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The overtone series is not a musical scale

We find a huge variety of musical scales around the globe. The search for a common ground for the different scales has led us to the overtones as a constitutive factor. While the overtones certainly play a constitutive role in all scales, they do not represent a scale themselves. The series of the overtones itself is not a musical scale - even if some musicians and scholars believe so. The serie of overtones When a physical object (e.g. a chord) vibrates, there is a certain frequency, with whitch the object vibrates with preference. This is its ground frequency. But

By Hans Rudolf Straub|2026-01-06T10:18:18+00:001. March 2021|Categories: music, Music scales|Tags: musical scales, Three worlds|Comments Off

Real Constraints for Musical Scales

This is a post about the theory of the three worlds and continues the post about the perception of the octave. Does the coincidence of the three worlds only work for the octave? The octave demonstrates how mathematics (Platonic world) enters the physical world, and how this convergence of mathematics (integral numbers) and physics (vibrating matters) gives rise to a very special phenomenon, namely resonance. This resonance, in turn, is perceived by us human subjectively (Penrose: mental world) in quite a special way: We subjectively recognise two tones at an octave’s distance from each other as identical tones. Each of us – regardless

By Hans Rudolf Straub|2025-11-15T13:15:00+00:009. February 2021|Categories: music|Tags: musical scales, Three worlds|0 Comments

The Perception of the Octave in the Mental World

This is a post about the theory of the three worlds and continues the post about the resonance of the octave. The subjective side The mathematical world (Pythagoras) with its simple ratios and the physical world with its resonance phenomena provide us with an understanding of the octave but still fail to explain why this interval is the basis of all musical scales in all cultures. To understand this, we will also have to look at the mental world, i.e. the world of our subjective perception. This world is accessible to everyone, but it will always remain your own and subjective perception. I can’t read

By Hans Rudolf Straub|2025-11-15T13:15:24+00:009. February 2021|Categories: Information, music, Theory of the Three Worlds, Music scales|Tags: musical scales, Three worlds|0 Comments

Resonance and Octave

This is a post about the theory of the three worlds and continues the post about the octave. We generate a resonance If you regard resonance as an abstract phenomenon – or as a musical phenomenon that you have not yet experienced – I recommend that you should conduct the following simple experiment: look for a piano (not a digital one) and for a tone on that piano that you can sing well. Press the key of this note and sing it. Of course, this already requires the resonance in your inner ear, otherwise you would not hit the tone. Then press the

By Hans Rudolf Straub|2025-11-15T13:16:05+00:006. January 2021|Categories: Information, music, Theory of the Three Worlds, Resonance, Music scales|0 Comments

The Octave

A remarkable common feature All the musical scales known to me encompass an octave. Even scales which tones unusual to us Europeans – Arabic, Indian, Japanese and African ones – encompass precisely an octave, i.e. the deepest and highest tones have a distance of precisely an octave, whatever scale this may be. I find this extremely remarkable. This is as if all the world’s languages, which after all have very different words, used the same word for a certain concept, had always done so, and done so independently of each other. What is the reason for this? The theory of

By Hans Rudolf Straub|2025-11-15T13:16:49+00:0010. December 2020|Categories: Information, music, Theory of the Three Worlds, Music scales|0 Comments

Musical Scales in the Theory of the Three Worlds

Scales are mathematical patterns When you hear a melody, it is based on a musical scale. The scale consist of the small number of tones which are allowed and may occur in the melody. In a linear sequence, these tones constitute the musical scale. Most melodies that can be heard in our cultural area can be traced back to one single scale, the Ionian or major scale, which is made up of seven notes in very specific scale steps. Thousands of scales However, there are thousands of different scales. Presumably you are familiar with the minor as well as with

By Hans Rudolf Straub|2025-11-15T13:17:43+00:0020. November 2020|Categories: Information, music, Theory of the Three Worlds, Music scales|0 Comments

The Physical World

The world of the natural sciences The physical world is what is explored by the natural sciences and by physics in particular. The successes of the natural science programme are obvious, both with regard to its insights into how the world works, i.e. theory, and with regard to the technologies this enables, i.e. practice. The natural sciences have changed our world fundamentally ever since Galileo Galilei. Objectivity The success became possible because from the Renaissance onwards, the thinkers and explorers in Europe did not solely refer to what had been handed down since ancient times, but conducted unprejudiced research and

By Hans Rudolf Straub|2025-11-15T13:18:25+00:0011. November 2020|Categories: music, Theory of the Three Worlds|0 Comments

The Platonic world

Why “Platonic”? Penrose calls one of the three worlds in the theory of three worlds as Platonic. Why? Plato The rich Athenian citizen Plato was a follower of the philosopher Socrates. He set up a school of philosophy in the 4th century B.C., which was fundamental for European philosophy and has crucially shaped philosophical discussions until the present day. If Roger Penrose thus calls one of the three worlds “Platonic”, he refers to Plato and specifically to one particular question and the discourse about it, which is still of great significance today. This question is, “Are ideas real?” Plato’s realism of ideas Subsequent

By Hans Rudolf Straub|2025-11-15T13:18:51+00:0028. October 2020|Categories: Information, music, Theory of the Three Worlds|Tags: mathematics, Nonlocality, Platonic world, problem of universals, Timelessness|2 Comments

The theory of the three worlds

The theory of the three worlds, according to Roger Penrose connects different fields of science and philosophy. The three worlds are: Die 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. Music in the three worlds Musical scales are part of all three worlds

By Hans Rudolf Straub|2025-11-15T13:19:40+00:0029. September 2020|Categories: Logic, music, Theory of the Three Worlds|0 Comments

The theory of the three worlds (Penrose)

The theory of the three worlds There are practical questions which concern our specific lives, and there are theoretical questions which seemingly don’t. However, there are also theoretical considerations which definitely concern our practical everyday lives. One of these is the three worlds theory, which deals with questions as to which worlds we specifically live in. On what foundation is our everyday existence based? The theory of the three worlds points to the fact that we simultaneously live in three completely different worlds. Practically, this does not constitute a problem for us; theoretically, however, the question arises as to how

By Hans Rudolf Straub|2025-09-23T12:44:32+00:0028. September 2020|Categories: Logic, Theory of the Three Worlds|1 Comment