source file: mills3.txt Date: Tue, 23 Dec 1997 21:02:13 +0100 Subject: 19-tone Equal Tetrachords From: Gregg Gibson Several years ago I had the idea of writing out the tetrachords of the 19-tone equal. Anyone can do this for himself, and very probably this has been done somewhere already, but perhaps it may not be taken amiss if I here supply them: 1. C C# Db F 2. C C# D F 3. C C# D# F 4. C C# Eb F 5. C C# E F 6. C C# E# F 7. C Db D F 8. C Db D# F 9. C Db Eb F 10. C Db E F 11. C Db Fb F 12. C D D# F 13. C D Eb F 14. C D E F 15. C D Fb F 16. C D# Eb F 17. C D# E F 18. C D# E# F 19. C Eb E F 20. C Eb Fb F 21. C E E# F Numbers 9, 13 & 14 are diatonic; numbers 8, 10 & 17 are chromatic; the others are enharmonic (at least one interval of 1/3 tone). These of course do not comprise all modal possibilities by any means, for which one must add (at least) the 'augmented tetrachord' such as occurs in the lydian mode. SMTPOriginator: tuning@eartha.mills.edu From: Gregg Gibson Subject: Mathematics and Tuning PostedDate: 23-12-97 21:11:36 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: 23-12-97 21:09:26-23-12-97 21:09:27,23-12-97 21:08:57-23-12-97 21:08:57 DeliveredDate: 23-12-97 21:08:57 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 C1256576.006EB70E; Tue, 23 Dec 1997 21:11:14 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA24665; Tue, 23 Dec 1997 21:11:36 +0100 Date: Tue, 23 Dec 1997 21:11:36 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA24635 Received: (qmail 28610 invoked from network); 23 Dec 1997 12:11:33 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 23 Dec 1997 12:11:33 -0800 Message-Id: <34A07D45.201F@ww-interlink.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu