source file: mills3.txt Date: Wed, 10 Sep 1997 03:11:30 +0200 Subject: RE: Tuning of the 2nd sruti From: alves@orion.ac.hmc.edu (Bill Alves) Manuel Op de Coul wrote: >The 22-tone sruti system is by no means uncontroversial, but >experiments where musicians tune instruments or oscillators have >produced tunings that are in good agreement with the theoretical >values. I would be very interested in your source for these experiments, if you have it handy. If the tuning of the srutis is controversial, then how can the experimenters have "theoretical values" to check recordings against? By the way, I mentioned earlier that the first mention of precise tunings that I know of comes from the Hrdayakautaka of Hrdaya Narayana of the late 17th century. I should have said that they are tunings of the 12 svaras, not the 22 srutis. Also, there is an ambiguity in the text that can lead to two different interpretations for some pitches. Here they are, reduced to ratios: interpretation #1 interpretation #2 (Bhatkande) (Levy) 1/1 1/1 27/25 27/25 9/8 9/8 6/5 6/5 54/43 72/57 4/3 4/3 162/113 36/25 3/2 3/2 18/11 18/11 27/16 12/7 9/5 9/5 81/43 36/19 2/1 2/1 Like some of our correspondents, Fox-Strangeways considered Bharata's 4 srutis to be a major tone (9/8) 3 to be a minor tone (10/9) and 2 to be a just semitone (16/15). However, there is no direct evidence for this interpretation in Bharata, nor in any of the treatises that I know of for more than a millineum following him. In fact, Bharata, like medieval European writers, considers the 3rd to be in the "assonant" (anuvadi) category -- that is, neither consonant nor dissonant. It could be argued that a 5/4 third would be considered consonant, though such a judgement is also very culturally bound. Notice that Narayana's tuning of the major third in both interpretations above is a rather complex ratio. Bill ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^ Bill Alves email: alves@hmc.edu ^ ^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^ ^ 301 E. Twelfth St. (909)607-4170 (office) ^ ^ Claremont CA 91711 USA (909)607-7600 (fax) ^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ SMTPOriginator: tuning@eartha.mills.edu From: Manuel.Op.de.Coul@ezh.nl Subject: RE: sruti details PostedDate: 12-09-97 07:24:59 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: 12-09-97 07:24:51-12-09-97 07:24:52,12-09-97 07:24:14-12-09-97 07:24:14 DeliveredDate: 12-09-97 07:24:14 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C1256510.001DBD86; Fri, 12 Sep 1997 07:24:50 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA26651; Fri, 12 Sep 1997 07:24:59 +0200 Date: Fri, 12 Sep 1997 07:24:59 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA26683 Received: (qmail 12770 invoked from network); 12 Sep 1997 05:24:55 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 12 Sep 1997 05:24:55 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu