source file: mills2.txt Date: Wed, 28 Feb 1996 14:20:40 -0800 Subject: English version of Schoenberg From: Kami Rousseau Here's my translation of Schoenberg's letter : Schoenberg : "I have given a lot of thoughts, altough in a different way, to your ideas about third-tones. I was convinced about quartertones, but I am now aware that this will happen by another mean than that of construction. Furthermore, one of my students calculated that the next octave subdivision that would have proportions similar to our division in twelve parts would introduce 53rd tones. If you use 18 third tones, it would come close to the same result, because 3 x 18 = 54. But then the half steps would disappear completely. For quartertones, at the time, I used the following notation.

#P #P> < and > are mathematical symbols. However, I do not believe that such a notation system will go far ; I strongly believe that our future notation should be simpler. I also have a different point of view about tonalties, and my music prooves it. I think that what we can do with 113 tonalties could easily be done with 2, 3 or 4 : major=minor, whole tone and chromatic. Anyway, I've been trying to get rid of the bounds of tonalty for a long time. My harmony doesn't use tonal chords and melodies anymore. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 28 Feb 1996 23:41 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id OAA04907; Wed, 28 Feb 1996 14:40:42 -0800 Date: Wed, 28 Feb 1996 14:40:42 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu