The major scale The major scale (Ionian mode) is the most widespread musical scale both in Europe and globally. It is a heptatonic scale, i.e. a musical scale with seven tones. It is characterised by very special resonance ratios, which serve well to explain its worldwide appreciation. Below, I have listed the tones of the major scale of C, ascending from the bottom to the top, together with the intervals between each tone and the fundamental tone. Of course, it is these intervals that constitute the musical scale. We could also start the musical scale with any other tone and

As we have seen in the previous post, the tones C – D – E – G – A – C constitute the standard major pentatonic scale. All in all, another four pentatonic scales can be created with the simple criteria for resonant pentatonic scales. These five pentatonic scales are the five musical scales which according to our mathematical criteria allow for resonances among all their tones. We will see later on that we are able to create all the musical scales traditionally used in Europe with our pool of the nine most resonant tones. In the heptatonic scales, however, for instance

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

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