source file: mills3.txt Date: Wed, 28 Jan 1998 20:19:05 +0100 Subject: Tuning of decatonic modes From: gbreed@cix.compulink.co.uk (Graham Breed) I've worked out that Paul Erlich's Pentachordal modes can be written as 10 JI notes plus three commas of 50/49. This interval is larger than a syntonic comma, so some tempering is advisable, but it should be small enough for the scales to function as 10 pitch classes. As 10 fixed pitches, the comma of 50/49 means that the tritones 10/7 and 7/5 must be equal. With just octaves, they must both be an exact half-octave. As these are the worst 7-limit intervals in 22-equal, that means there is no better way of tuning decatonic modes unless you allow more than 10 notes. SMTPOriginator: PErlich@acadian-asset.com From: "Paul H. Erlich" Subject: Purvutation & Marvulation PostedDate: 28-01-98 21:53:13 SendTo: CN=coul1358/OU=AT/O=EZH $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: 28-01-98 21:53:18-28-01-98 21:53:19,28-01-98 21:52:04-28-01-98 21:52:05 DeliveredDate: 28-01-98 21:52:05 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 C125659A.0072BCCD; Wed, 28 Jan 1998 21:53:14 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00844; Wed, 28 Jan 1998 21:54:12 +0100 Received: from shore.shore.net by ns (smtpxd); id XA00842 Received: from mail.acadian-asset.com (mail.acadian-asset.com [207.244.72.210]) by shore.shore.net (8.8.7/8.8.7) with SMTP id PAA17631 for ; Wed, 28 Jan 1998 15:53:26 -0500 (EST) Received: from MARS by mail.acadian-asset.com via smtpd (for shore.shore.NET [192.233.85.136]) with SMTP; 28 Jan 1998 20:47:13 UT Received: by mars.acadian-asset.com with SMTP (Microsoft Exchange Server Internet Mail Connector Version 4.0.995.52) id <01BD2C04.D7F0DD60@mars.acadian-asset.com>; Wed, 28 Jan 1998 15:53:15 -0500 Message-Id: From: "Paul H. Erlich" To: "'Manuel.Op.de.Coul@ezh.nl'" Subject: Purvutation & Marvulation Date: Wed, 28 Jan 1998 15:53:13 -0500 X-Mailer: Microsoft Exchange Server Internet Mail Connector Version 4.0.995.52 Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Can you tell me more about Erv's mutations? SMTPOriginator: tuning@eartha.mills.edu From: Alexandre Enkerli Subject: Electronic tuner ad JI PostedDate: 29-01-98 05:42:39 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: 29-01-98 05:41:52-29-01-98 05:41:53,29-01-98 05:40:38-29-01-98 05:40:38 DeliveredDate: 29-01-98 05:40:38 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 C125659B.0019CA1C; Thu, 29 Jan 1998 05:41:41 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01105; Thu, 29 Jan 1998 05:42:39 +0100 Date: Thu, 29 Jan 1998 05:42:39 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01103 Received: (qmail 19536 invoked from network); 28 Jan 1998 20:41:53 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 28 Jan 1998 20:41:53 -0800 Message-Id: <199801290440.XAA14359@ulys.POSTE.UMontreal.CA> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu