source file: mills2.txt Date: Mon, 7 Jul 1997 02:00:30 +0200 Subject: Octave invariance From: DFinnamore@aol.com Graham Breed writes: >If you allow for the octave equivalence of intervals, all triadic >inversions contain the same intervals. How so? The way I larnt it, a simple C major triad in root position consists of a minor third stacked on top of a major third. In first inversion, it consists of a perfect fourth stacked on top of the minor third. In second inversion it's that perfect fourth with the major third stacked above it. From what perspective are those the same set of intervals? > ... However, if you disallow octave >equivalence of intervals, and you define harmony in terms of intervals, >you must also reject the octave equivalence of harmony. Inversional >invariance follows from octave invariance, unless you have a >privileged root to lift the otonal/utonal degeneracy. I don't quite follow all that, especially the "privileged root" part, with which concept I am unfamiliar. Could you give an example? > ... none of this >implies that octave transpositions are harmonically negligible. Many >people state this, and I believe it to be a result of sloppy thinking. To my great surprise, I am increasingly inclined to agree with you on that. After all, orchestrators and arrangers have known the importance of appropriate "voicing," or spacing of intervals across octaves, for about as long as there has been 4-part harmony. David J. Finnamore Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 7 Jul 1997 05:47 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA06109; Mon, 7 Jul 1997 05:48:14 +0200 Date: Mon, 7 Jul 1997 05:48:14 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA06112 Received: (qmail 27470 invoked from network); 7 Jul 1997 03:48:10 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 7 Jul 1997 03:48:10 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu