source file: mills2.txt Date: Wed, 27 Sep 1995 19:38:13 +0000 Subject: Re: FWD: Bach's tuning From: Aleksander Frosztega Paul Hahn wrote: >> I have never seen (I don't think) 18th-century German ear tuning >> instruction that use fifths as a tempering device for Equal >> Temperament. >> They all used rows of MAJOR THIRDS which were to be made wide! >> (Sorge gave explicit instructions that each successive third should be >> made somewhat *wider* than the last.) > Eh? If one is wider than another, then they're not equal, are they? Remember that Sorge's were *ear tuning* instructions. Because frequency doubles with every octave, the beating of any fixed interval *increases* as the frequency of the lower tone of the pair increases. Although Sorge's major thirds remain the same size linearly speaking, they would beat faster with each successive third of the row, hence Sorge's instructions to make each of the thirds a little wider than the last. >> Yes, this is the F#-C# fifth in Kirnberger I though III. However, it is not >> tempered by 1/12 Pythagorean comma; it is tempered by the >> *schisma.* Kirnberger was not the best mathematician in the world >> and Marpurg, in fact, corrects Kirnberger's calculations in Marpurg's >> _Versuch._ >Let me get this straight: you castigate Jorgenson for insisting on .1 >cent accuracy, and now you're making a fuss about a difference of (my >calculator puts it) .0012817 cents? Sounds like straining at gnats and >swallowing camels to me. I was merely pointing out that there is a difference between 1/12 of a Ditonic Comma and the schisma. For all intents and purposes (thank you, Michael), they are the same thing and difference between them is imperceptible in actual tuning... even to your dog. Aleksander Frosztega ------------------------------------------------------- Aleksander Frosztega "Odi summusos; proinde aperte University of Utrecht dice quid sit quod times." The Netherlands ------------------------------------------------------- Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 28 Sep 1995 13:45 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id EAA16230; Thu, 28 Sep 1995 04:45:32 -0700 Date: Thu, 28 Sep 1995 04:45:32 -0700 Message-Id: <950928114206_71670.2576_HHB30-3@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu