source file: mills3.txt Date: Mon, 22 Dec 1997 01:55:21 +0100 Subject: Greek musical intervals, Partch From: John Chalmers Gregg: Aristoxenos said that melody admits 1/4, 1/3 and 1/2 tones, but nothing smaller and that no one can sing a sequence of more than 2 dieses, which can be any of these intervals. In his own genera, he uses all of these intervals plus an interval of about 75 cents, the hemiolic chromatic diesis. Since we have several actual fragments of music written in the enharmonic genus with quarter-tones, I think it is clear that they were used in real Greek melodies and there is suggestive evidence from Winnington-Ingram's analysis of the Spondeion scale that the 3/4 interval was also used. The interval 12/11 occurs in Ptolemy's scales as well and may represent the practice of 2nd Century CE Alexandria. There is some question as to how large the 1/4-tone diesis was. It is thought that in the late 5th century BCE, the limma in the original limmatal-ditonal enharmonic trichord was split into two microtones of roughly 45 cents, though the ancient writers do not give the exact measures. The earliest actual enharmonic tuning we have is Archytas's (390 BCE) and his enharmonic tetrachord consists of an approximate 1/3-tone, a 1/4-tone and a major third. The 28/27 first interval is thought to have been chosen in order to make a 7/6 with the note a 9/8 below the first note of the tetrachord (hyperhypate, mese). The archaic enharmonic Dorian harmonia of Aristeides Kointilianos has this note and it is used prominently in the Orestes fragment. Bacchios calls this interval an ekbole or eklysis and it apparently occurred in the chromatic genus as well. Although the enharmonic genus fell into disuse in the 3rd century, the theorists continued to describe enharmonic tunings with either nearly equal quarter-tones such as Eratosthenes's 40/39 x 39/38 x 19/15, which is acoustically almost identical to the earlier Pythagorean tuning (and close to Aristoxenos's theoretical 50 + 50 + 400 cents), and Didymos's 32/31 x 31/30 x 5/4 or very unequal microtones such as Ptolemy's 46/45 x 24/23 x 5/4. What one sees is a gradual widening of the enharmonic diesis from a very narrow quarter-tone though a third-tone and a 3/8-tone to a semitone. While the Greek form of the chromatic genus eventually died out as well, Hellenistic (and Roman) music was diatonic with some chromaticism, sometimes of the modern Near Eastern type using tetrachords of the form 1/2 3/2 1/2 (Winnington-Ingram). I don't deny, though, that the 1/3 is a valid musical interval. Greek Orthodox liturgical music uses intervals close to third tones in some scales according to some authorities. I feel you are somewhat misinformed about the popularity of Harry Partch's music. I once heard a new listener come up to HP after a concert and tell him that she had never heard real music before. A national magazine once described his music as the only new music that listeners really like. While no type of "experimental" music is overwhelmingly popular with the general public, Partch's recordings continue to sell well and his music continues to inspire composers, theorists, and instrument builders. I would hazard that a significant part of this List became interested in non-12 tone music because of Harry Partch's music. --John SMTPOriginator: tuning@eartha.mills.edu From: Steven Rezsutek Subject: Steel is Cool PostedDate: 22-12-97 15:40:01 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: 22-12-97 15:37:51-22-12-97 15:37:52,22-12-97 15:37:24-22-12-97 15:37:25 DeliveredDate: 22-12-97 15:37:25 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 C1256575.00505C47; Mon, 22 Dec 1997 15:39:41 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA23710; Mon, 22 Dec 1997 15:40:01 +0100 Date: Mon, 22 Dec 1997 15:40:01 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA22875 Received: (qmail 10312 invoked from network); 22 Dec 1997 06:39:58 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 22 Dec 1997 06:39:58 -0800 Message-Id: <199712221439.JAA19836@doghouse.hq.nasa.gov> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu