source file: mills3.txt Date: Tue, 30 Dec 1997 01:21:50 +0100 Subject: RE: 19, 22, etc From: "Paul H. Erlich" Firstly, I want to order Neil Haverstick's new CD as well as "Beethoven in the Temperaments". Will you guys send me the ordering info? >Bob Valentine wrote, >}> > Regarding 19TET in particular, perhaps it is the last temperment which >}> > preserves "sameness" of the "big" and "small" major seconds (9:8, 10:9). > >To which Gary Morrison replied, > >}> Perhaps this isn't very important (or maybe it is), but this strikes me >}> as a strange way to think of it. The historical and probably >}> psychoacoustic basis of Western tuning is Ptolemaic JI, which has two >}> different sizes of whole step. There is therefore no meaning to >preserving >}> an abstraction that represents those two intervals identically. You can't >}> preserve something ahistorical. > >Gary, Bob didn't mean "last" and "preserve" in a historical sense, he meant >it in a counting sense, going from 12TET up to higher and higher ETs. Of >course he was not correct, as 31, 43, 50, and 55 demonstrate. > >By the way, Gary is incorrect that modern Western musical practice is >historically derived from Graeco-Roman practice, a point Johnny Reinhard has >made before. I dispute the psychoacoustic connection as well. Ptolemy >described many scales, and the reason moderns have for focusing on just one, >when ascribed to Ptolemy, is a complete distortion of history. If anything, >the West started with Pythagorean tuning, and progressed from there through >schismatic to meantone and finally to 12TET (could've been 19 or 31 but for >convenience and expense). > >}The next line in my mail was, "but is this a good thing?", to which I >}don't know the answer. > >I tried to make the case that it is a good thing. > >}It was since explained to me that "sameness of the big and small major >}seconds" is another way of saying "meantone" and there is >}a historic precedence suggesting that for Western, harmonically oriented >}music, meantone will result in less (or no) "drift" vs. a non-meantone >}tuning. > >Meantone results in no drift. A C is a C is a C. Other tunings will drift, C >will often end up around where B used to be. Ben Johnston, a JI composer, has >used this fact in writing Beethoven-style passages, which he follows with >other passages that cause the music to drift back up. > >Also the equal sizes of whole step are easier to hear, to sing, and make >modulation much easier. I don't buy that 9:8 and 10:9 are easier to sing as >purely melodic steps than any mean-whole-tone. Johnny Reinhard will agree >that the ability to accurately produce melodic intervals acoustically more >complex than a perfect fourth is a function of rote learning. > >}let >} P5 = number of tempered units per perfect fifth >} M3 = number of tempered units per major third >} T = temperment, number of notes per octave > >}If I was correct in my understanding, a succinct definition of >}meantone is that > >} 4 * P5 - M3 = T / 2. > >T*2, not T/2. Otherwise you are correct. > >}Is there a special word for tunings defined by > >} 4 * P5 - M3 - 1 = T / 2? > >If you mean T*2 instead of T/2, I believe the term "having a syntonic comma >of one degree" is the most concise description out there. The only such >tunings I find interesting are 15 and 22. JI is interesting as well, and 34, >41, 46, and 53 are HASCOOD approximations to JI, which make them second-order >interesting :) 27 is HASCOOD as well. SMTPOriginator: tuning@eartha.mills.edu From: mr88cet@texas.net (Gary Morrison) Subject: Re: PLANCK CONSTANT PostedDate: 30-12-97 03:30:09 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: 30-12-97 03:27:52-30-12-97 03:27:53,30-12-97 03:27:17-30-12-97 03:27:18 DeliveredDate: 30-12-97 03:27:18 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 C125657D.000D85DF; Tue, 30 Dec 1997 03:29:38 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA27361; Tue, 30 Dec 1997 03:30:09 +0100 Date: Tue, 30 Dec 1997 03:30:09 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA27532 Received: (qmail 24329 invoked from network); 29 Dec 1997 18:30:07 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Dec 1997 18:30:07 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu