Randomness of the 12 Tone Technique Also Applies to our math. The initial proponent of this technique was Arnold Schoenberg (1874–1951), Austrian-American composer. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key.
Randomness of Music and Numbers
Our modern use of numbers parallels the 12 tone technique. The 12 tone technique is best described as willful randomness. Antiquity thought of numbers one to nine as belonging to a system. It was called the 3 x 3 number square. In our music that is set in the circle of fifths, this is called a key signature. The numerical key signature of the ancients was the vehicle of the number square. They favored 7 primary number squares. This could equate with 7 key signatures. The simplest and first was 3 x 3. Their favored squares ranged from 3 x 3 to 9 x 9. They did use higher numeric squares. However, the basic 7 were most common. Sacred prayers in Judaism coded higher number squares. Two favored ones were 13 x 13 and 17 x 17. I have blogs on this subject on DSOworks.com. Some 10,000 years ago, and maybe further back in time, all numbers belonged to unified systems. They were also connected to words. For example, “order” could be 264. Each symbol of the ancients represented a letter and a number. There were no separate letters and numbers. Their unity called by a Greek name, gematria. Look it up online. At one time there was no randomness. You can sample ancient unity on the 3 x 3 number square picture below.
- Any two opposite numbers around the perimeter total 10. Examples are 4 + 6= 10 ; 9 + 1 = 10; etc.
- The average of any two opposite numbers around the perimeter is 5. Five is the core number.
- Each number contributes to a perimeter whose total around #5 equals 40.
- The total of all the numbers on the square is 45. . (That equals the sum of the numbers from 1 to 9).
- Each number is set so that any row of three totals 15. This is true vertically, horizontally or diagonally.
The high level of organization of numbers in antiquity is staggering. Today, with our modern sciences, we totally lack such an organizing system for our numbers. I believe that result is social conflict. The genius of Arnold Schoenberg made a powerful musical statement as to where our culture was heading. Let us return to the way of the ancients. Reviving number squares is what many of my blogs are about. Enjoy the illuminating sample of the 12 tone technique below!