About Pure Consonances and Dissonances

And now for the musical and intellectual background of the instrument. The SPO instrument makes the essential difference between pure consonances and dissonances clear. The pure consonances are fundamentally anchored in our psycho-physical existence. The dissonances are not. Schönberg's harshness lies in assigning pure consonances to dissonances and dividing the octave into 12 equal parts, via the 12th root of 2. He called it “composing with only 12 tones related to each other”. He continued what the tempered tunings had already established: the underlying pure consonances. Here, “only” the pure consonances were subsumed; in Schönberg's case, the division of the octave into 12 equal intervals is complete. The tempered tunings and Schönberg's method lost the pure consonances. To further illustrate the difference between pure consonances and dissonances: the pure consonances can be clearly determined mathematically, as well as aurally. When we hear a pure prime of 440 Hz, i.e. two tones at the same frequency, if one tone is only 1 Hz higher or lower, then the human ear, the human mind, can hear this difference. At an interval of a semitone, we cannot determine exactly whether we hear the distance as too great or too small. We are in the approximate here, we determine the pitch approximately. We can only determine the distance exactly mathematically, using the 12th root of 2. But then even the pure consonances can no longer be heard. How would a tone system have to be designed that takes into account this diametrical difference between pure consonances and dissonances? In 2005, I gave 7 lectures on the elements of tone shape at the Denkbar in Frankfurt. On January 15, 2025, I began to discuss this issue with ChatGPT: “Tonsystem auf der Grundlage der fundamentalen Differenz zwischen Reinen Konsonanzen und den Dissonanzen” (Tonal System Based on the Fundamental Difference between Pure Consonances and Dissonances). I have now started to find solutions for such a tonal system in 7 conversations. You can find these conversations in the form of PDF files on Facebook and soon on my website.