source file: mills2.txt Date: Tue, 1 Jul 1997 15:10:43 +0200 Subject: Re: Limits, Octave equivalence From: mr88cet@texas.net (Gary Morrison) >Second, some of us evidently don't believe that octave equivalence (2:1, give >or take a few cents :-) should be taken for granted ... Holy cow! ... >one of which has a frequency at a power-of-two of the other, the lower one >will cross the zero point only at points at which the higher one is crossing >as well. Hmmm... Well, certainly you can phase them so that the zero-crossings never correspond, or microscopically detune them, by 1/5Hz for example, they will not correspond very closely for very long, and yet we recognize both as octaves. Here's another curious observation to throw into this line of inquiry. I suppose it could be just me, but I'd be surprised if so: I have found there to be something interesting about ratios of the form (N+1):N. I've noticed that if I listen to a narrow range of small, adjacent Ns for long enough, they start masquerading as one another. An easy example to hear occurs when I practice singing the distinction between 6:5 and 7:6 thirds. After I sing and think about nothing but those two intervals for five minutes or so, I find that the 6:5 starts having the sensation I normally associate with 5:4. "Sensation" in the sense that I'm inclined to momentarily misidentify 6:5 as 5:4 - an auditory illusion in essence. And further, when I suddenly toss into the mix a 5:4, it starts seeming like a 4:3, and 3:2 seems like an octave. I'd be curious as to whether anybody else has noticed this effect too. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 1 Jul 1997 16:22 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17143; Tue, 1 Jul 1997 16:22:25 +0200 Date: Tue, 1 Jul 1997 16:22:25 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA17136 Received: (qmail 12362 invoked from network); 1 Jul 1997 14:17:28 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 1 Jul 1997 14:17:28 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu