source file: mills3.txt Date: Thu, 28 Aug 1997 16:44:40 +0200 Subject: 5-Limit in India? From: John Chalmers A 4th century CE (AD) date for the Indian 22 shruti scale certainly allows for Greek influence. Alexander the Great reached the Indus in the 4rd century BCE and a Greek state lasted in Khorasmia until Roman times. Greek astronomy clearly influenced Indian astronomy (the Paulisa Siddhanta, Romaka Siddhanta, Surya S. etc. ) at an early date, thought to be around 4th century CE by Neugebauer). Since the chief music theorists of the Hellenistic period were also astronomers, I see no problem with their being a Greek influence on music as well, or at least on music theory. Because of the skhismic relationship, 5 limit relations may be approximated by a long Pythagorean cycle. 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. The point is that 5 and 7 limits intervals in theory and in melody were recognized by the Greeks in the 4th century BC (Archytas) and later in Alexandria in Hellenistic times (Didymos, Eratosthenes, Ptolemy). India could have borrowed these concepts or developed them independently. I don't think we can decide on present evidence (the Indians made no secret of having learned astronomy from the Greeks as the Surya Siddhanta recounts someone being ordered to go West to the land of the Ionians (Yavanas), become incarnated as a barbarian, and learn astronomy. (Ethnic prejudice is not a dead, white European, male value, evidently). The Paulisa S. is thought to be named after Paulus Alexandrinus, a 4th century CE astronomer. Actually all of the ancient world was in pretty close cultural contact, particularly after Alexander, though Greek mathematics owes a lot to Babylon and somewhat less to Egypt. They took what they wanted and ran with it... --John SMTPOriginator: tuning@eartha.mills.edu From: nowitzky@pacificnet.net Subject: Re: Matrices (digest 1166 topic 2) PostedDate: 28-08-97 18:35:22 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: 28-08-97 18:35:27-28-08-97 19:13:26,28-08-97 19:13:14-28-08-97 19:13:15 DeliveredDate: 28-08-97 19:13:15 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C1256501.005B21C1; Thu, 28 Aug 1997 18:35:24 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04167; Thu, 28 Aug 1997 18:35:22 +0200 Date: Thu, 28 Aug 1997 18:35:22 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA04191 Received: (qmail 22027 invoked from network); 28 Aug 1997 16:35:19 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 28 Aug 1997 16:35:19 -0000 Message-Id: <2.2.16.19970828092939.2d375326@pacificnet.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu