source file: mills3.txt Date: Sun, 31 Aug 1997 19:47:38 +0200 Subject: Re: Demisemitones From: gbreed@cix.compulink.co.uk (Graham Breed) Gary Morrison wrote: >> The definition only applies to syntonic meantones. > I musta missed something: Which definition are you referring to? The > disemitone/quartertone? A demisemitone is the difference between an augmented unison and a minor second. An augmented unison is the approximation of a chromatic semitone, and a minor second of a diatonic semitone, in a syntonic meantone. This is the only definition of these intervals I know, and it only applies to syntonic meantones. Hence the same is true of demisemitones. 24tet is a special case, because a subset of it is a syntonic meantone temperament. The interval 7/4 is called a subminor seventh. If you define that as a minor seventh flattened by a demisemitone, you have a definition of an interval. In syntonic meantones, 7/4 is an augmented sixth, so the two definitions agree. I have adopted the / and \ symbols to notate boosts of this kind of demisemitone. There is technically a lesser demisemitone being the difference between a greater demisemitone and an augmented unison. In JI, there are 2 minor sevenths -- 16/9 and 9/5 -- so there are two greater demisemitones defined the 7-limit way. One is (4 -2 0 0)H - (-2 0 0 1)H = (6 -2 0 -1)H and the other is (0 2 -1 0)H - (-2 0 0 1)H = (2 2 -1 -1)H. The former is a septimal comma, and has priority over the \ symbol. / and \ can be used generally to denote small deviations from the 5 prime limit when meantone (eg staff) notation is used for JI. Does whoever originally suggested them object to this? To unite two threads, if you define the sruti scale: r q r q r q r q r q r q r r q r q r q r q r S r R g G M m P d D n N S' in a manner consistent with 22 octave reduced fifths, a septimal comma is well approximated by q, so these small srutis are demisemitones and, for example, the first sruti is r\. SMTPOriginator: tuning@eartha.mills.edu From: PErlich@Acadian-Asset.com Subject: RE: 5-limit in India? PostedDate: 31-08-97 16:16:01 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: 01-09-97 17:09:22-01-09-97 17:38:02,01-09-97 17:37:45-01-09-97 17:37:48 DeliveredDate: 01-09-97 17:37:48 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C1256505.00532AA8; Mon, 1 Sep 1997 17:08:24 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09708; Sun, 31 Aug 1997 16:16:01 +0200 Date: Sun, 31 Aug 1997 16:16:01 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA09705 Received: (qmail 25552 invoked from network); 31 Aug 1997 14:15:56 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 31 Aug 1997 14:15:56 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu