source file: mills2.txt Date: Sat, 3 May 1997 02:08:18 -0700 Subject: Re: TUNING digest 1056 From: mr88cet@texas.net (Gary Morrison) >please, someone, give me a hand. I don't understand thee fraction >representaions. (e.g. 3/2 G ? why ? etc) >however, I am in the most advanced class in math around :( Fortunately, the math involved isn't terribly complicated. Also 3/2 (same as 3:2) doesn't really necessarily imply a G. It does only in the key of C. This harkens back to the age-old, venerable, and still pretty much accepted, observation attributed to Pythagoras, that our ears are exceptionally sensitive to simple ratios of vibrational frequency. This is the basis behind just intonation - tunings built around precise renderings of these simple ratios, rather than approximations to them like our usual tuning (12-Tone-per-octave Equal-Temperament, often abbreviated "12-equal", "12TET", "12tET", or "12ET"). The simple ratio for an octave is 2:1, meaning that the vibrational frequency of the higher note is twice the frequency of the lower one. The ratio for the perfect fifth (G being a P5 above C), is 3:2. Here are some others: Perfect Fourth P4 4:3 Major Third M3 5:4 Minor Third m3 6:5 Major Sixth M6 5:3 Minor Sixth m6 8:5 Major Second M2 either 9:8 or 10:9, the difference between the two being a "syntonic comma", or Paul R. would presumably call it a Just Syntonic Comma or perhaps a 5-limit Just Syntonic Comma. Major Seventh M7 15:8 And heading into nontraditional harmonies: Septimal subminor third Septimal minor third 7:6 Septimal subminor seventh Septimal minor seventh 7:4 Neutral third 11:9 (11:9 is the most commonly-discussed neutral third, but there are others.) And there are many many others in this comparatively unexplored realm. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 3 May 1997 13:34 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03436; Sat, 3 May 1997 13:34:34 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA03481 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id EAA24778; Sat, 3 May 1997 04:32:55 -0700 Date: Sat, 3 May 1997 04:32:55 -0700 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu