How our Scales were Created
As an amateur jazz pianist, I have been interested in scales for a long time:
- There are thousands of different scales in the world.
- All these scales have exactly one octave – why?
- What else do the different scales have in common?
- And why?
- How do they differ?
- Is there a logic behind them?
These questions have surprising answers that make perfect sense. You can find a detailed treatise on the origin of our scales on this overview page on scales. It is surprising that this very simple, coherent explanation, which is compatible with the findings of physics, is not taught at music academies.
- The simple mathematics can be plausibly derived from physics! How exactly?
- Our subjective perceptions of consonance and dissonance, major and minor, and much more can be derived from simple mathematical and physical reasoning. How exactly does this work?
The amazing thing is: there are very clear and simple answers to these questions.
More about the Origins of our Scales
On this website, you will find a blog series on the origin of our scales.
On YouTube I explain this in a short film
-> Quintenexperiment (in German)
On the new browser programme LDC (Logo-Dynamic Cards) you will find a systematic compilation of the theory of the
-> scales on logodynamic cards (in German)
A summary of the illustrations for resonance-based scale theory can be found in a
-> summarising slide presentation (in German)
Three Worlds
I arrived at the topic of the origin of scales via Roger Penrose’s Three Worlds Theory, as an example of the application of his three worlds:
- The platonic world contains objects that are non-local and „timeless“.
- The physical world contains objects which can be examined from outside.
- The mental world is how we experience things in our head.
During my research, the scales proved to be a surprisingly illuminating example of the interplay between the three worlds.
–> Penrose’s Three World Theory
Resonance
The second surprise for me was the very decisive role – not of the overtones according to the usual literature – but of the resonance between the frequencies. The resonance can be
- easily explained physically (physical world)
- represented mathematically as a fraction and used as a fraction for further considerations (mathematical world)
- and explains the subjective experience of the intervals within the scales (mental world).
Another surprise was the discovery that the phenomenon of resonance links music and quantum physics. The connection is simple and obvious.
Resonance phenomena are everywhere.
–> The role of resonance (in German)