Physical Modelling

AI can do many things that humans cannot. For example, it can process huge amounts of data. AI can also extract the smallest nuances in data. Finally, it is an objective description of e.g. sensations, which are otherwise very subjective in verbal description.

Fig. 1: Time series of saxophone, bass drum, cello and cymbal (from top to bottom) with corresponding phase plots.

Nevertheless, AI has limitations. One limitation is that AI simulates a brain. Like us, AI only knows what it has been taught. Thus, it always has a limited view. Also, so-called echo chambers arise. If an AI detects a pattern, then this is recognized as typical and suggested to a user again and again. This corresponds to a prejudice, so it is very human, but often not intentional.

Vid. 1: 2D Echo chamber. Simulation with Ray Tracing

Vid. 2: 3D Echo chamber. Simulation with Ray Tracing

An alternative to AI that avoids such problems is Physical Modeling. There, the individual physically existing parts of a system with their interactions are set up as a model of reality. This can be musicians in an ensemble interacting with their musical instruments, with the room in which they play music, and with their fellow musicians.

Fig. 2: Live performance by the Phantom Brothers at the Starcub, which could be visited in Hamburg’s St. Pauli district until 1969.
Fig. 3: Model of the Star Clubs
Fig. 4: Modelling with view of the stage

But these can also be individual parts of a musical instrument, so in the case of a guitar, for example, string, top, bottom tlate, air cavity, etc. This can be a brain, in which individual neurons interact with each other, resulting in the overall brain activity. This can also be a whole society, i.e. including economy, politics or international relations. Since Physical Modeling models real physics, it can also include ecology, animals, plants, water or climate.

Vid. 3: Physical modelling of the guitar as a “digital guitar workshop”.

This is also how the brain works, in which nerve impulses are exchanged between nerve cells, whereby a nerve cell only sends out a new impulse when it has been stimulated by other nerve cells, i.e. these have sent their impulses to the nerve cell. The brain is thus constantly synchronizing and de-synchronizing. In music, this corresponds to musical tension and relaxation. Electronic dance music (EDM), techno or dubstep often build up long arcs of tension, which then suddenly break off as the bass drum kicks in in a four-to-the-floor groove. In classical music, the cadence of chords I-IV-V-I has a tension progression. There are also longer tension progressions there like in EDM. Our brain synchronizes more and more, towards an expected tension peak, only to de-synchronize again.

Die EEG Messung zeigt, dass die gemessenen Hirnströme dem dynamischen Aufbau des Musikstückes folgt. Der spektrale Zentroid zeigt eine umgedrehte Proportionalität zur Amplituden- und EEG-Information.
Fig. 9: EEG measurements of brain synchronisation with the climactic structure of electronic dance music. The synchronisation (top) correlates with the amplitude information (2nd from top). Furthermore, fractal dimensions (3rd from top) and the spectral centroids (bottom) of the time series can be calculated.

At the top right of the image we see the synchronization of the brain measured by EEG in a person listening to an EDM piece. The curve corresponds to the voltage curve of the piece, which can be seen in the analyses of the piece as shown below. Here, the Amplitude corresponds to the Loudness, the Fractal Dimension corresponds to the Complexity, and the Spectral Centroid corresponds to the Brightness of the piece. On the left side we see the networks in the brain that synchronize during the piece. These are very complex and change frequently.

The Physical Culture Theory, which uses Physical Modeling as a method, models these interactions mathematically using an Impulse Pattern Formulation (IPF). This assumes energy pulses that travel back and forth between the actors of a system. Starting from a point of view within the system, an impulse is emitted, arrives at other actors, is complexly processed or attenuated by them, returns to the starting point and causes it again to emit a new impulse.

Fig. 5: Interaction of the individual guitar components
Vid. 4: Guitar fitted with magnets. Transient measurement by laser interferometry

This can be observed with a violin string. When the bow is torn from the string, an impulse is created which spreads along the string, is reflected at the ends and returns to the bow. There it tears-off the bow again and thus an impulse pattern is created, the violin tone.

Vid 5: Physical Model of the Oscillation of a String Excited with a Bow

This results in the most complicated patterns in the system, they are called bifurcations, bi-stable states or chaos. But a system can also ‘agree’ on a stable state.  The result is often a chaotic and hardly overseeable sequence of impulses.

Das Bifurkationsregime der logistischen Gleichung wird oft mit der Population von Hasen erklärt. Man geht hierbei davon aus, dass die Population ab einer bestimmten Wachstumsrate über die Zeit keinen stabilen Grenzwert mehr bildet, sondern zwischen mehreren Grenzwerten schwankt. Mit steigender Wachstumsrate nimmt hierbei die Anzahl der möglichen Grenzwerte immer weiter zu, die Hasenpopulation nimmt also über die Zeit verschieden stark zu oder ab. Schließlich gehen die Zustände ins Chaos über, einen Bereich, in dem die Hasenpopulation über die Zeit beliebig zu oder ab nimmt. Im musikalischen Kontext gibt es Parameter, wie den Anblasdruck bei Blasinstrumenten, die erhöht werden können und somit Verhaltensweisen zeigen, die ebenfalls mit der logistischen Gleichung erklärt werden können.
Fig. 6: Bifurcation regime of an impulse pattern formulation. Shown on the left, it can be seen that for small parameter values 1/alpha there is only one stable fixed point, which at 2.0 changes into two alternating accumulation points. At approx. 2.4, the state changes to chaos.
Fig. 7: Example of an Impulse Pattern Formulation (IPF)
Fig. 8: Another example of an IPF

Surprisingly, it can also lead to the fact that this chaotic system orders itself. Then it can also happen that a few different phenomena occur simultaneously or repetitively one after the other. Such states are called bifurcations, which occur frequently in music, for example in multiphonics in wind instruments or in a rough voice. However, the system can also ‘agree’ on a single stable state.  Then the system is called self-organized. Self-organization is also the explanation for life in general. Life sustains itself through just these mechanisms of self-organization. So for example also for NASA self-organization is the most important component of the definition of extraterrestrial life.

Musical instruments are also self-organizing systems that function by means of impulse patterns. The energy transmission of a guitar string to the soundboard is a short energy pulse, which is periodically repeated. The same is true for the piano.

Vid. 6: High-speed recording of a guitar string. The impulse running over the string when excited becomes visible
Vid. 7: Highspeed recording of hammer and string of a piano

In wind instruments, the mouthpiece sends a short pressure pulse into the tube, which travels down the tube, is reflected at the end, travels back to the mouthpiece, and generates a new pulse there. In musical instruments, the chaotic states are the transient processes, while the stable state is the tone. Music thus consists of a constant alternation of chaos and order.

Vid. 8: CFD simulation of vortex formation in the mouthpiece of a saxophone.