Music scales-Archiv - Page 2 of 2

Expressions around waves and sine waves

Sine waves play a crucial part for our considerations of resonance. On this page, I would like to explain the terms that I use in this respect. Wave A wave is a motion in time which oscillates around a baseline. A wave can have different shapes. For our considerations of resonance, we use pure sine waves; such a wave is shown in the graph above. Amplitude The amplitude is the deviation of a wave from the baseline. It does not play any primary role in our considerations. Period A period lasts as long as the wave takes to arrive in the same

By Hans Rudolf Straub|2025-11-15T13:12:24+00:009. May 2021|Categories: Information, music, Theory of the Three Worlds, Music scales|Tags: musical scales, Three worlds|0 Comments

Calculating with frequencies and intervals

On this page, I will explain some rules which are applicable when we calculate with intervals and their frequencies. Intervals are fractions An interval ranges from a lower tone to a higher one. The fraction of the interval is calculated by dividing the frequency of the higher tone by the frequency of the lower tone, for instance E = 330 Hz A = 440 Hz 440/330 = 4/3. This is a fourth. The interval of the fourth is always 4/3: in the fourth, the higher tone is precisely 4/3 times as fast as the lower tone. What counts here are

By Hans Rudolf Straub|2025-11-12T10:44:22+00:006. May 2021|Categories: music, Theory of the Three Worlds, Music scales|Tags: musical scales, Three worlds|0 Comments

“Breaking down” the Fifth

The fifth Let us first have a look at the fifth. It is a feature of practically all the musical scales of human cultures. Musical scales without this pure fifth do exist, but these musical scales strike me either as artificial and deliberately designed like the whole tone scales or rather uncommon like the Locrian mode. The blues scale makes use of the “blues note” – the “flat five”, a note close to the fifth known as the diminished fifth – but also uses the perfectly normal fifth. After the octave, the fifth is certainly the interval that occurs most

By Hans Rudolf Straub|2025-11-15T13:13:40+00:0017. March 2021|Categories: Information, music, Theory of the Three Worlds, Music scales|Tags: fifth, frequency, musical scales, Three worlds|0 Comments

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

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