source file: mills2.txt Date: Mon, 13 Nov 1995 21:55:42 -0800 Subject: RE: definition of JI From: Mmcky@aol.com I guess it's pretty well accepted that JI tuning is tuning using small whole number frequency ratios. The difficult part is defining small. I guess no one would be surprised that my approach to the matter is based, in part, on the Least Common Multiple. The other part is absolute frequency. The LCM of tones sounded simultaneously, together with the absolute frequency determine the length of patterns in the sound in the time domain. I think the ear/brain as the ability to remember what is heard for a certain length of time and remember it in great detail. When the patterns in the sounds are comfortably within that length of time, the ear/brain experiences the "pleasure" of easily decoding the patterns. As length of time it takes to reapeat the sound patterns approaches the capacity of the sound memory, the ear/brain has difficulty decoding the patterns, and we register that difficulty as distress, or dissonance. Some patterns actually take a very long time to repeat, but include smaller patterns that are not actually alike, but are very nearly alike. The ear can decode these patterns easily, and also registers the fact that they are not exactly alike. This, of course, is a description of tempered music. But here we have a possible physiological basis for a definition of small. Small would be when the ear can easily decode the pattern. Large would be when the ear can't decode the pattern. Marion Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 14 Nov 1995 18:55 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA19575; Tue, 14 Nov 1995 08:54:57 -0800 Date: Tue, 14 Nov 1995 08:54:57 -0800 Message-Id: <199511141625.RAA18992@musik.auc.dk> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu