source file: mills2.txt Date: Fri, 1 Nov 1996 16:29:47 -0800 Subject: Re: Johnny's Lingua Franca Notation From: PAULE >History has done away with Savarts which are larger than cents >in favor a system which, thankfully, anchors on good old 12-tone ET (e.g. >100 cents is a semitone, 200 cents is a whole tone, etc.) Dare we admit >that this is of value? Denying this would be cutting oneself from 99.99% of Western teaching and performance practices. >Amazingly, most musicians do not realize that the ear does not hear >logarithmically. It learns by rote. There seems to be plenty of psychoacoustical evidence that refutes the first claim. We do indeed hear pitch logarithmically, where pitch is defined as the "virtual pitch" that is assigned to any harmonic or near-harmonic set of partials. However, due to beats and combination tones, we can detect much finer deviations from an arithmetic or harmonic series in a chord than deviations from a geometric (logarithmic) series in either a chord or a melody. This leads talented performers to essentially mutate the 12-tone grid to achieve 5-limit just intonation in sustained harmonies. It also leads people to think of just intonation as representing the way we actually hear, but it just ain't so. >For example, sing alound a 7/4 and >then try to find the logarithmic midpoint that bisects the interval. >Knowing this interval is made up of 969 cents, one can calculate a center. Knowing that it is 9 2/3 semitones (you can't hear a 2-cent discrepancy under performance conditions), one can calculate a center even more easily: 4 5/6 semitones (beats won't help you tune this one!). Sixths of semitones can be taught systematically, through 11-limit JI harmonies and Arabic and Byzantine scales, while cents imply a lot of guesswork. (I'm thinking of how to best educate, and notate music for, tomorrow's musicians, not necessarily Johnny's highly-skilled ensemble). I suppose if Johnny wins out, I would recommend restricting the allowed deviations to 17, 33, and 50 cents when first beginning a course of microtonal education, so that certain points of reference can be established. It's just that having to attach numbers like 17 and 33 to these sounds seems like an unnecessary burden. For the extreme purists among the JI advocates, I would say that really good performers of 11-limit vocal and string music will intuitively mutate the 72-tone grid (by no more than 4 cents) in sustained harmonies to achieve absolute perfection; more accurate notation would not be of any help to those with inferior ears. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 2 Nov 1996 02:52 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14123; Sat, 2 Nov 1996 02:53:26 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA12721 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA25608; Fri, 1 Nov 1996 17:53:23 -0800 Date: Fri, 1 Nov 1996 17:53:23 -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