source file: mills3.txt Date: Mon, 11 Aug 1997 20:42:15 +0200 Subject: 13 From: "George Kahrimanis" This is in response to a recent (Sat, 2 Aug 1997) posting by Joe Downing, , mentioning use of intervals built on 13 in music by Chris Mannigan. (I wish we could have some sonic samples available.) I am new in the list, so I just suppose that there must have been several discussions here already on the musical merits of 13. In my personal experience, all fractions between 13/7 and 13/12 are too difficult to fine tune. This, by the way, is the criterion I use in assessing intervals: if we can be guided by the beats in fine tuning the intervals, the interval is useful in music. The most promising among those intervals is 13/9, 637 cents. Now I have to mention that in 1988 I examined the fragments of Greek music (those known then), interpreting the notation in a stable way rather than the variable way that is currently used ("my" method applies only to pieces written before the 2nd century AD). I checked every melodic interval in order to identify its fraction (for intervals larger than a tone). I found only two clear cases of intervals which cannot easily be matched to ratios. Interestingly, it was exactly the same interval (same signs), its size being about a fifth minus a thirdtone, and in both cases set over the word "mortals". (The one instance in the Hymn to Nemesis and the other in the First Delphic Hymn.) I have also seen Mersenne approve of a certain composer's setting two falling minor thirds (= 5th - small semitone, unless the one third is subminor) over the word "morir" {sp?}. (John Chalmers tells me that both thirds are 6/5 here.) I am not sure whether I should relate this with the two Greek examples. George Kahrimanis Queens, NY ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com SMTPOriginator: tuning@eartha.mills.edu From: gbreed@cix.compulink.co.uk Subject: Re: notation PostedDate: 11-08-97 20:44:32 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: 11-08-97 20:44:34-11-08-97 20:44:35,11-08-97 20:43:00-11-08-97 20:43:00 DeliveredDate: 11-08-97 20:43:00 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C12564F0.0066F0E2; Mon, 11 Aug 1997 20:44:23 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA08065; Mon, 11 Aug 1997 20:44:32 +0200 Date: Mon, 11 Aug 1997 20:44:32 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA08045 Received: (qmail 20567 invoked from network); 11 Aug 1997 18:42:46 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 11 Aug 1997 18:42:46 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu