source file: mills2.txt Date: Mon, 3 Mar 1997 12:43:08 -0800 Subject: Major tonic endings From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE >Even if >the figure were to have originated in a just or meantone environment >(approximating /6:/5:/4) - and its obiquity in the lute repertoire speaks >against this - the adoption into other tuning systems would have meant that >the figure was frequently heard without the psychoacoustic effect that you >claim. The psychoacoustic effect I claim? Do I sense another deliberate misunderstanding? What I claimed was that the minor triad was not considered stable enough to serve as a final chord until its tuning became standardized near 16:19:24. The major triad is still more stable in any tuning, so the picardy third is appropriate in any tuning. My claim is that ending a _tonal_ piece of music with a long, sustained minor tonic chord did not become a convincing compositional gesture until composers heard 16:19:24 minor triads. Note that a Pythagorean minor triad is just as good as a 12-equal one for approximating 16:19:24, so there is no need to enter the debate about well-temperament vs. equal temperament. >the figure ['s] archaicizing >quality was already well established in the late meantone repertoire (hence >Rousseau's label identifying the figure with gothic Picardie). Well, if the historical evidence proves me wrong, so be it, but my ears tell me quite clearly which note is the root of a 19:16 interval, while a 6:5 interval has a different effect. Minor tonics tuned to just 10:12:15 or meantone just don't work for me, while ET or Pythagorean minor tonics work fine. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 3 Mar 1997 21:53 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03289; Mon, 3 Mar 1997 21:53:39 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA03300 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id MAA15784; Mon, 3 Mar 1997 12:50:06 -0800 Date: Mon, 3 Mar 1997 12:50:06 -0800 Message-Id: <009B0BA3FA068AFB.5883@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu