Scales catalogs in an other approach


One of the groundbreaking features of Pénzes Methodology is creating the two scale catalogs; the one-octave and the two-octave ones, which are systematically described in the following sections:

Sometimes the fact that I created all this gets me thinking; Why me? Why am I the first one to come up with all this? It has been all in the air ever since the twelve-tone equal temperament, after a long progress, became prevalent in music 300 years ago.


Since the basic principles of scales catalogs were defined once the one-octave scale catalog was created, making the two-octave scale catalog was relatively easy.


In these scale catalogs, numbers represent the scale structure; for instance a major scale looks like 101011010101. What's more to this fact is that these numbers represent the respective scale structure not only on a given pitch but on any pitch. This means that the note combinations of not only the twelve-tone equal temperament, but any musical temperament, can be described by this system.


I think the two-octave system, which we could call 24-tone temperament, better explains the concept behind this; the basic idea of this was to stretch the scale catalog range to two octaves thus making it consist of 24 tones instead of just 12. But the digit-defined scale combinations that can be derived from this system by scale modeling can be used not only for my 24-tone temperament but also for any other system that defines 24 different tones. For instance, one of them is the 24-semitone temperament, which is derived from the twelve-tone equal temperament and literally means further splitting the twelve semitones into half. As an interesting fact, there were many attempts to create this 24-semitone temperament during the 20th century. ( Alois Hába) - Scales catalogs in an other approach