source file: mills3.txt Date: Tue, 16 Dec 1997 22:36:46 +0100 Subject: Very Brief History of the 19-tone Equal Temperament From: Gregg Gibson This post is meant to assist students of the 19-tone equal temperament. M. Joel Mandelbaum's doctoral treatise "Multiple Division of the Octave and the Tonal Resources of 19-tone Temperament" (1961) is the single best treatment of the 19-tone equal I have found in English. It is not highly original, nor is it at all complete; nevertheless it is a very convenient summary of part of the history of the 19-tone equal. Francisco Salinas' De Musica, in Latin (16th century) is the first known mathematically reference to the 1/3 comma mesotonic, which very closely approximates the 19-tone equal. Zarlino (16th century) reports on the 1/3 comma mesotonic, which he found (in comparison to the 2/7 comma and 1/4 comma mesotonics) "a little languid, but... quite usable." Mersenne (17th century) briefly mentions 'a certain organist' (Titelouze) who enthusiastically used 1/3 tones. The celebrated French composer Costeley in a famous preface (1570) which has been hitherto ignored by anglophones, specifically refers to his use of 1/3 tones, which he praises as the ultimate perfection of the tuning art. I shall give the complete translation (it is not terribly long) in another post. Gesualdo is said to have owned a 19-tone clavier; his master, Nenna, is known for certain to have used the 19-tone equal, as did many of the 17th-century Neapolitans. The German Luython, who as I recall had links with this school, owned a 19-tone keyboard. The modern advocates of the 19-tone equal tend to be much more fantastical than the older writers, and prone to all kinds of dubious, extravagant assertions - the bane of our age is self-exhibitionism. Yasser in his Theory of Evolving Tonality seethes with ideas, some wonderful, others absurd. But he is well worth reading. In antiquity it is known that the Greeks definitely used 1/3 tones (the references are a commonplace, both in Aristoxenos and the Arabs who preserve many of the lost Greek writers). Whether the Greeks made the next logical step to 19-tone equal is open to debate, but this is by no means an abstruse or difficult step. But the vast majority of their musical writings have perished, so we shall never know for sure. Very probably at least a few of them used approximations to the 19-tone equal, just as some of them certainly used approximations to the 12-tone equal. For anyone wishing to inform himself concerning the 19-tone equal, this will do to begin with, in the way of history and basic references. SMTPOriginator: tuning@eartha.mills.edu From: Carl Lumma Subject: Re: TUNING digest 1269 PostedDate: 16-12-97 23:17:05 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: 16-12-97 23:15:05-16-12-97 23:15:05,16-12-97 23:14:44-16-12-97 23:14:44 DeliveredDate: 16-12-97 23:14:44 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 C125656F.007A3796; Tue, 16 Dec 1997 23:16:52 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17315; Tue, 16 Dec 1997 23:17:05 +0100 Date: Tue, 16 Dec 1997 23:17:05 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA17318 Received: (qmail 1354 invoked from network); 16 Dec 1997 14:16:59 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 16 Dec 1997 14:16:59 -0800 Message-Id: <19971216221628343.AAA254@ascend571.nni.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu