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III MODELS III.1 (W Mar 02) The role of models in music theory. &. 50‘000 years ago: music appears. 543 mio. years ago: cambrium explosion. monochord. Pythagoras. tetractys. Johann Wolfgang von Goethe (letter to Carl Friedrich Zelter):

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III.1 (W Mar 02) The role of models in music theory



50‘000 years ago: music appears

543 mio. years ago: cambrium explosion






Johann Wolfgang von Goethe (letter to Carl Friedrich Zelter):

Ich sprach mir’s aus: als wenn die ewige Harmonie sich mit sich selbst unterhielte, wie sich’s etwa in Gottes Busen, kurz vor der Weltschöpfung, möchte zugetragen haben, so bewegte sich’s auch in meinem Innern, und es war mir, als wenn ich weder Ohren, am wenigsten Augen und weiter keine übrigen Sinne besässe noch brauchte.

I said this to myself: „As if the eternal harmony would have a conversation with itself, like what could have happened in God‘s chest before the world‘s creation—in such a way my interior was also agitated, and I felt as if I would not have or need ears, and the least eyes or other senses.


op. 23.5



Arnold Schönberg


Peter Sloterdijk („Selbstversuch“):

Wir sagen nicht mehr, die Welt ist alles, was uns von Gott so eingerichtet ist, wie es ist — nehmen wir es hin; wir sagen auch nicht, die Welt ist ein Kosmos, ein Ordnungsjuwel — fügen wir uns an der richtigen Stelle ein. Statt dessen meinen wir, die Welt ist alles, was der Fall ist. Nein, auch das ist noch zu scholastisch ausgedrückt, denn in Wahrheit leben wir, als wollten wir uns zum Satz bekennen: Die Welt ist alles, womit wir bis zum Zerbrechen experimentieren.

Peter Sloterdijk („Experiment on Oneself“):

We do not say any longer „the world is all that has been arranged by God for us the way it is—accept it as is; we do not say either „the world is a cosmos, a jewel of order—let us fit in at the right place.“ Instead we contend that the world is all that is the case. No, this is too scholastically expressed, for in reality we live as if we would confess the sentence: „The world is all upon which we experiment to the disruption.“


Robert Jourdain („Music, Brain, and Ecstasy“):

May be the music currently needs less a new Beethoven than a new Newton who makes accessible to musical analysis the deepest musical relations.


Martin Heidegger:

Warum ist überhaupt Seiendes

und nicht vielmehr Nichts?

(Why is there being and not rather nothing?)

Stephen Hawking (easier):

Warum ist das Seiende so

und nicht anders?

(Why is being as it is and not completely different?)



anthropic principle






What is a model?

  • Do we need models?
  • What is the embodiment of music in a fictitious „physical“ (metaphysical?) realm (forces among musical objects)?
  • Do we have such eternal laws or do we need such, even only temporarily?
  • Revolution vs. and distruction: Anything goes?
  • Is creativity possible within such a lawful framework?
  • Is the creation of „antiworlds“ the point?
  • What do you want to communicate about these worlds?
  • What is the role of physical vs. symbolic (mental) reality?

A model is a principle for building musical formulas (yielding schemes for compositions)

  • it must be such that it has been understood as a double negation, i.e.,

1. it is embedded in a space of variants (negation) and

2. can be distinguished from them by its characteristic position (negation of negation, „anthropic principle“)