source file: mills2.txt Date: Sat, 5 Jul 1997 21:20:06 +0200 Subject: Re: Definitions, pure fifths tuning From: mr88cet@texas.net (Gary Morrison) >To check against paper, using the ratio for the 5th or 3/2, or 1.5, >and using A220, (a) for conveince, four fifths gives a frequency of >220*1.5^4 (as entered on the W95 calculator, OK so ^ is the x^y key) >or 1113.75. So two octaves down or /4 gives 278.4375 for c# ' . >Hmm already that is sharper than 277.183 called for by ET. That's because you used 3:2 exactly rather than tempering it downward. Quarter-comma meantone's fifth is tempered downward by a quarter of a (syntonic) comma, 81:80. That makes a stack of four of them land you on an exact 5:4 ratio. Mathematically, QC meantone's fifth represents a frequency multiplier of 1.5 divided by the fourth root of 81/80, which works out to about 1.49535, or a pitch difference of about 696.6 cents. Using an exact 3:2 gives you Pythagorean tuning, which as you correctly pointed out has that very sharp 81:64 M3. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 5 Jul 1997 21:20 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05397; Sat, 5 Jul 1997 21:20:49 +0200 Date: Sat, 5 Jul 1997 21:20:49 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05388 Received: (qmail 15922 invoked from network); 5 Jul 1997 19:20:41 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 5 Jul 1997 19:20:41 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu