[CAUT] ET vs UET was RE: using as ETD

[Ed Sutton]

Graupner.

Jorgensen, in a flurry of understanding that must have been dictated by angels, or perhaps on a time machine, first explains that Graupner could not have done what he intended to do, and then calculates Graupner's mistaken "Equal-beating Quasi-equal Temperament" to the one hundred thousandth of a cent. Each fifth is slightly different, ranging from 700.56001 cents down to 699.32161. 

I am not making this up!!!

To tune "the authentic way," Jorgensen suggests tempering each fifth narrow by 0.843587838 beats per second!!! (p.403)

Statements like that are meaningless. Accuracies of that sort do not exist in the world. I feel sick reading it.

Ed Sutton
 

  ----- Original Message ----- 
  From: Jeff Tanner 
  To: caut at ptg.org 
  Sent: Tuesday, April 20, 2010 4:10 PM
  Subject: Re: [CAUT] ET vs UET was RE: using as ETD


  ----- Original Message ----- 
    From: Laurence Libin 
    To: caut at ptg.org 
    Sent: Monday, April 19, 2010 12:47 PM
    Subject: Re: [CAUT] ET vs UET was RE: using as ETD


    I don't doubt that pre-1880 Continental tuners (we can't know how many) often sought to make all keys sound alike on the piano, but whether their solutions measured up to ET is debatable; we have no way of knowing, and the imprecision of tuning instructions leaves the question open. 
  As far as that goes, can we really claim that what we do today measures up to ET? Considering scaling inharmonicity inconsistency, etc.? Our instructions should get us pretty close, but in practice, from tuner to tuner and from instrument to instrument, all kinds of variations exist.  

  This is an extreme example, of course, but the Baldwin 500 (spinet) scale, when equally divided with an ETD at the 4th partial, will produce contiguous thirds in the C28-C40 octave which do not progress evenly, but actually will progress in reverse, getting slower as you go up the scale, if the C28-C40 octave is to wind up anywhere close to acceptable.  An aural tuning of this scale will create all sorts of problems if we try to force on it our aural definitions for ET.  The errors in better scales certainly won't be as noticeable, but they will be there to some degree.
  Jeff
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