting composition and the formulas is not so easy to understand or learn. (However, it is, after all, much easier to learn than the contents of a music course that leads one to become a composer, because typically the users are already familiar with the laws of arithmetic from school.) But probably the most intuitive user interface one can think of to tackle this problem is one in which the user himself makes music and the system adapts to the music-making. Here this is done without losing direct access to the formula structure.

In other words: ... First I roughly define a formula structure and listen to what "Chick" (the piano sound which is controlled by the algorithm) then plays. Then, next, I define which parameters in the formulas may be changed by an optimizer. Then the live performance starts, where every sound of the musician is timestamped. The optimizer then tries to adjust the formulas so that "Chick" the same HAD played in the past on the stored timestamps. Through this artifice emerges a permanent temporary coherence between the real and the virtual player. This means that the formulas deliver something suitable for the musician's playing at the current time.

The stage of development presented here still lacks a concept for the design of the piano's playing technique, but initially concentrates only on the musical structure. And those who become too exhausted by it over time can still switch over to the wonderful original duo for relaxation: