source file: mills2.txt Date: Wed, 10 Jul 1996 14:07:33 -0700 Subject: Another post from McLaren From: John Chalmers From: mclaren Subject: Equal-beating chromatic scale -- In vol. 29, No. 4 of the Journal of the Acoustical Society of America, April 1957, A. L. Leigh Silver published an interesting article called "Equal Beating Chromatic Scale." Silver appears to use a process of successive substitution and iterated fractions to generate a scale which he claims produces equal beats for each fifth. Silver notes that "A further disadvantage, to which little attention has been paid, is that when just and unjust intervals are mixed, the dissonances of the latter are intensified by the comparison. If, for example, an ET fifth is introduced into a series of just fifths, it is recognized as an unjust interval more quickly than when sounded alone." [Silver, Al. L. L., "Equal Beating Chromatic Scale," J. Acoust. Soc. Am., Vol. 29, No. 4, April 1957, pg. 478] Silver further points out that his EBS is a circulating irregular temperament but that "any deviations from ET are so small that it may be argued that any advantage exists only in the imagination, or in the realms of numerology. I am of the opinion, however, that the numerous small variations are accumulative and noticeable when combined in melody and harmony." The Equal Beating Charomatic Scale has the pitches: A4 = 440 Hz Ab4 = 415.16 Hz G4 = 391.89 Hz F#4 = 369.81 Hz F4 = 349.13 Hz E4 = 329.50 Hz Eb4 = 311.12 Hz D4 = 293.67 Hz C#4 = 277.10 Hz C4 = 261.59 Hz B3 246.87 Hz Bb3 = 233.09 Hz A3 = 220.00 Hz Silver further notes that "In my experience, few tuner in this country (england) make a serious attempt to tune ET accurately and any approximation that given twelve equally usable keys is considered adequate." --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 11 Jul 1996 08:06 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id XAA16630; Wed, 10 Jul 1996 23:05:27 -0700 Date: Wed, 10 Jul 1996 23:05:27 -0700 Message-Id: <960711055934_71670.2576_HHB42-1@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu