| Thought experiment operations in mathematics |
Thought experiment operations in the art of music |
| 1. Isolation of a constituent part of a geometric figure and its consideration as an independent one |
1. Isolation of the motive from a theme and its consideration as an independent entity in a special section of the form - development |
| 2. Quantitative transformation. Increase of a subject (to infinity) |
2. Increase of the theme’s polyphony (in a fugue), in reprises of sonata form by rhythmic changes |
| 3. Decrease to a point |
3. Decrease of the theme in fugues (acceleration of time) |
| 4. Introduction of new elements (additional constructions) |
4. Adding new elements in variations, creating a contrast between the main part and the side one (new); input of interludes with sequences in a fugue (the new element plays the role of a logical connection, transition to a new section of the form) |
| 5. Strengthening the basic properties of the subject |
5. Strengthening of the basic properties is achieved in the developmental sections of the form, for example, development. The contradiction (conflict) reaches its limit due to the transformation of the theme and its elements towards the intensification of its activity |
| 6. Transformation of an object towards infinity with a transition to a new mathematical concept |
6. Musical structures are organic in nature, in the development it is possible to reach a nodal point, the limit of emotional intensity, after which a logical transition to a new state follows |
| 7. Idealization of an object, abstraction |
7. An idealized subject (theme) is created by abstraction |
| 8. Connection with logical categories |
8. The musical literary text contains categories: discontinuity and continuity, stability and instability, changeability and immutability, quantity and quality, instantaneousness and duration, etc. |
| 9. Geometric figures are model images, covering the whole (integral structural formations) |
9. A piece of music is a model image that encompasses a holistic structural formation |
| 10. Geometric figure is a visual construct |
10. The musical theme in the musical text is a visual construct |
