source file: mills2.txt Date: Mon, 14 Jul 1997 21:48:40 +0200 Subject: Re: Historical temperaments From: Paul Hahn On Fri, 11 Jul 1997, Joseph Downing wrote: > It is true that there are a lot of people today who can tune a passable > 12TET with no more reference than a starting pitch. But Jorgensen (thanks > for the name) and others point out that this technique was not known until > late in the nineteenth century. There are no early references to > counting beats per second, etc. One of the feature of Meantone tunings > (and well-tempered tunings are a sub-category of mean-tone) is that they > depend upon finding the 'mean' pitch. A common 18th century technique > would have you tune several intervals purely, then advise: Tune D to Bb > purely. Now sharpen the D until Bb/D beats at the same rate as D/F#. > Most anyone without too much experience can do this. It takes a LOT of > practice to hear 12TET thirds and fifths. 1. A fair number of writers were advocating 12TET by the mid-1700s. Most of them had plenty of experience tuning (and in some cases building) keyboard instruments. Why shouldn't some of them have had sufficient practise to hear 12TET thirds and fifths? (Someone once posted a quote from Werckmeister to this list in which he describes distributing the comma equally among all 12 fifths, then says that a circulating temperament sufficed for a local church, but only ET was suitable for a court.) To be sure, having an exact scheme would make things much easier, but I don't see why someone with a good ear couldn't make a passable ET with enough fiddling. 2. A big problem with Jorgensen (many think) is that he makes too much of equal beating. If you look at most surviving tuning instructions, they're worded far too vaguely for one to confidently presume that they actually refer to intervals beating _at the same rate_. It's quite plausible that the language merely refers to the fact that tempered intervals beat, and that two intervals are tempered about the same distance from just. It doesn't take Helmholtz to figure out that equally tempered intervals beat faster the higher they are in pitch. --pH http://library.wustl.edu/~manynote <*> O /\ "Foul? What the hell for?" -\-\-- o "Because you are chalking your cue with the 3-ball." Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 14 Jul 1997 21:52 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12041; Mon, 14 Jul 1997 21:53:31 +0200 Date: Mon, 14 Jul 1997 21:53:31 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA11889 Received: (qmail 1156 invoked from network); 14 Jul 1997 18:53:15 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 14 Jul 1997 18:53:15 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu