The method of composing with 12-tones arranged in a specific order to avoid tonality (thus Atonality) was developed/invented by Arnold Schoenberg in the 1920's. The Magic square which offered the composer the inversions and transpositions of the original 12-tone set or row could be easily presented in front of the composer by use of the "magic square." It is also called a Matrix and also a Babbitt square, named after Milton Babbitt who invented this square in the 1950's. Before then, the inversions and transpositions were written out on staff paper. Milton Babbitt's father was a mathematician so there was some intellectual thinking going on in their minds.
When I attended college in the late 1980's I took a course on 20th century harmony. It was here I was introduced to 12-tone technique, serialism/ atonality. It was an acquired taste but I became very intrigued with how ordered and structured this music was and the end result of it. Soon I purchased a couple Arnold Schoenberg record LPs. During Schoenberg's time when he played his 12-tone works to audiences they rebelled and on some occasion fights broke out and even a riot. The music was too dissonant for many but there were always some who seen and heard the genius in it.
My biggest surprise on You tube over the years of putting up videos (very few atonal) is the number of people who have viewed those few videos (over 120,000). So there is an interest in this music even if at an academic level, people are finding it more acceptable. Therefore, I decided to post perhaps the most important key in all of this serialism/atonality/12-tone technique subject; "THE MAGIC SQUARE/MATRIX."
I do believe I was the first person to put up an atonal serialism guitar work on You Tube when the video network was just in it's infancy. (who else would want to you might ask) I know this is music that most folk cannot tolerate. Some love it and some hate it. That's fine. In Schoenberg's day it was the same. But this video is for those who like it and want to know how to fill out the square so they have all the inversions and transpositions at their fingertips.
If you want to know more about this system of writing please check out my "7 Tips for Atonal writing" (with 12-tone technique)
This product will include portions of this video, the 7 tips, and many of my 12-tone works and videos.http://guitarjourney.tripod.com
Ray Tutaj Jr.