source file: mills3.txt Date: Thu, 4 Sep 1997 21:22:12 +0200 Subject: RE: Tuning of the 2nd sruti From: gbreed@cix.compulink.co.uk (Graham Breed) Paul Erlich wrote: >Unfortunately for theorists, practice does not always conform to the >theoretical value schisma=1 sruti. Being only 2 cents, it should not be >surprising that musicians would tend to ignore it in practice. The most >common occurence of this practice is at sruti 12, which can be used as >729/512 (611.730 cents) or 64/45 (609.776 cents) depending on the situation. >But the diaschismatic interpretation of the sruti system implies that 729/512 >is 12 srutis while 64/45 is 11. Perhaps the best theoretical remedy would be >to consider a 10-sruti schisma-augmented perfect fourth (499.999 cents) a >consonant interval in its own right, and fix 729/512 as the correct tuning of >sruti 12. On the evidence I've got, which is purely the modes Manuel put on this list as well as the FTP site, I wouldn't say that a schisma is even theoretically 1 sruti. As it took me a while to sort this out, I'll share my thoughts with the list. First, the sruti scale I'm using is: s p r p s p r p s|p r p s|s p r p s p r p s With s a limma, r a chromatic semitone and p a syntonic comma. I think these work out as: (s) ( 8 -5 0) (r) = (-3 -1 2)H (p) (-4 4 -1) Setting a schisma=0 means s=p+r. Setting a diaschisma=0 means s=r. Most of the scales work as 5-limit harmony with the just version of this scale. In some cases the schismic and diaschismic approximations both work. The following scale doesn't make sense to me: 3 2 4 3 2 4 4 Gandhaara Grama (Sarngadeva der. ma-grama) I suggest that Pa should be flat by p rather than s, so that the interval of 3 steps separating the tetrachords is a minor tone. Either this uses a different version of the sruti scale, or it is assumed that people will guess the correct tuning. Or, my interpretation is wrong. This scale works as a diaschismic but not a schismic scale: 2 6 1 4 2 6 1 Raga Bhairav I'm assuming the intervals of 6 steps should be just minor thirds, but I have no proof of this. I think the following scales imply schismic tuning: 1 4 6 2 1 7 1 Raga Todi 1 7 1 4 2 2 4 1 Raga Saurastra 1 4 7 1 1 6 2 Raga Varali The intervals of 7 steps aren't right for diaschismic major thirds, so I'm assuming they should be schismic minor thirds. The upper tetrachord of Varali suggests the same _diaschismic_ approximation as in Bhairav above! That's consistent with the sruti scale being a kind of well temperament with no single interpretation. Because the tonic is always sruti 0, you don't have to worry about transpositional invariance, so this sort of thing is allowed. Then again, the 6 steps could denote a Pythagorean minor third (5 -3)H. There are also some that may have 7-prime-limit intervals. The following is the only one that doesn't work schismically: 4 2 4 3 3 3 3 Gandhaara Grama (Narada der. sa-grama) The middle of the three 3's is 2s+p. This can't be a minor tone. I suggest it should be the interval (-1 1 1 -1)H or 15/14. It can be better represented as either r+r+p or s+p. The two are identical in a schismic temperament, and the former is the diaschismic equivalent of 2s+p. One of the other 3's will be (2 0 -2 1)H to compensate. It's also possible that all the 3's are supposed to be roughly equal intervals, and no 7-limit interpretation is intended. SMTPOriginator: tuning@eartha.mills.edu From: mr88cet@texas.net Subject: 2-D FFTs PostedDate: 06-09-97 01:15:48 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: 06-09-97 01:15:55-06-09-97 01:15:56,06-09-97 01:15:28-06-09-97 01:15:28 DeliveredDate: 06-09-97 01:15:28 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C1256509.007FC8E7; Sat, 6 Sep 1997 01:15:45 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA15687; Sat, 6 Sep 1997 01:15:48 +0200 Date: Sat, 6 Sep 1997 01:15:48 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA15690 Received: (qmail 18551 invoked from network); 5 Sep 1997 23:15:38 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 5 Sep 1997 23:15:38 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu