source file: mills2.txt Date: Thu, 16 Jan 1997 11:53:12 -0800 Subject: Arabic Tuning From: gbreed@cix.compulink.co.uk (Graham Breed) In a list of scales, the exact provenance of which I forget, I found the following: Rast Medieval arabic scale t 2s r t 2s r t Zenkouleh Medieval arabic scale t 2s r 2s t t+r Rahawi Medieval arabic scale 2s t r 2s r t t Hhosaini Medieval arabic scale 2s r t 2s r t t Hhidjazi Medieval arabic scale 2s r t 2s t r These are based on the intervals t major tone log(9/8) s limma log(256/243) r apotome t-s log(2187/2048) On the face of it, these are all good Pythagorean scales. However, intervals of 2s look a bit suspicious. In fact, if you substitute each 2s for a minor tone and each r for a semitone, you will see that these are really much more friendly looking scales in disguise. Rast, in fact, looks suspiciously like a major, and Hhosaini like a minor. This approximation rests on the Pythagorean and syntonic commas being nominally equal, and is very good -- to within 2 cents. Presumably I wasn't the first to notice this, although I have heard from two separate sources that Arabic music is based on Pythagorean tunings, rather than a Pythagorean notation for just tunings. The following questions therefore arise: 1. How typical are these scales of modern and medieval Arabic music? 2. Are the scale definitions, which I converted from the frequency ratios, from a reliable, contemporaneous source? 3. How closely do observed modern tunings conform to JI? 4. Have all Arabic musicians and scholars followed this dogmatic Pythagorean interpretation? I would appreciate your answers to these questions. And, while I'm at it, what exactly does CPS mean? Graham Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 16 Jan 1997 21:20 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12562; Thu, 16 Jan 1997 21:24:09 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA12517 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id MAA17175; Thu, 16 Jan 1997 12:24:06 -0800 Date: Thu, 16 Jan 1997 12:24:06 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu