source file: mills3.txt Date: Fri, 29 Aug 1997 18:22:16 +0200 Subject: RE: 5-Limit in India? From: "Paul H. Erlich" <PErlich@Acadian-Asset.com> John Chalmers wrote, >I read a paper in an ethnomusicology journal that >suggested that the 22 tone scale grew out of the modes of the 12-tone >Pythagorean series. I gave my copy of the paper to Erv Wilson, who agreed, >but I don't recall the details any more. Hence one could use essentially 5 >limit intervals while not recognizing 5 as a factor at all. I believe that the sa- and ma- gramas were tuned by ear (with 5-limit intervals) by musicians before theorists decided to quantify them in terms of a 22-tone scale. A 22-tone Pythagorean series, aka the union of 11 modes of the 12-tone Pythagorean series, approximates the hypothetical 5-limit gramas with a maximum error of 2 cents (the skhisma). The Pythagorean series was more important in ancient musical theory than it is now; for example the medieval Arabs used a 17-tone Pythagorean series to quantify some apparently 5-limit scales. When I said India achieved the 5-limit before the West I was thinking it terms of presently existing musical traditions; the music of ancient Greece >is, to my knowledge, a lost art. SMTPOriginator: tuning@eartha.mills.edu From: mr88cet@texas.net Subject: Re: Demisemitones PostedDate: 30-08-97 01:29:55 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 30-08-97 01:30:06-30-08-97 01:30:07,30-08-97 01:29:53-30-08-97 01:29:53 DeliveredDate: 30-08-97 01:29:53 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C1256502.00811505; Sat, 30 Aug 1997 01:29:55 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09095; Sat, 30 Aug 1997 01:29:55 +0200 Date: Sat, 30 Aug 1997 01:29:55 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA09089 Received: (qmail 954 invoked from network); 29 Aug 1997 23:29:51 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Aug 1997 23:29:51 -0000 Message-Id: <v01541100b02cd28b95b9@DialupEudora> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu