source file: mills3.txt Date: Mon, 29 Dec 1997 10:35:30 +0100 Subject: re 19, 22, etc From: Bob Valentine > > > Regarding 19TET in particular, perhaps it is the last temperment which > > preserves "sameness" of the "big" and "small" major seconds (9:8, 10:9). > > Perhaps this isn't very important (or maybe it is), but this strikes me > as a strange way to think of it. The historical and probably > psychoacoustic basis of Western tuning is Ptolemaic JI, which has two > different sizes of whole step. There is therefore no meaning to preserving > an abstraction that represents those two intervals identically. You can't > preserve something ahistorical. > The next line in my mail was, "but is this a good thing?", to which I don't know the answer. It was since explained to me that "sameness of the big and small major seconds" is another way of saying "meantone" and there is a historic precedence suggesting that for Western, harmonically oriented music, meantone will result in less (or no) "drift" vs. a non-meantone tuning. let P5 = number of tempered units per perfect fifth M3 = number of tempered units per major third T = temperment, number of notes per octave If I was correct in my understanding, a succinct definition of meantone is that 4 * P5 - M3 = T / 2. (a few examples T M3 P5 12 4 7 19 6 11 31 10 18) Is there a special word for tunings defined by 4 * P5 - M3 - 1 = T / 2? (a few examples T M3 P5 22 7 13 34 11 20 53 17 31) thanks, and by the way, what does 88cet mean? Each tone having 88 cents? Bob Valentine SMTPOriginator: tuning@eartha.mills.edu From: BUYO-BUYO-IGOR Subject: cheezy 1/2 interactive project PostedDate: 29-12-97 11:46:51 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $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: 29-12-97 11:44:34-29-12-97 11:44:35,29-12-97 11:43:59-29-12-97 11:44:00 DeliveredDate: 29-12-97 11:44:00 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125657C.003AFFB8; Mon, 29 Dec 1997 11:46:21 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA26976; Mon, 29 Dec 1997 11:46:51 +0100 Date: Mon, 29 Dec 1997 11:46:51 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA17990 Received: (qmail 14149 invoked from network); 29 Dec 1997 02:46:44 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Dec 1997 02:46:44 -0800 Message-Id: <34A7FDBC.5342@db3.so-net.or.jp> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu