music

How resonances explain our musical scales and chords

Have you ever wondered why the musical scales in all musical cultures, whether in the jungle, in the concert hall or in the football stadium, span precisely an octave? Or why children without any musical education the world over quite spontaneously find the major triad “beautiful”? The explanation lies in the resonances. No matter how different musical cultures are, they still have a common core. This consists of the resonances which emerge between the notes of the musical scales and chords. Two strings in resonance Mathematics and physics in music Classical music theory is aware of the fact

By Hans Rudolf Straub|2025-12-03T14:42:21+00:007. April 2025|Categories: music, Theory of the Three Worlds, Resonance, Music scales|0 Comments

What is Resonance?

Oscillations: the physical basis of resonance Resonance is always based on the natural oscillations of two physical objects and their mutual coupling Coupling of natural oscillations of physical objects Natural vibrations are standing waves whose frequency is determined by the properties of the physical medium (size, shape, material, etc.). Two such media can enter into resonance through their oscillations. The resonance is created by coupling the two oscillations so that the two physical media form a coupled unit in their oscillating behaviour. The coupling takes place through a physical exchange of energy, either directly or indirectly, e.g. through the air. The

By Hans Rudolf Straub|2025-12-03T14:47:57+00:0013. November 2024|Categories: music, Theory of the Three Worlds, Resonance, Music scales|0 Comments

The Semiotic Triangle

Words and their Objects When we speak, we use words to describe the objects in our environment. With words, however, we do not possess the objects, but only describe them, and as we all know, words are not identical to the objects they describe. It is obvious that there is no identity. Some funny examples of the not always logical use of words can be found in the following text (in German), which explains why the quiet plays loudly and the loud plays quietly. Fig 1: The piano (the quiet one) Fig. 2: The lute (the wood) But how does the

By Hans Rudolf Straub|2025-12-03T14:49:07+00:0020. September 2024|Categories: music, Semantics|Tags: lute, piano, semantics, semiotic triangle, words|0 Comments

The mental world

What is the mental world? The mental world is the world in our heads. It is the way in which we perceive the world; it consists of our sensations, feelings and thoughts. It is a completely subjective world. In the theory of the three worlds, the mental world is the third world besides the physical and the Platonic worlds. Difference from the physical world Whereas the physical world is objectively comprehensible, the mental world remains subjective. In other words: whereas we can observe the objects of the physical world from the outside, this is impossible with the objects of the

By Hans Rudolf Straub|2025-11-15T12:37:39+00:0028. March 2022|Categories: music, Semantics, Theory of the Three Worlds|Tags: Mental World, physical world, Qualia, Three worlds|0 Comments

What are the advantages of the equal temperament?

The equal temperament has prevailed in our occidental music culture – despite the obvious shortcoming that its intervals are not pure any longer. This was only possible because some substantial advantages offset the flaw of impurity: 1. One single tuning serves all keys: the fundamental tone is freely selectable. In pure intonation, instruments basically have to be retuned for each key and each fundamental tone. With a harpsichord, this concerns a few strings, but with an organ, this is really a great undertaking in view of the vast number of registers and pipes. The further the keys are apart from

By Hans Rudolf Straub|2025-11-15T12:38:31+00:0017. March 2022|Categories: music, Theory of the Three Worlds, Music scales|Tags: musical scales, Three worlds|0 Comments

Why resonance also works with imprecision

When does resonance occur? Resonance between two physical media depends on the frequency ratio of their natural vibrations. When the two frequencies constitute a simple fraction such as 2/1 or 3/2, resonance can occur. In an earlier post, I explained how the ten simplest frequency ratios lead with mathematical necessity to the ten tones which appear in our musical scales, no matter whether they are major scales, the various minor scales, the ecclesiastical modes, the major pentatonic scales, the minor pentatonic scales, the blues scale, etc. Ten tones are sufficient to build all these different scales. Pure intonation and temperament

By Hans Rudolf Straub|2025-11-15T13:05:58+00:0022. February 2022|Categories: music, Resonance|Tags: frequency ratio, impure temperament, pure temperament, resonance|0 Comments

The equal temperament

Initial wish: changing the fundamental tone during a piece of music In the preceding post, we saw that the just intonation is not pure any more when the fundamental tone is changed since certain intervals change. The further removed the key, the more tones fail to accord with the calculated, i.e. resonant tones. If the frequencies of the scale tones are very slightly shifted – i.e. tempered – then we can also change over into neighbouring keys, i.e. we can modulate. In the equal temperament, we can actually change over to any fundamental tone whatever, and this temperament has successfully

By Hans Rudolf Straub|2025-11-15T13:06:47+00:0014. February 2022|Categories: music, Theory of the Three Worlds|Tags: equal temperament, musical scales, resonance|0 Comments

How the tempered scales came into being

Musical scales before tempering Natural musical scales The musical scales of human cultures developed naturally, i.e. without any conscious mathematical considerations whatsoever, in the course of millennia. The fact that there is a great deal of mathematics behind them nonetheless has something to do with the resonances between the scale tones and the fundamental tone. These resonances strike us as attractive, and music that is based on such resonances is capable of uniting human communities. Mathematically, resonances can be traced back to fractions with as low numbers as possible, and we were able to deduce mathematically which nine intervals have

By Hans Rudolf Straub|2025-11-15T13:07:43+00:001. February 2022|Categories: music, Theory of the Three Worlds, Music scales|Tags: Tempering, Three worlds|0 Comments

Two Less Resonant Intervals for the Gaps

Starting point: two gaps In the previous post, we saw that in the sequence of the ten scales tones found so far, there are two gaps. Can we find resonant tones there, too? We already know the following: We already know the ten most resonant intervals in the octave. These ten intervals serve to constitute the five standard pentatonic scales and our major and minor scales. There, the gaps are not obtrusive; they are only conspicuous in the distribution of all the ten potential scale tones. Intervals do not occur on their own, either in a chord or in a melody. Thus

By Hans Rudolf Straub|2025-11-15T13:08:05+00:0027. December 2021|Categories: music, Theory of the Three Worlds, Music scales|Tags: musical scales, Three worlds|Comments Off

The Distribution of Tones within the Octave

The ten most resonant tones within the octave In this series of texts, we examine musical scales from the perspective of the three worlds. All three worlds are involved, as we saw, for example, when we answered the question as to why the musical scales of all musical cultures always cover precisely one octave. This cannot be explained in purely mathematical or physical terms. It is only through the involvement of the third world, namely our mental world, that the significance of the octave becomes evident. The selection of the tones used in a musical scale is determined by all three worlds through